Reference home Curriculum 3A Chapter 1 Answer key

3A · Instructor & learner reference

Chapter 1 complete answer key

Explanations for every question in nine lessons, both consolidation units, the chapter review, and the practice examination.

This is the complete instructor/learner answer key. For student-only printing, print the practice pages; their expandable solutions are hidden on paper.

Lesson 1: Numbers to 10,000

Prerequisite checks

  1. 30
    Three groups of ten contain 3 × 10 = 30 ones.
  2. 10
    One thousand is 10 × 100.

Worked checks

  1. 30 hundreds
    3,000 ÷ 100 = 30.
  2. seven thousand forty
    Seven thousands and four tens; no hundreds or ones.
  3. 5,019
    Five thousands, zero hundreds, one ten, and nine ones.

Guided

  1. three thousand eighty‑five
    Read the thousands group, then the remaining hundreds/tens/ones: three thousand eighty‑five.
  2. 6,007
    The words describe 6,000 + 7, which is 6,007.
  3. nine thousand ten
    Read the thousands group, then the remaining hundreds/tens/ones: nine thousand ten.
  4. 8,230
    The words describe 8,000 + 200 + 30, which is 8,230.

Independent

  1. one thousand two hundred forty‑eight
    Read the thousands group, then the remaining hundreds/tens/ones: one thousand two hundred forty‑eight.
  2. 5,036
    The words describe 5,000 + 30 + 6, which is 5,036.
  3. eight thousand seven hundred ten
    Read the thousands group, then the remaining hundreds/tens/ones: eight thousand seven hundred ten.
  4. 6,009
    The words describe 6,000 + 9, which is 6,009.
  5. nine thousand nine hundred ninety‑nine
    Read the thousands group, then the remaining hundreds/tens/ones: nine thousand nine hundred ninety‑nine.
  6. 4,011
    The words describe 4,000 + 10 + 1, which is 4,011.
  7. two thousand three hundred
    Read the thousands group, then the remaining hundreds/tens/ones: two thousand three hundred.
  8. 10,000
    The words describe 0, which is 10,000.

Challenge

  1. 10,000
    Each bundle is 1,000. Ten bundles are 10 × 1,000 = 10,000.
  2. 2 zeros
    7,070 contains two zero digits, in the hundreds and ones places.

Exit

  1. 7,042
    The words describe 7,000 + 40 + 2, which is 7,042.
  2. nine thousand five hundred one
    Read the thousands group, then the remaining hundreds/tens/ones: nine thousand five hundred one.
  3. 10
    Ten hundreds make one thousand.

Lesson 2: Place Value — Part 1

Prerequisite checks

  1. four thousand sixty
    Read the thousands group, then the remaining hundreds/tens/ones: four thousand sixty.
  2. 7,312
    The words describe 7,000 + 300 + 10 + 2, which is 7,312.

Worked checks

  1. 700
    The hundreds digit is 7; each unit has value 100, so its value is 7 × 100 = 700.
  2. 40
    Each thousand is ten hundreds, so four thousands are forty hundreds.
  3. 40
    The tens digit is 4; each unit has value 10, so its value is 4 × 10 = 40.

Guided

  1. 300
    The hundreds digit is 3; each unit has value 100, so its value is 3 × 100 = 300.
  2. 30
    The tens digit is 3; each unit has value 10, so its value is 3 × 10 = 30.
  3. 7,000
    The thousands digit is 7; each unit has value 1,000, so its value is 7 × 1,000 = 7,000.
  4. 5
    The ones digit is 5; each unit has value 1, so its value is 5 × 1 = 5.

Independent

  1. 60
    The tens digit is 6; each unit has value 10, so its value is 6 × 10 = 60.
  2. 900
    The hundreds digit is 9; each unit has value 100, so its value is 9 × 100 = 900.
  3. 1
    The ones digit is 1; each unit has value 1, so its value is 1 × 1 = 1.
  4. 9,000
    The thousands digit is 9; each unit has value 1,000, so its value is 9 × 1,000 = 9,000.
  5. 0
    The tens digit is 0; each unit has value 10, so its value is 0 × 10 = 0.
  6. 600
    The hundreds digit is 6; each unit has value 100, so its value is 6 × 100 = 600.
  7. 6
    The ones digit is 6; each unit has value 1, so its value is 6 × 1 = 6.
  8. 1,000
    The thousands digit is 1; each unit has value 1,000, so its value is 1 × 1,000 = 1,000.

