This grade 5 powers worksheet answer key solves all 26 problems of the place value and powers of 10 worksheet step by step.
Every solution shows the place-value reasoning, the digit shift and the final answer in bold. Compare your steps with the key, and look again at any problem where a decimal point or a zero ended up in the wrong place.
Grade 5 Powers Worksheet Answer Key: problems 1–5
Problem 1: Comparing two 6s
The left 6 is in the thousands place: \(6,000\). The right 6 is in the hundreds place: \(600\). Since \(6,000 : 600 = 10\), the left 6 is worth 10 times as much.
10 times as much.
Problem 2: Tenths and hundredths
\(0.5\) is 50 hundredths and \(0.05\) is 5 hundredths. Since \(50 : 5 = 10\), \(0.5\) is 10 times as much as \(0.05\).
10 times as much.
Problem 3: One tenth and ten times
- \(0.3 : 10 = 0.03\). 0.03
- \(40 : 10 = 4\). 4
- \(0.07 \times 10 = 0.7\). 0.7
Problem 4: Times 10 and divided by 10
- \(8.5 \times 10 = 85\). 85
- \(8.5 : 10 = 0.85\). 0.85
- \(0.062 \times 10 = 0.62\). 0.62
- \(62 : 10 = 6.2\). 6.2
Problem 5: Reading the power-of-10 picture
- \(10^{3} = 10 \times 10 \times 10 = 1,000\). 1,000
- 10,000 has four zeros, so \(10,000 = 10^{4}\). \(10^{4}\)
- \(10^{5} = 100,000\) (five zeros). 100,000
Grade 5 Powers Worksheet Answer Key: problems 6–10
Problem 6: Powers of 10 and zeros
- Five factors of 10: \(10^{5}\).
- 100,000,000 has eight zeros: \(10^{8}\).
- Four factors of 10 give 4 zeros: 10,000.
Problem 7: Evaluating powers of 10
- \(10^{2} = 100\). 100
- \(10^{4} = 10,000\). 10,000
- \(10^{7} = 10,000,000\) (seven zeros). 10,000,000
Problem 8: Counting zeros
- The exponent 9 means 9 zeros: \(10^{9} = 1,000,000,000\). 9 zeros
- 1 followed by 5 zeros is 100,000, so \(10^{5}\).
Problem 9: Multiplying by 10, 100 and 1,000
- \(6.3 \times 10 = 63\). 63
- \(6.3 \times 100 = 630\). 630
- \(6.3 \times 1,000 = 6,300\). 6,300
Problem 10: Shifting digits left
Move each digit 2 places left: the 3 goes to hundreds, the 4 to tens and the 5 to ones.
\(3.45 \times 10^{2} = 345\). 345
Grade 5 Powers Worksheet Answer Key: problems 11–15
Problem 11: Decimals times powers of 10
- \(0.48 \times 100 = 48\). 48
- \(0.048 \times 1,000 = 48\). 48
- \(7.5 \times 1,000 = 7,500\). 7,500
- \(0.9 \times 10 = 9\). 9
Problem 12: Dividing 530 by powers of 10
- \(530 : 10 = 53\). 53
- \(530 : 100 = 5.3\). 5.3
- \(530 : 1,000 = 0.53\). 0.53
Problem 13: Shifting digits right
Move each digit 2 places right: the 5 goes from hundreds to ones, and the 2 goes from tens to tenths.
\(520 : 10^{2} = 5.2\). 5.2
Problem 14: Decimals divided by powers of 10
- \(4.7 : 10 = 0.47\). 0.47
- \(36 : 100 = 0.36\). 0.36
- \(0.8 : 10 = 0.08\). 0.08
- \(5 : 1,000 = 0.005\). 0.005
Problem 15: Missing exponent in multiplication
- 4.2 becomes 4,200 when the digits move 3 places: \(3\).
- 0.75 becomes 75 after 2 places: \(2\).
- 6 becomes 600,000 with 5 zeros added: \(5\).
Grade 5 Powers Worksheet Answer Key: problems 16–20
Problem 16: Missing exponent in division
- 9,000 to 9 is 3 places right: \(3\).
- 560 to 0.56 is 3 places right: \(3\).
- 31 to 3.1 is 1 place right: \(1\).
Problem 17: Power-of-10 patterns
- Each number is 10 times the last: \(0.4 \times 10 = 4\) and \(4 \times 10 = 40\). 4 and 40
- Each number is divided by 10: \(20 : 10 = 2\) and \(2 : 10 = 0.2\). 2 and 0.2
Problem 18: Which is greater?
- \(10 \times 0.36 = 3.6\) and \(0.36 : 10 = 0.036\). \(10 \times 0.36\) is greater.
- \(0.5 \times 1,000 = 500\) and \(5.2 \times 100 = 520\). \(5.2 \times 10^{2}\) is greater.
Problem 19: Find the error
Liam only added zeros at the end, which does not change the value: \(2.500 = 2.5\). Multiplying by 100 moves each digit 2 places left, so the 2 goes to hundreds and the 5 to tens, with a zero in the ones place.
\(2.5 \times 100 = 250\). 250
Problem 20: Explain with place value
Dividing by \(10^{2}\) moves each digit 2 places right. The 8 starts in the ones place, moves to the tenths place, and then to the hundredths place. An 8 in the hundredths place is \(0.08\).
\(8 : 10^{2} = 0.08\)
Grade 5 Powers Worksheet Answer Key: problems 21–25
Problem 21: Apple crates
Each crate has 100 apples. \(46 \times 10^{2} = 4,600\).
4,600 apples.
Problem 22: Running laps
\(0.65 \times 10 = 6.5\). The digits move 1 place left.
6.5 miles.
Problem 23: Stack of cardstock
\(0.012 \times 10^{2} = 1.2\). The 1 moves from hundredths to tenths and the 2 from thousandths to hundredths.
1.2 inches.
Problem 24: Honey at the farmers market
Total: \(6.40 \times 10^{2} = 640\), so $640. Each envelope: \(640 : 10 = 64\).
$64 per envelope.
Problem 25: Sticker packs
Total: \(0.45 \times 10^{2} = 45\), so $45. Each share: \(45 : 10 = 4.5\).
$4.50 each.
Grade 5 Powers Worksheet Answer Key: problems 26–26
Problem 26: Milk bottles
Total milk: \(0.35 \times 10^{3} = 350\) gallons. Each tank: \(350 : 10^{2} = 3.5\).
3.5 gallons per tank.
How to use this grade 5 powers worksheet answer key
Read this grade 5 powers worksheet answer key after trying each problem yourself, and redo any problem you missed.
See every chapter on the Grade 5 math page.