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

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

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

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

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.

All Grade 5 chapters: Grade 5 math.

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