Place Value and Powers of 10: Grade 5 Math Worksheet Answer Key – PDF Download

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

1. \(0.3 : 10 = 0.03\). 0.03
2. \(40 : 10 = 4\). 4
3. \(0.07 \times 10 = 0.7\). 0.7

Problem 4: Times 10 and divided by 10

1. \(8.5 \times 10 = 85\). 85
2. \(8.5 : 10 = 0.85\). 0.85
3. \(0.062 \times 10 = 0.62\). 0.62
4. \(62 : 10 = 6.2\). 6.2

Problem 5: Reading the power-of-10 picture

1. \(10^{3} = 10 \times 10 \times 10 = 1,000\). 1,000
2. 10,000 has four zeros, so \(10,000 = 10^{4}\). \(10^{4}\)
3. \(10^{5} = 100,000\) (five zeros). 100,000

Grade 5 Powers Worksheet Answer Key: problems 6–10

Problem 6: Powers of 10 and zeros

1. Five factors of 10: \(10^{5}\).
2. 100,000,000 has eight zeros: \(10^{8}\).
3. Four factors of 10 give 4 zeros: 10,000.

Problem 7: Evaluating powers of 10

1. \(10^{2} = 100\). 100
2. \(10^{4} = 10,000\). 10,000
3. \(10^{7} = 10,000,000\) (seven zeros). 10,000,000

Problem 8: Counting zeros

1. The exponent 9 means 9 zeros: \(10^{9} = 1,000,000,000\). 9 zeros
2. 1 followed by 5 zeros is 100,000, so \(10^{5}\).

Problem 9: Multiplying by 10, 100 and 1,000

1. \(6.3 \times 10 = 63\). 63
2. \(6.3 \times 100 = 630\). 630
3. \(6.3 \times 1,000 = 6,300\). 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

1. \(0.48 \times 100 = 48\). 48
2. \(0.048 \times 1,000 = 48\). 48
3. \(7.5 \times 1,000 = 7,500\). 7,500
4. \(0.9 \times 10 = 9\). 9

Problem 12: Dividing 530 by powers of 10

1. \(530 : 10 = 53\). 53
2. \(530 : 100 = 5.3\). 5.3
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

1. \(4.7 : 10 = 0.47\). 0.47
2. \(36 : 100 = 0.36\). 0.36
3. \(0.8 : 10 = 0.08\). 0.08
4. \(5 : 1,000 = 0.005\). 0.005

Problem 15: Missing exponent in multiplication

1. 4.2 becomes 4,200 when the digits move 3 places: \(3\).
2. 0.75 becomes 75 after 2 places: \(2\).
3. 6 becomes 600,000 with 5 zeros added: \(5\).

Grade 5 Powers Worksheet Answer Key: problems 16–20

Problem 16: Missing exponent in division

1. 9,000 to 9 is 3 places right: \(3\).
2. 560 to 0.56 is 3 places right: \(3\).
3. 31 to 3.1 is 1 place right: \(1\).

Problem 17: Power-of-10 patterns

1. Each number is 10 times the last: \(0.4 \times 10 = 4\) and \(4 \times 10 = 40\). 4 and 40
2. Each number is divided by 10: \(20 : 10 = 2\) and \(2 : 10 = 0.2\). 2 and 0.2

Problem 18: Which is greater?

1. \(10 \times 0.36 = 3.6\) and \(0.36 : 10 = 0.036\). \(10 \times 0.36\) is greater.
2. \(0.5 \times 1,000 = 500\) 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.