Challenge

  1. 100
    3,000 ÷ 30 = 100.
  2. 60,000
    Every move left multiplies its value by ten: 600 × 100 = 60,000. This extends beyond the current number range.

Exit

  1. 0
    The hundreds digit is 0; each unit has value 100, so its value is 0 × 100 = 0.
  2. 40
    The tens digit is 4; each unit has value 10, so its value is 4 × 10 = 40.
  3. 400
    4 tens are 40; ten times 40 is 400.

Lesson 3: Place Value — Part 2

Prerequisite checks

  1. 200
    The hundreds digit is 2; each unit has value 100, so its value is 2 × 100 = 200.
  2. 0
    The tens digit is 0; each unit has value 10, so its value is 0 × 10 = 0.

Worked checks

  1. 7,000 + 400 + 8
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 7,000 + 400 + 8.
  2. 53
    Each hundred is worth 100. Divide 5,300 by 100: there are 53 complete hundreds.
  3. Yes
    5,000 + 1,200 + 4 = 6,204.

Guided

  1. 6,000 + 80 + 2
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 6,000 + 80 + 2.
  2. 5,207
    Add 5,000 + 200 + 0 + 7 = 5,207.
  3. 36
    Each hundred is worth 100. Divide 3,600 by 100: there are 36 complete hundreds.
  4. 9,000 + 400 + 50
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 9,000 + 400 + 50.

Independent

  1. 7,000 + 200 + 90 + 3
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 7,000 + 200 + 90 + 3.
  2. 2,836
    Add 2,000 + 800 + 30 + 6 = 2,836.
  3. 72
    Each hundred is worth 100. Divide 7,200 by 100: there are 72 complete hundreds.
  4. 4,000 + 10 + 5
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 4,000 + 10 + 5.
  5. 3,609
    Add 3,000 + 600 + 0 + 9 = 3,609.
  6. 840
    Each ten is worth 10. Divide 8,400 by 10: there are 840 complete tens.
  7. 8,000 + 900
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 8,000 + 900.
  8. 7,042
    Add 7,000 + 0 + 40 + 2 = 7,042.

Challenge

  1. 14 hundreds
    The missing thousand becomes 10 hundreds; combine with the original 4 hundreds to make 14.
  2. 78 hundreds, 90 ones
    7,890 = 78 × 100 + 90. A leftover 90 cannot make another complete hundred.

Exit

  1. 8,000 + 50 + 4
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 8,000 + 50 + 4.
  2. 47
    Each hundred is worth 100. Divide 4,700 by 100: there are 47 complete hundreds.
  3. 4,408
    Add 3,000 + 1,400 + 0 + 8 = 4,408.

Lesson 4: Comparing and Ordering Numbers

Prerequisite checks

  1. 6,000
    The thousands digit is 6; each unit has value 1,000, so its value is 6 × 1,000 = 6,000.
  2. 5,000 + 90
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 5,000 + 90.

Worked checks

  1. >
    Compare digits from the highest place that differs. 7,421 > 7,412.
  2. <
    Compare digits from the highest place that differs. 8,999 < 9,000.
  3. 6,009 < 6,090 < 6,900 < 6,990
    Compare the thousands place first, then hundreds, tens, and ones: 6,009, 6,090, 6,900, 6,990.

Guided

  1. >
    Compare digits from the highest place that differs. 6,742 > 6,472.
  2. >
    Compare digits from the highest place that differs. 5,040 > 5,004.
  3. 8,024 < 8,204 < 8,240
    Compare the thousands place first, then hundreds, tens, and ones: 8,024, 8,204, 8,240.
  4. <
    Compare digits from the highest place that differs. 9,998 < 10,000.

