5th Grade Place Value and Powers of Ten Worksheet Solutions (PDF)

5th Grade math worksheet solutions: Place Value and Powers of Ten – Maths PDF

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This powers of ten answers for 5th Grade covers place value and powers of ten (Common Core 5.NBT.A.1, 5.NBT.A.2), with a free PDF to print.

This answer key explains how the decimal point moves in each of the 20 problems. Multiplying by 10, 100 or 1,000 moves the point right 1, 2 or 3 places. Dividing moves it left. Count the zeros or read the exponent to know how many places to move.

Grade 5 · Common Core State Standards: 5.NBT.A.1, 5.NBT.A.2

Powers of ten answers: exercises 1 to 10

Exercise 1 – Tens and hundreds

The 7 in the thousands place is worth 7,000. The 7 in the hundreds place is worth 700.

$7{,}000\div700=10$.

Answer: 10 times

Exercise 2 – One tenth

The 4 in the hundreds place is 400. The 4 in the tens place is 40.

$40\div400=\frac{1}{10}$.

Answer: $\frac{1}{10}$

Exercise 3 – Compare digits in 3.33

The 3 in the ones place is worth 3. The 3 in the tenths place is worth 0.3.

$3\div0.3=10$.

Answer: 10 times

3 is 10 times 0.3.

Exercise 4 – Multiply by 10

Multiplying by 10 moves the decimal point 1 place right.

(a) 37 (b) 4.6 (c) 520

Exercise 5 – Divide by 10

Dividing by 10 moves the decimal point 1 place left.

(a) 45 (b) 6.3 (c) 0.8 (d) 0.25

Exercise 6 – Multiply by 100

Multiplying by 100 moves the decimal point 2 places right.

(a) 600 (b) 38 (c) 450 (d) 7

One place left.

Exercise 7 – Divide by 100

Dividing by 100 moves the decimal point 2 places left.

(a) 72 (b) 5.3 (c) 0.09 (d) 0.465

Two places right.

Exercise 8 – Multiply by 1,000

Multiplying by 1,000 moves the decimal point 3 places right.

(a) 900 (b) 3,250 (c) 12,000 (d) 4

Exercise 9 – Write the exponent

Count the zeros. The number of zeros is the exponent.

(a) 100 has 2 zeros: $10^{2}$

(b) 10,000 has 4 zeros: $10^{4}$

Exercise 10 – Evaluate powers of 10

(a) 10

(b) $10\times10\times10$ = 1,000

Exercises 11 and up

Exercise 11 – Multiply by powers of 10

(a) Move 2 places right: 420

(b) Move 3 places right: 67

(d) Move 1 place right: 5

10^5 = 100,000.

Exercise 12 – Divide by powers of 10

(a) Move 2 places left: 8.4

(b) Move 3 places left: 0.006

(d) Move 3 places left: 9

10^5 = 100,000.

Exercise 13 – Missing exponent

(a) 3.4 to 3,400 is 3 places right: 3

(b) 0.056 to 56 is 3 places right: 3

(d) 15 to 0.015 is 3 places left: 3

Exercise 14 – Missing number

(a) 8,500 is 85 moved 2 places: 85

(b) 62 to 0.62 is 2 places left: 2

(d) 0.9 to 90 is 2 places right: 2

Exercise 15 – Pencil boxes

$10^{3}$ = 1,000 pencils and $10^{2}$ = 100 pencils per box.

$10^{3}\div10^{2}=1{,}000\div100=10$.

The store filled 10 boxes.

Exercise 16 – Line of ants

Multiply by 100: $0.3\times100=30$.

The line is 30 inches long.

Exercise 17 – Weekly savings

10 weeks: $2.35\times10=23.5$, so $\$23.50$.

100 weeks: $2.35\times100=235$, so $\$235$.

Exercise 18 – Crayon cartons

Boxes: $6{,}000\div100=60$.

Cartons: $60\div10=6$.

Answer: 60 boxes and 6 cartons

Exercise 19 – Mei's product

Mei added zeros but did not move the decimal point. Multiplying by 100 moves the point 2 places right.

$0.35\times100=35$.

Correct product: 35

Exercise 20 – Bake sale quarters

Total: $0.25\times10^{2}=0.25\times100=25$, so $\$25$.

One tenth: $25\div10=2.5$.

Diego gives $\$2.50$ to the shelter.

Key facts behind this powers of ten answers

Key facts

Each place is 10 times the place to its right and 1/10 of the place to its left.
The exponent of a power of 10 tells how many 10s are multiplied and how many zeros the value has.
Multiplying by a power of 10 moves the decimal point right by the exponent.
Dividing by a power of 10 moves the decimal point left by the exponent.
10 to the third power means 10 × 10 × 10 = 1,000, not 3 × 10.

How to use this powers of ten answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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