5th Grade Place Value and Powers of Ten Worksheets with Answers (Free PDF)

5th grade powers of ten worksheet – Maths PDF

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

Key takeaway: This worksheet helps fifth grade students practice comparing place values, multiplying and dividing by powers of ten, and using exponents.

Topic: Place Value and Powers of Ten (5th grade)
Content: 20 worksheet problems, from easy to challenging
Standards: 5.NBT.A.1, 5.NBT.A.2
Answers: On a separate page, so you can try every worksheet problem first
Format: Free printable PDF, US Letter, black and white

This worksheet helps fifth grade students practice comparing place values, multiplying and dividing by powers of ten, and using exponents. Also, charts, pictures, and stories about pencils, ants, and savings show where powers of ten appear.

There are 20 problems. The first three compare digits in place value, and the next five multiply and divide whole numbers and decimals by 10, 100, and 1,000. Four problems write and evaluate powers of ten, and the next two use exponents in products and quotients. The last eight find missing exponents and numbers, then solve pencil, ant, savings, crayon, and bake sale stories. Then, allow about 35 minutes.

These 20 problems practice place value and powers of 10 (Common Core 5.NBT.A.1 and 5.NBT.A.2). You will compare the value of digits in neighboring places, write powers of 10 with exponents, and multiply and divide whole numbers and decimals by 10, 100 and 1,000.

Watch the decimal point move. It moves right when you multiply and left when you divide. The last six problems are word problems.

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

5th grade powers of ten worksheet: worksheet problems 1 to 10

1 – Tens and hundreds

First, in the number 7,700, how many times the value of the 7 in the hundreds place is the 7 in the thousands place?

2 – One tenth

Next, in the number 440, the 4 in the tens place is what fraction of the value of the 4 in the hundreds place?

3 – Compare digits in 3.33

Then, the chart shows the number 3.33. How many times the value of the 3 in the tenths place is the 3 in the ones place?

A place value chart.

4 – Multiply by 10

Now, find each product.

$3.7\times10$
$0.46\times10$
$52\times10$

5 – Divide by 10

Also, find each quotient.

$450\div10$
$63\div10$
$8\div10$
$2.5\div10$

6 – Multiply by 100

First, find each product.

$6\times100$
$0.38\times100$
$4.5\times100$
$0.07\times100$

7 – Divide by 100

Next, find each quotient. The picture shows how the point moves in the first problem.

$7{,}200\div100$
$530\div100$
$9\div100$
$46.5\div100$

Two places left.

8 – Multiply by 1,000

Then, find each product.

$0.9\times1{,}000$
$3.25\times1{,}000$
$12\times1{,}000$
$0.004\times1{,}000$

Worksheet problem 9 and after

9 – Write the exponent

Now, write each number as a power of 10 with an exponent.

$100$
$10{,}000$
$1{,}000{,}000$

Count the 10s.

10 – Evaluate powers of 10

Also, write each power of 10 as a standard number.

$10^{1}$
$10^{3}$
$10^{5}$

Worksheet problems 11 and up

11 – Multiply by powers of 10

First, find each product.

$4.2\times10^{2}$
$0.067\times10^{3}$
$35\times10^{4}$
$0.5\times10^{1}$

12 – Divide by powers of 10

Next, find each quotient.

$840\div10^{2}$
$6\div10^{3}$
$25.3\div10^{1}$
$9{,}000\div10^{3}$

13 – Missing exponent

Then, find the missing exponent.

$3.4\times10^{?}=3{,}400$
$0.056\times10^{?}=56$
$720\div10^{?}=7.2$
$15\div10^{?}=0.015$

14 – Missing number

Now, find the missing number.

$?\times10^{2}=8{,}500$
$62\div10^{?}=0.62$
$?\times10^{3}=4{,}200$
$0.9\times10^{?}=90$

15 – Pencil boxes

Also, the school store ordered $10^{3}$ pencils. Each box holds $10^{2}$ pencils. Write the division with powers of 10 and find how many boxes the store filled.

Each box holds 100 pencils.

16 – Line of ants

First, an ant is 0.3 inch long. A line of 100 ants walks head to tail. How long is the line in inches?

Each ant is 0.3 inch long.

17 – Weekly savings

Ethan saves $\$2.35$ each week. How much does he save in 10 weeks? How much in 100 weeks?

18 – Crayon cartons

Then, a factory has 6,000 crayons. It packs 100 crayons in each box and 10 boxes in each carton. How many boxes and how many cartons does it fill?

Worksheet problem 19 and after

19 – Mei's product

Mei multiplies 0.35 by 100 and writes 0.3500. Explain her mistake and find the correct product.

20 – Bake sale quarters

Also, at a bake sale, Diego sells $10^{2}$ brownies for $\$0.25$ each. He gives away $\frac{1}{10}$ of the money to the animal shelter. How much money does he give?

Each brownie costs 25 cents.

Key facts behind this 5th grade powers of ten worksheet

Key facts

Each place is 10 times the place to its right and 1/10 of the place to its left.
Next, 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.

Common mistakes with this 5th grade powers of ten worksheet

Students count the digit’s value as 10 times when the places are two apart. Instead, two places apart means 100 times as much.
Students write extra zeros after multiplying a decimal by a power of ten. Also, move the digits and drop trailing zeros that do nothing.
Students use the exponent as the number to multiply. Instead, ten to the third power is 1,000, not 30.
Students stop after the first step in a packing story. Use each result for the next grouping. Slow down at that step and check it twice.

Tips before you start the worksheet problems

Write the number in a chart and shift the digits the correct number of places. Then read the new number.
Check each answer by multiplying or dividing back. Finally, if you multiplied by 100, dividing by 100 should return the start.
Teachers can ask students to explain one problem by moving digits in a chart. Repeat this habit on every problem for the best results.

Download the 5th grade powers of ten worksheet as a PDF with the button below and keep it with your notes.

5th grade powers of ten worksheet: frequently asked questions

How do you divide a decimal by 100?

Move the decimal point two places left, adding zeros if needed. For 7.3 divided by 100, move the point two places to get 0.073. The number gets smaller, since it is cut into 100 equal parts.

How do you write a power of ten from a number?

Count the zeros and use that as the exponent. The number 100,000 has five zeros, so it is 10 to the fifth power. Check by multiplying five tens. A quick check like this takes only a few seconds and prevents most errors.

How do you use powers of ten in a money story?

Multiply the price by the power of ten that matches the number of items. For 100 items at 0.40 dollars each, move the point two places right to get 40 dollars. A quick check like this takes only a few seconds and prevents most errors.

All Grade 5 chapters: Grade 5 math.

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