Independent

  1. >
    Compare digits from the highest place that differs. 3,817 > 3,187.
  2. <
    Compare digits from the highest place that differs. 5,509 < 5,590.
  3. >
    Compare digits from the highest place that differs. 9,081 > 9,008.
  4. 7,021 < 7,120 < 7,201 < 7,210
    Compare the thousands place first, then hundreds, tens, and ones: 7,021, 7,120, 7,201, 7,210.
  5. <
    Compare digits from the highest place that differs. 4,999 < 5,000.
  6. 9,803 > 9,308 > 9,038
    Compare the thousands place first, then hundreds, tens, and ones: 9,803, 9,308, 9,038.
  7. =
    Compare digits from the highest place that differs. 4,066 = 4,066.
  8. 6,001 < 6,010 < 6,100 < 6,110
    Compare the thousands place first, then hundreds, tens, and ones: 6,001, 6,010, 6,100, 6,110.

Challenge

  1. 8,420 and 2,048
    For the greatest, arrange digits descending. For the least, start with the smallest nonzero digit (2), then 0, 4, 8.
  2. 5,208; 5,209; 5,210
    Strictly between excludes both endpoints.

Exit

  1. >
    Compare digits from the highest place that differs. 7,830 > 7,803.
  2. 4,098 < 4,809 < 4,908
    Compare the thousands place first, then hundreds, tens, and ones: 4,098, 4,809, 4,908.
  3. >
    Compare digits from the highest place that differs. 10,000 > 9,999.

Lesson 5: The Number Line

Prerequisite checks

  1. >
    Compare digits from the highest place that differs. 4,100 > 4,010.
  2. 4,250
    Add one thousand to the thousands place: 3,250 + 1,000 = 4,250.

Worked checks

  1. 200
    The total distance is 600. Divide by 3 equal intervals: 200.
  2. 5,450
    Add 3 intervals of 50: 5,300 + 3 × 50 = 5,450.
  3. 7,700
    The gap is 600, and halfway is 300 above 7,400.

Guided

  1. 3,200
    Add 3 intervals of 200: 2,600 + 3 × 200 = 3,200.
  2. 200
    The total distance is 600. Divide by 3 equal intervals: 200.
  3. 7,300
    Add 4 intervals of 50: 7,100 + 4 × 50 = 7,300.
  4. 500
    The total distance is 2,000. Divide by 4 equal intervals: 500.

Independent

  1. 2,500
    Add 5 intervals of 100: 2,000 + 5 × 100 = 2,500.
  2. 4,100
    Add 2 intervals of 250: 3,600 + 2 × 250 = 4,100.
  3. 200
    The total distance is 600. Divide by 3 equal intervals: 200.
  4. 7,700
    Add 5 intervals of 50: 7,450 + 5 × 50 = 7,700.
  5. 200
    The total distance is 1,000. Divide by 5 equal intervals: 200.
  6. 4,450
    Add 4 intervals of 75: 4,150 + 4 × 75 = 4,450.
  7. 150
    The total distance is 600. Divide by 4 equal intervals: 150.
  8. 7,100
    Add 4 intervals of 125: 6,600 + 4 × 125 = 7,100.

Challenge

  1. 150
    Six marks create five equal intervals. The distance is 750, so each interval is 750 ÷ 5 = 150.
  2. 7 cm
    The difference is 175 units. At 4 cm per 100, distance is 175/100 × 4 = 7 cm.

Exit

  1. 200
    The total distance is 600. Divide by 3 equal intervals: 200.
  2. 5,000
    Add 2 intervals of 150: 4,700 + 2 × 150 = 5,000.
  3. 6
    Each neighboring pair creates one interval; 7 ticks produce 6 intervals.

Lesson 6: Number Patterns

Prerequisite checks

  1. 1,300
    Add 3 intervals of 100: 1,000 + 3 × 100 = 1,300.
  2. 2,400
    Add two hundreds to 22 hundreds to get 24 hundreds.

Worked checks

  1. 3,900, 4,025
    The same signed step, +125, connects consecutive terms. Continue twice.
  2. 4,000
    The first and third terms span two equal steps: (3,800 − 4,200) ÷ 2 = -200 per step.
  3. 9,900, 10,000
    The same signed step, +100, connects consecutive terms. Continue twice.

