Chapter 1 — cumulative chapter review
Semester 4A · Chapter 1 · 34 questions
This review integrates every chapter learning objective. Try questions before revealing answers.
How many complete groups of 100 can be made from 58,143 objects, and how many remain?
Show answer & reasoning
58,143 = 581 × 100 + 43.
In 200,962, what is the value of the digit in the hundred-thousands place?
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The digit 2 represents 2 groups of 100,000, or 200,000.
Extend this pattern: 934,120, 934,370, 934,620, ___.
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Each term increases by 250; add that step once more.
Order these numbers from least to greatest: 873,669, 856,294, 948,515.
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Compare digit lengths first, then compare the greatest differing place.
Round 48,003 to the nearest 100.
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The bounding multiples are 48,000 and 48,100. The midpoint is 48,050, so the nearer benchmark is 48,000.
Round 507,649 to the nearest 1,000.
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The bounding multiples are 507,000 and 508,000. The midpoint is 507,500, so the nearer benchmark is 508,000.
A teacher partitions 613,900 counters into equal groups of 100. How many counters are in each group?
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Each group has 613,900 ÷ 100 = 6,139 counters.
In 18,820, what is the value of the digit in the ten-thousands place?
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The digit 1 represents 1 groups of 10,000, or 10,000.
Find 893,434 − 892,434 and explain the place-value change.
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Only the increment changes: 893,434 − 892,434 = 1,000.
A sequence begins at 428,216 and increases by 1,000 each time. What is its fifth term?
Show answer & reasoning
The fifth term is four equal steps after the first: 428,216 + 4 × 1,000.
Insert <, >, or =: 149,180 ___ 158,948.
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Compare the leftmost place where the digits differ: 149,180 is less than 158,948.
Round 14,467 to the nearest 100.
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The bounding multiples are 14,400 and 14,500. The midpoint is 14,450, so the nearer benchmark is 14,500.
What is the midpoint between 925,000 and 926,000?
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Half of the interval of 1,000 is 500. Add it to the lower benchmark.
Calculate 7,321 × 100 using place value.
Show answer & reasoning
Every place-value unit becomes 100 times as large; 7,321 × 100 = 732,100.
Find 24,542 − 14,542 and explain the place-value change.
Show answer & reasoning
Only the increment changes: 24,542 − 14,542 = 10,000.
How many complete groups of 100 can be made from 181,798 objects, and how many remain?
Show answer & reasoning
181,798 = 1817 × 100 + 98.
Extend this pattern: 992,785, 993,035, 993,285, ___.
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Each term increases by 250; add that step once more.
Insert <, >, or =: 376,090 ___ 366,451.
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Compare the leftmost place where the digits differ: 376,090 is greater than 366,451.
What is the midpoint between 21,500 and 21,600?
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Half of the interval of 100 is 50. Add it to the lower benchmark.
Round 601,061 to the nearest 1,000.
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The bounding multiples are 601,000 and 602,000. The midpoint is 601,500, so the nearer benchmark is 601,000.
Calculate 292,000 ÷ 100 by grouping place-value units.
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Dividing by 100 reduces each place-value unit by a factor of 100. The quotient is 2,920.
How many complete groups of 100 can be made from 67,606 objects, and how many remain?
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67,606 = 676 × 100 + 6.
In 696,662, what is the value of the digit in the hundred-thousands place?
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The digit 6 represents 6 groups of 100,000, or 600,000.
Extend this pattern: 421,870, 426,870, 431,870, ___.
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Each term increases by 5,000; add that step once more.
Order these numbers from least to greatest: 251,265, 269,772, 634,634.
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Compare digit lengths first, then compare the greatest differing place.
Round 68,623 to the nearest 100.
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The bounding multiples are 68,600 and 68,700. The midpoint is 68,650, so the nearer benchmark is 68,600.
Round 765,211 to the nearest 1,000.
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The bounding multiples are 765,000 and 766,000. The midpoint is 765,500, so the nearer benchmark is 765,000.
A student says the 2 in 24,105 means 2 ones. Explain its actual value.
Show answer & reasoning
The 2 occupies the ten-thousands position, representing 2 groups of 10,000.
A student removes the zeros from 304,006, saying zeros never affect place value. Explain why this is incorrect.
Show answer & reasoning
The zeros preserve each digit position: the number contains 3 hundred-thousands, 4 thousands, and 6 ones. Removing them changes the value.
A student predicts 12,526 after the pattern 12,126, 12,226, 12,326. Explain and give the correct next term.
Show answer & reasoning
Adjacent terms each differ by 100; add it once to 12,326.
Which is greater, 178,090 or 179,010? A student compares only the last digit. Explain the mistake.
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Compare from the highest place where digits differ. 179,010 exceeds 178,090 by 920, regardless of the final digit.
A student rounds 67,450 to the nearest hundred as 67,400. Explain why this is wrong.
Show answer & reasoning
67,450 is halfway between 67,400 and 67,500; our rounding convention sends halfway values up.
A student rounds 685,500 down to 685,000 to the nearest thousand. Explain and correct it.
Show answer & reasoning
The midpoint between 685,000 and 686,000 is 685,500; halfway rounds upward.
A learner multiplies 7,200 by 100 and writes 72,000. Identify the scaling mistake and give the correct result.
Show answer & reasoning
Multiplying by 100 makes every place value one hundred times larger. The correct product is 720,000.