Place Value & Powers of 10 — Answer Key
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.
Corrected: In 4.73 the digit 3 is in the hundredths place. The 7 is in the tenths place.
The corrected sentence is: "In 4.73 the digit 3 is in the hundredths place. The 7 is in the tenths place." The error was decimal place misidentification: the original sentence "In 4.73 the digit 3 is in the tenths place." needed to be fixed.
2. Fix the sentence:
When you divide 820 by 100 you get 82.
Corrected: When you divide 820 by 100 you get 8.2, not 82. Each digit shifts two places to the right.
The corrected sentence is: "When you divide 820 by 100 you get 8.2, not 82. Each digit shifts two places to the right." The error was wrong quotient: the original sentence "When you divide 820 by 100 you get 82." needed to be fixed.
3. Fix the sentence:
Multiplying 0.06 by 10 gives 6.
Corrected: Multiplying 0.06 by 10 gives 0.6. The decimal point moves one place to the right, not two.
The corrected sentence is: "Multiplying 0.06 by 10 gives 0.6. The decimal point moves one place to the right, not two." The error was incorrect decimal shift: the original sentence "Multiplying 0.06 by 10 gives 6." needed to be fixed.
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.
The first digit after the decimal point is the tenths place, so in 12.58 the 5 is in the tenths place and represents 0.5.
2. 0.4 × 100 = 40.
Multiplying by 100 shifts the decimal point two places to the right, so 0.4 becomes 40.
3. 350 ÷ 1,000 = 0.35.
Dividing by 1,000 shifts each digit three places to the right, so 350 becomes 0.350, which simplifies to 0.35.
4. The value of the 9 in 0.09 is nine hundredths.
The 9 is two places to the right of the decimal point, which is the hundredths place, so it represents nine hundredths or 0.09.
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.
Sample 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.
A good answer includes: 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.
Sample answer: 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.
A good answer includes: 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.