Guided

  1. 2,800, 2,950
    The same signed step, +150, connects consecutive terms. Continue twice.
  2. 7,050, 6,850
    The same signed step, -200, connects consecutive terms. Continue twice.
  3. 1,475
    The first and third terms span two equal steps: (1,650 − 1,300) ÷ 2 = 175 per step.
  4. 8,500, 8,375
    The same signed step, -125, connects consecutive terms. Continue twice.

Independent

  1. 4,550, 4,675
    The same signed step, +125, connects consecutive terms. Continue twice.
  2. 7,100, 6,850
    The same signed step, -250, connects consecutive terms. Continue twice.
  3. 3,500
    The first and third terms span two equal steps: (3,800 − 3,200) ÷ 2 = 300 per step.
  4. 3,200, 3,650
    The same signed step, +450, connects consecutive terms. Continue twice.
  5. 8,800, 8,625
    The same signed step, -175, connects consecutive terms. Continue twice.
  6. 7,075
    The first and third terms span two equal steps: (6,950 − 7,200) ÷ 2 = -125 per step.
  7. 7,400, 7,625
    The same signed step, +225, connects consecutive terms. Continue twice.
  8. 8,475, 8,350
    The same signed step, -125, connects consecutive terms. Continue twice.

Challenge

  1. 2,125
    Sixth term is five steps after first: 1,250 + 5 × 175 = 2,125.
  2. 3,000
    Changes are +100,+200,+300, so next change is +400: 2,600 + 400 = 3,000. This is an extension, not a constant-step pattern.

Exit

  1. 3,875, 4,000
    The same signed step, +125, connects consecutive terms. Continue twice.
  2. 6,350
    The first and third terms span two equal steps: (6,200 − 6,500) ÷ 2 = -150 per step.
  3. +250
    1,500 − 1,250 = 250, and 1,750 − 1,500 = 250.

Lesson 7: Rounding to the Nearest Thousand

Prerequisite checks

  1. 1,000
    The total distance is 2,000. Divide by 2 equal intervals: 1,000.
  2. >
    Compare digits from the highest place that differs. 6,501 > 6,500.

Worked checks

  1. 7,000
    It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 7,000.
  2. 9,000
    It lies between 8,000 and 9,000; the midpoint is 8,500. With halfway values rounded up, choose 9,000.
  3. 9,000
    It lies between 9,000 and 10,000; the midpoint is 9,500. With halfway values rounded up, choose 9,000.

Guided

  1. 2,000
    It lies between 2,000 and 3,000; the midpoint is 2,500. With halfway values rounded up, choose 2,000.
  2. 3,000
    It lies between 2,000 and 3,000; the midpoint is 2,500. With halfway values rounded up, choose 3,000.
  3. 8,000
    It lies between 8,000 and 9,000; the midpoint is 8,500. With halfway values rounded up, choose 8,000.
  4. 10,000
    It lies between 9,000 and 10,000; the midpoint is 9,500. With halfway values rounded up, choose 10,000.

Independent

  1. 1,000
    It lies between 1,000 and 2,000; the midpoint is 1,500. With halfway values rounded up, choose 1,000.
  2. 2,000
    It lies between 1,000 and 2,000; the midpoint is 1,500. With halfway values rounded up, choose 2,000.
  3. 5,000
    It lies between 4,000 and 5,000; the midpoint is 4,500. With halfway values rounded up, choose 5,000.
  4. 8,000
    It lies between 7,000 and 8,000; the midpoint is 7,500. With halfway values rounded up, choose 8,000.
  5. 7,000
    It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 7,000.
  6. 8,000
    It lies between 8,000 and 9,000; the midpoint is 8,500. With halfway values rounded up, choose 8,000.
  7. 10,000
    It lies between 9,000 and 10,000; the midpoint is 9,500. With halfway values rounded up, choose 10,000.
  8. 5,000
    5,000 is already an exact multiple of 1,000.

