This set introduces decimal place value alongside the shifting-digits rule. Fifth graders correct a sentence that puts the 3 in 4.73 in the tenths place, fix the wrong quotient when 820 is divided by 100, and repair the claim that 0.06 multiplied by 10 equals 6. They name the place of the 5 in 12.58, compute 0.4 × 100 and 350 ÷ 1,000, and explain why 72 ÷ 10 is not 7.02.
These problems build the careful decimal-point tracking students rely on for measurement, money, and the exponent work coming next.
Style:
Place Value & Powers of 10
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
In 4.73 the digit 3 is in the tenths place.
Rewrite: In 4.73 the digit 3 is in the hundredths place. The 7 is in the tenths place.
2. Fix the sentence:
When you divide 820 by 100 you get 82.
Rewrite: When you divide 820 by 100 you get 8.2, not 82. Each digit shifts two places to the right.
3. Fix the sentence:
Multiplying 0.06 by 10 gives 6.
Rewrite: Multiplying 0.06 by 10 gives 0.6. The decimal point moves one place to the right, not two.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In the number 12.58 the digit 5 is in the tenths place.
2. 0.4 × 100 = 40.
3. 350 ÷ 1,000 = 0.35.
4. The value of the 9 in 0.09 is nine hundredths.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. What happens to each digit in a number when you multiply by 10? Use the example 3.45 × 10 in your answer.
Each digit shifts one place to the left. 3.45 × 10 = 34.5 because the 3 moves from the ones to the tens, the 4 moves from tenths to ones, and the 5 moves from hundredths to tenths.
2. A student says 72 ÷ 10 = 7.02. Is the student correct? Explain the mistake.
The student is incorrect. 72 ÷ 10 = 7.2. The 7 moves to the ones place and the 2 moves to the tenths place. The student inserted a zero in the wrong position.
Place Value & Powers of 10
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
In 4.73 the digit 3 is in the tenths place.
Rewrite: In 4.73 the digit 3 is in the hundredths place. The 7 is in the tenths place.
2) Fix the sentence:
When you divide 820 by 100 you get 82.
Rewrite: When you divide 820 by 100 you get 8.2, not 82. Each digit shifts two places to the right.
3) Fix the sentence:
Multiplying 0.06 by 10 gives 6.
Rewrite: Multiplying 0.06 by 10 gives 0.6. The decimal point moves one place to the right, not two.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) In the number 12.58 the digit 5 is in the tenths place.
2) 0.4 × 100 = 40.
3) 350 ÷ 1,000 = 0.35.
4) The value of the 9 in 0.09 is nine hundredths.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) What happens to each digit in a number when you multiply by 10? Use the example 3.45 × 10 in your answer.
Each digit shifts one place to the left. 3.45 × 10 = 34.5 because the 3 moves from the ones to the tens, the 4 moves from tenths to ones, and the 5 moves from hundredths to tenths.
2) A student says 72 ÷ 10 = 7.02. Is the student correct? Explain the mistake.
The student is incorrect. 72 ÷ 10 = 7.2. The 7 moves to the ones place and the 2 moves to the tenths place. The student inserted a zero in the wrong position.
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9 Questions
15-20 minutes
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