Powers of 10 worksheets
Aligned with Common Core 5.NBT.A.2
Printable fifth-grade powers of 10 worksheets and a how-to teaching page: exponents like 10³, how a digit is worth 10 times as much one place to the left and 1/10 as much one place to the right, and multiplying and dividing whole numbers and decimals by 10, 100 and 1,000.
The worksheets
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How Powers of 10 Work
10¹ to 10⁴ written as exponents, as multiplication and as numbers, and a place value chart from thousands to thousandths showing 10 times as much to the left and 1/10 as much to the right.
Exponents of 10
Rows that show a power of 10 one way, to fill in the other two ways. Fewer has 6 rows up to 10³, Standard has 8 up to 10⁵, and More has 10 up to 10⁶ with problems like 4 × 10² and 80,000 = 8 × 10⁴. Includes an answer key.
Ten Times or One Tenth
Pairs of numbers with the same digit shaded, to compare, like "the 9 in 98.6 is 100 times as much as the 9 in 0.9." Fewer has 6 pairs one place apart, Standard has 8 up to two places apart, and More has 10 down to thousandths. Includes an answer key.
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How to Multiply and Divide by Powers of 10
3.45 × 100 and 72 ÷ 1,000 shown on place value charts, with each digit moving to its new place and zeros filling the empty places.
Multiply and Divide by 10, 100 and 1,000
Multiplication and division by 10, 100 and 1,000, mixed on every sheet. Fewer has 10 problems with whole numbers, Standard has 12 with decimals, and More has 14 written with exponents, like 2.72 × 10³. Includes an answer key.
Find the Power of 10
Missing-number problems like 39.3 ÷ ___ = 0.393, plus × and ÷ patterns to finish. Fewer uses whole numbers, Standard uses decimals, and More asks for the exponent. Includes an answer key.
Print the whole packet
One copy of every sheet above, in order. Tap + for more copies (up to 10).
For the parent or teacher
What it is
In 4th grade, students saw that a digit is worth 10 times as much one place to the left. Now that works for decimals too, and going right, a digit is worth 1/10 as much. Students also learn exponents for powers of 10: 10³ means 10 × 10 × 10, which is 1,000. The exponent tells how many tens are multiplied, and how many zeros the number has. Then they multiply and divide by 10, 100 and 1,000, moving each digit one place for every zero.
What comes next
Volume.
How to teach it
- Teach in order or jump to whatever your student needs. A student may read exponents easily and still be building an understanding of what a digit is worth in each place.
- Write a place value chart from thousands to thousandths and move a single digit left and right to see its value change.
- Count the zeros together. 10⁴ has 4 tens multiplied and 10,000 has 4 zeros.
- Read 10³ as "ten to the third power," or "ten cubed."
Common mistakes
- Reading 10³ as 10 × 3 = 30.
- Counting a place to the right as 10 times bigger instead of 1/10 as big.
- Losing track of the places when a decimal point is in the way.
- Mixing up 10 times and 100 times when the digits are two places apart.
- Adding a zero to the end of a decimal to multiply by 10, like 3.4 × 10 = 3.40.