Challenge

  1. 5,500
    The interval of whole numbers rounding to 6,000 starts halfway below, at 5,500, and ends at 6,499 (with halfway values rounded up).
  2. 9,499
    9,500 rounds to 10,000, so the largest whole number still rounding to 9,000 is 9,499.

Exit

  1. 3,000
    It lies between 3,000 and 4,000; the midpoint is 3,500. With halfway values rounded up, choose 3,000.
  2. 4,000
    It lies between 3,000 and 4,000; the midpoint is 3,500. With halfway values rounded up, choose 4,000.
  3. 8,500
    Half the 1,000 gap is 500; add to 8,000.

Lesson 8: Rounding to the Nearest Hundred

Prerequisite checks

  1. 7,000
    It lies between 7,000 and 8,000; the midpoint is 7,500. With halfway values rounded up, choose 7,000.
  2. 50
    The total distance is 100. Divide by 2 equal intervals: 50.

Worked checks

  1. 3,500
    It lies between 3,400 and 3,500; the midpoint is 3,450. With halfway values rounded up, choose 3,500.
  2. 9,900
    It lies between 9,900 and 10,000; the midpoint is 9,950. With halfway values rounded up, choose 9,900.
  3. 4,500 and 4,000
    4,480 is ≥4,450 and <4,500, so 4,500 to hundred; it is <4,500, so 4,000 to thousand.

Guided

  1. 3,700
    It lies between 3,700 and 3,800; the midpoint is 3,750. With halfway values rounded up, choose 3,700.
  2. 3,800
    It lies between 3,700 and 3,800; the midpoint is 3,750. With halfway values rounded up, choose 3,800.
  3. 5,100
    It lies between 5,000 and 5,100; the midpoint is 5,050. With halfway values rounded up, choose 5,100.
  4. 10,000
    It lies between 9,900 and 10,000; the midpoint is 9,950. With halfway values rounded up, choose 10,000.

Independent

  1. 1,200
    It lies between 1,200 and 1,300; the midpoint is 1,250. With halfway values rounded up, choose 1,200.
  2. 1,600
    It lies between 1,500 and 1,600; the midpoint is 1,550. With halfway values rounded up, choose 1,600.
  3. 4,600
    It lies between 4,600 and 4,700; the midpoint is 4,650. With halfway values rounded up, choose 4,600.
  4. 4,800
    It lies between 4,700 and 4,800; the midpoint is 4,750. With halfway values rounded up, choose 4,800.
  5. 7,300
    It lies between 7,200 and 7,300; the midpoint is 7,250. With halfway values rounded up, choose 7,300.
  6. 8,800
    It lies between 8,700 and 8,800; the midpoint is 8,750. With halfway values rounded up, choose 8,800.
  7. 10,000
    It lies between 9,900 and 10,000; the midpoint is 9,950. With halfway values rounded up, choose 10,000.
  8. 6,000
    It lies between 6,000 and 6,100; the midpoint is 6,050. With halfway values rounded up, choose 6,000.

Challenge

  1. 7,150
    The interval of whole numbers rounding to 7,200 starts halfway below, at 7,150, and ends at 7,249 (with halfway values rounded up).
  2. Two-stage: 5,000; direct: 4,000
    First 4,450 rounds to 4,500 at the hundred, then 4,500 rounds to 5,000 at the thousand. Direct rounding of the original 4,450 to the nearest thousand gives 4,000 because it is below the midpoint 4,500. Repeated rounding can mislead.

Exit

  1. 5,600
    It lies between 5,600 and 5,700; the midpoint is 5,650. With halfway values rounded up, choose 5,600.
  2. 5,700
    It lies between 5,600 and 5,700; the midpoint is 5,650. With halfway values rounded up, choose 5,700.
  3. 8,350
    The two hundreds are 100 apart; halfway is 50 beyond 8,300.

Lesson 9: Rounding to the Nearest Ten

Prerequisite checks

  1. 6,700
    It lies between 6,700 and 6,800; the midpoint is 6,750. With halfway values rounded up, choose 6,700.
  2. 10
    The total distance is 20. Divide by 2 equal intervals: 10.

