Chapter practice examination

Twenty-six fresh original questions; an untimed mastery check

Attempt independently and untimed. This is a public practice examination, not a secure placement test. Reassess with other problems later.

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Exam · 26 questions

Problems

A mixed assessment of the competencies developed so far.

E1 Write 7,804 in words.
Show answer and reasoning
Answer: seven thousand eight hundred four
Read the thousands group, then the remaining hundreds/tens/ones: seven thousand eight hundred four.
E2 Write “three thousand ninety” using digits.
Show answer and reasoning
Answer: 3,090
The words describe 3,000 + 90, which is 3,090.
E3 In 9,506, what is the value of the digit in the hundreds place?
Show answer and reasoning
Answer: 500
The hundreds digit is 5; each unit has value 100, so its value is 5 × 100 = 500.
E4 In 4,018, what is the value of the digit in the tens place?
Show answer and reasoning
Answer: 10
The tens digit is 1; each unit has value 10, so its value is 1 × 10 = 10.
E5 Expand 8,604 into the sum of its nonzero place values.
Show answer and reasoning
Answer: 8,000 + 600 + 4
Use thousands, hundreds, tens, ones in order. Zero-value places may be omitted: 8,000 + 600 + 4.
E6 What number is 3 thousands + 14 hundreds + 0 tens + 7 ones?
Show answer and reasoning
Answer: 4,407
Add 3,000 + 1,400 + 0 + 7 = 4,407.
E7 How many complete hundreds are in 7,300?
Show answer and reasoning
Answer: 73
Each hundred is worth 100. Divide 7,300 by 100: there are 73 complete hundreds.
E8 Insert <, >, or =: 6,780 ___ 6,708.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 6,780 > 6,708.
E9 Arrange from least to greatest: 5,021, 5,201, 5,012, 5,120.
Show answer and reasoning
Answer: 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.
E10 A number line runs from 2,100 to 3,300 in 4 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 300
The total distance is 1,200. Divide by 4 equal intervals: 300.
E11 A number line begins at 6,750 and each tick increases by 125. What is the value at tick 3 after the start?
Show answer and reasoning
Answer: 7,125
Add 3 intervals of 125: 6,750 + 3 × 125 = 7,125.
E12 Find the next two numbers: 1,250, 1,425, 1,600, 1,775, ___, ___.
Show answer and reasoning
Answer: 1,950, 2,125
The same signed step, +175, connects consecutive terms. Continue twice.
E13 Complete the pattern: 7,400, ___, 7,050, 6,875.
Show answer and reasoning
Answer: 7,225
The first and third terms span two equal steps: (7,050 − 7,400) ÷ 2 = -175 per step.
E14 Round 6,499 to the nearest thousand.
Show answer and reasoning
Answer: 6,000
It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 6,000.
E15 Round 6,500 to the nearest thousand.
Show answer and reasoning
Answer: 7,000
It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 7,000.
E16 Round 9,850 to the nearest hundred.
Show answer and reasoning
Answer: 9,900
It lies between 9,800 and 9,900; the midpoint is 9,850. With halfway values rounded up, choose 9,900.
E17 Round 4,764 to the nearest ten.
Show answer and reasoning
Answer: 4,760
It lies between 4,760 and 4,770; the midpoint is 4,765. With halfway values rounded up, choose 4,760.
E18 A whole number rounds to 3,800 to the nearest hundred. What is the smallest whole number it could have been?
Show answer and reasoning
Answer: 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).
E19 A student claims 4,099 is greater than 4,100 because 99 is greater than 0. Correct the mistake.
Show answer and reasoning
Answer: 4,099 < 4,100
Compare the full numbers from leftmost place: 4 thousands tie; hundreds 0 < 1.
E20 How many complete hundreds fit inside 9,650?
Show answer and reasoning
Answer: 96
9,650 = 96 hundreds + 50 ones.
E21 A line has 7 labeled ticks from 2,500 to 4,000, equally spaced. What is the value of one interval?
Show answer and reasoning
Answer: 250
Seven ticks create six spaces; 4,000 − 2,500 = 1,500; divide by 6.
E22 A whole number rounds to 6,000 to the nearest thousand. What is the greatest possible such whole number?
Show answer and reasoning
Answer: 6,499
Halfway to 7,000 is 6,500, so 6,499 is the last value rounding to 6,000.
E23 Round 7,451 to nearest hundred and thousand.
Show answer and reasoning
Answer: 7,500; 7,000
Hundred midpoint 7,450 has been passed, but thousand midpoint 7,500 has not.
E24 The first pattern term is 2,050 and each following term adds 225. Find the fourth term.
Show answer and reasoning
Answer: 2,725
The fourth is three increments after first: 2,050 + 3 × 225 = 2,725.
E25 A 10,000-bead collection is packed into boxes of 100. How many boxes are needed?
Show answer and reasoning
Answer: 100
10,000 ÷ 100 = 100 groups of 100.
E26 A student rounded 4,450 to 4,500 (nearest hundred), then claimed nearest thousand is 5,000. Explain the mistake.
Show answer and reasoning
Answer: 4,000
Round the original 4,450 directly to the nearest thousand; 4,450 is below 4,500 midpoint. Repeated rounding can distort.

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