Worked checks

  1. 5,720
    It lies between 5,720 and 5,730; the midpoint is 5,725. With halfway values rounded up, choose 5,720.
  2. 2,070
    It lies between 2,060 and 2,070; the midpoint is 2,065. With halfway values rounded up, choose 2,070.
  3. 10,000
    It lies between 9,990 and 10,000; the midpoint is 9,995. With halfway values rounded up, choose 10,000.

Guided

  1. 1,620
    It lies between 1,620 and 1,630; the midpoint is 1,625. With halfway values rounded up, choose 1,620.
  2. 1,630
    It lies between 1,620 and 1,630; the midpoint is 1,625. With halfway values rounded up, choose 1,630.
  3. 3,500
    It lies between 3,490 and 3,500; the midpoint is 3,495. With halfway values rounded up, choose 3,500.
  4. 7,000
    It lies between 7,000 and 7,010; the midpoint is 7,005. With halfway values rounded up, choose 7,000.

Independent

  1. 2,370
    It lies between 2,370 and 2,380; the midpoint is 2,375. With halfway values rounded up, choose 2,370.
  2. 4,880
    It lies between 4,870 and 4,880; the midpoint is 4,875. With halfway values rounded up, choose 4,880.
  3. 6,580
    It lies between 6,580 and 6,590; the midpoint is 6,585. With halfway values rounded up, choose 6,580.
  4. 9,510
    It lies between 9,500 and 9,510; the midpoint is 9,505. With halfway values rounded up, choose 9,510.
  5. 1,050
    It lies between 1,040 and 1,050; the midpoint is 1,045. With halfway values rounded up, choose 1,050.
  6. 10,000
    It lies between 9,990 and 10,000; the midpoint is 9,995. With halfway values rounded up, choose 10,000.
  7. 5,000
    It lies between 5,000 and 5,010; the midpoint is 5,005. With halfway values rounded up, choose 5,000.
  8. 7,350
    It lies between 7,340 and 7,350; the midpoint is 7,345. With halfway values rounded up, choose 7,350.

Challenge

  1. 3,855
    The interval of whole numbers rounding to 3,860 starts halfway below, at 3,855, and ends at 3,864 (with halfway values rounded up).
  2. 7,490; 7,500; 7,000
    Nearest ten: halfway 7,485 rounds up. Nearest hundred: ≥7,450 rounds to 7,500. Nearest thousand: <7,500 rounds to 7,000.

Exit

  1. 2,590
    It lies between 2,580 and 2,590; the midpoint is 2,585. With halfway values rounded up, choose 2,590.
  2. 9,540
    It lies between 9,540 and 9,550; the midpoint is 9,545. With halfway values rounded up, choose 9,540.
  3. 9,000
    8,999 is one away from 9,000, and nine away from 8,990.

Practice A

  1. six thousand forty‑two
    Read the thousands group, then the remaining hundreds/tens/ones: six thousand forty‑two.
  2. 5,079
    The words describe 5,000 + 70 + 9, which is 5,079.
  3. 300
    The hundreds digit is 3; each unit has value 100, so its value is 3 × 100 = 300.
  4. 40
    The tens digit is 4; each unit has value 10, so its value is 4 × 10 = 40.
  5. 9,000 + 50 + 2
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 9,000 + 50 + 2.
  6. 4,381
    Add 4,000 + 300 + 80 + 1 = 4,381.
  7. 54
    Each hundred is worth 100. Divide 5,400 by 100: there are 54 complete hundreds.
  8. <
    Compare digits from the highest place that differs. 5,301 < 5,310.
  9. 8,007 < 8,070 < 8,077 < 8,700
    Compare the thousands place first, then hundreds, tens, and ones: 8,007, 8,070, 8,077, 8,700.
  10. 2,000
    Add 3 intervals of 250: 1,250 + 3 × 250 = 2,000.
  11. 300
    The total distance is 1,500. Divide by 5 equal intervals: 300.
  12. 6,600
    The distance is 600, so add half (300) to 6,300.
  13. 5,010
    The only whole number strictly between these consecutive bounds is 5,010.
  14. 200
    From left to right the second 2 is in the hundreds place.
  15. Yes
    5,000 + 1,200 + 3 = 6,203.
  16. 8
    Distance 800 ÷ 100 = 8 spaces.

Practice B

  1. 2,850, 3,025
    The same signed step, +175, connects consecutive terms. Continue twice.
  2. 7,700, 7,450
    The same signed step, -250, connects consecutive terms. Continue twice.
  3. 3,525
    The first and third terms span two equal steps: (3,750 − 3,300) ÷ 2 = 225 per step.
  4. 3,000
    It lies between 3,000 and 4,000; the midpoint is 3,500. With halfway values rounded up, choose 3,000.
  5. 4,000
    It lies between 3,000 and 4,000; the midpoint is 3,500. With halfway values rounded up, choose 4,000.
  6. 9,600
    It lies between 9,500 and 9,600; the midpoint is 9,550. With halfway values rounded up, choose 9,600.
  7. 9,500
    It lies between 9,400 and 9,500; the midpoint is 9,450. With halfway values rounded up, choose 9,500.
  8. 4,790
    It lies between 4,780 and 4,790; the midpoint is 4,785. With halfway values rounded up, choose 4,790.
  9. 9,000
    It lies between 9,000 and 9,010; the midpoint is 9,005. With halfway values rounded up, choose 9,000.
  10. 6,150
    The interval of whole numbers rounding to 6,200 starts halfway below, at 6,150, and ends at 6,249 (with halfway values rounded up).
  11. 6,500 and 6,000
    It rounds up to the nearest ten, but is below 6,500 so rounds down to the nearest thousand.
  12. Different rounding places have different midpoints
    4,450 is below the thousand midpoint (4,500), but at the hundred midpoint (4,450). Use the original number for both.
  13. 3,499
    3,500 is the first value rounding to 4,000.
  14. 9,150
    9,150 is halfway between 9,100 and 9,200, so it rounds upward.
  15. 10,000
    Regroup 10 ones, tens, hundreds, and thousands across the boundary.
  16. 500
    Fifth term is four steps after the first: 1,000 − 4 × 125 = 500.

Chapter review

  1. four thousand sixty‑two
    Read the thousands group, then the remaining hundreds/tens/ones: four thousand sixty‑two.
  2. 9,015
    The words describe 9,000 + 10 + 5, which is 9,015.
  3. 50
    The tens digit is 5; each unit has value 10, so its value is 5 × 10 = 50.
  4. 0
    The hundreds digit is 0; each unit has value 100, so its value is 0 × 100 = 0.
  5. 6,000 + 300 + 7
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 6,000 + 300 + 7.
  6. 7,124
    Add 6,000 + 1,100 + 20 + 4 = 7,124.
  7. 85
    Each hundred is worth 100. Divide 8,500 by 100: there are 85 complete hundreds.
  8. <
    Compare digits from the highest place that differs. 5,299 < 5,300.
  9. <
    Compare digits from the highest place that differs. 9,009 < 9,090.
  10. 4,053 < 4,305 < 4,350 < 4,530
    Compare the thousands place first, then hundreds, tens, and ones: 4,053, 4,305, 4,350, 4,530.
  11. 300
    The total distance is 1,200. Divide by 4 equal intervals: 300.
  12. 5,200
    Add 4 intervals of 125: 4,700 + 4 × 125 = 5,200.
  13. 7,500
    Distance 500; half is 250 above 7,250.
  14. 3,100, 3,275
    The same signed step, +175, connects consecutive terms. Continue twice.
  15. 8,650
    The first and third terms span two equal steps: (8,400 − 8,900) ÷ 2 = -250 per step.
  16. 6,000, 5,775
    The same signed step, -225, connects consecutive terms. Continue twice.
  17. 3,000
    It lies between 3,000 and 4,000; the midpoint is 3,500. With halfway values rounded up, choose 3,000.
  18. 8,000
    It lies between 7,000 and 8,000; the midpoint is 7,500. With halfway values rounded up, choose 8,000.
  19. 9,600
    It lies between 9,500 and 9,600; the midpoint is 9,550. With halfway values rounded up, choose 9,600.
  20. 4,900
    It lies between 4,800 and 4,900; the midpoint is 4,850. With halfway values rounded up, choose 4,900.
  21. 7,490
    It lies between 7,480 and 7,490; the midpoint is 7,485. With halfway values rounded up, choose 7,490.
  22. 10,000
    It lies between 9,990 and 10,000; the midpoint is 9,995. With halfway values rounded up, choose 10,000.
  23. 4,500
    The interval of whole numbers rounding to 5,000 starts halfway below, at 4,500, and ends at 5,499 (with halfway values rounded up).
  24. 7,150
    The interval of whole numbers rounding to 7,200 starts halfway below, at 7,150, and ends at 7,249 (with halfway values rounded up).
  25. 2,068
    Thousands digit cannot be zero; use 2 first, then the remaining digits ascending.
  26. 576
    5,760 ÷ 10 = 576; distinguish count of tens from the tens digit.
  27. 4,000
    The thousand midpoint is 4,500; 4,450 is below it.
  28. 5
    Intervals are gaps between adjacent marks, so one fewer than the number of ticks.
  29. 2,760; 2,800; 3,000
    Use 2,764 for each requested place; compare with the relevant midpoints.
  30. 5,000
    4,850 + 150 = 5,000; crosses a thousand boundary.

Practice examination

  1. seven thousand eight hundred four
    Read the thousands group, then the remaining hundreds/tens/ones: seven thousand eight hundred four.
  2. 3,090
    The words describe 3,000 + 90, which is 3,090.
  3. 500
    The hundreds digit is 5; each unit has value 100, so its value is 5 × 100 = 500.
  4. 10
    The tens digit is 1; each unit has value 10, so its value is 1 × 10 = 10.
  5. 8,000 + 600 + 4
    Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 8,000 + 600 + 4.
  6. 4,407
    Add 3,000 + 1,400 + 0 + 7 = 4,407.
  7. 73
    Each hundred is worth 100. Divide 7,300 by 100: there are 73 complete hundreds.
  8. >
    Compare digits from the highest place that differs. 6,780 > 6,708.
  9. 5,012 < 5,021 < 5,120 < 5,201
    Compare the thousands place first, then hundreds, tens, and ones: 5,012, 5,021, 5,120, 5,201.
  10. 300
    The total distance is 1,200. Divide by 4 equal intervals: 300.
  11. 7,125
    Add 3 intervals of 125: 6,750 + 3 × 125 = 7,125.
  12. 1,950, 2,125
    The same signed step, +175, connects consecutive terms. Continue twice.
  13. 7,225
    The first and third terms span two equal steps: (7,050 − 7,400) ÷ 2 = -175 per step.
  14. 6,000
    It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 6,000.
  15. 7,000
    It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 7,000.
  16. 9,900
    It lies between 9,800 and 9,900; the midpoint is 9,850. With halfway values rounded up, choose 9,900.
  17. 4,760
    It lies between 4,760 and 4,770; the midpoint is 4,765. With halfway values rounded up, choose 4,760.
  18. 3,750
    The interval of whole numbers rounding to 3,800 starts halfway below, at 3,750, and ends at 3,849 (with halfway values rounded up).
  19. 4,099 < 4,100
    Compare the full numbers from leftmost place: 4 thousands tie; hundreds 0 < 1.
  20. 96
    9,650 = 96 hundreds + 50 ones.
  21. 250
    Seven ticks create six spaces; 4,000 − 2,500 = 1,500; divide by 6.
  22. 6,499
    Halfway to 7,000 is 6,500, so 6,499 is the last value rounding to 6,000.
  23. 7,500; 7,000
    Hundred midpoint 7,450 has been passed, but thousand midpoint 7,500 has not.
  24. 2,725
    The fourth is three increments after first: 2,050 + 3 × 225 = 2,725.
  25. 100
    10,000 ÷ 100 = 100 groups of 100.
  26. 4,000
    Round the original 4,450 directly to the nearest thousand; 4,450 is below 4,500 midpoint. Repeated rounding can distort.