5.NBT.2: Multiply and Divide by Powers of 10
Also written as 5.NBT.A.2 and CCSS.MATH.CONTENT.5.NBT.A.2 · Cluster: Understand the place value system.
The Official Wording
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Common Core State Standards, Grade 5, Number & Operations in Base Ten · Read it at the source · Checked October 14, 2026
What 5.NBT.2 Means in Plain English
Fifth graders write 1,000 as 10³ and explain why 36 × 10³ = 36,000: every digit moves three places left, so three zeros fill in behind. With decimals the digits move the same way, so 4.7 × 10² = 470 and 4.7 ÷ 10² = 0.047.
The explanation matters more than the shortcut: “move the decimal point” is a description, and the reason is 5.NBT.1, each place being ten times the one to its right. It underpins decimal multiplication (5.NBT.7) and metric conversions (5.MD.1), and 6th graders use exponents on any base in 6.EE.1.
5.NBT.2 I Can Statements
- I can write 10 × 10 × 10 as 10³ and as 1,000.
- I can explain why 36 × 1,000 ends in three zeros.
- I can tell where the decimal point lands when I divide by 100.
5.NBT.2 Worked Example
One decimal, multiplied and then divided by a power of 10, with the digits tracked place by place rather than the point.
Find 2.5 × 10³ and 2.5 ÷ 10², and explain where the digits go.
- Write the power of 10 as a number first. The exponent counts the factors of 10.10³ = 10 × 10 × 10 = 1,000
- Multiplying by 10 once makes every digit worth ten times as much, so each digit shifts one place left. Three factors of 10 means three shifts.2.5 × 10 = 25, × 10 = 250, × 10 = 2,500
- The digits 2 and 5 never changed. They moved three places left, and zeros filled the empty tens and ones places.2.5 × 10³ = 2,500
- Dividing by 10 is the reverse: each digit becomes one tenth, so it shifts one place right. 10² means two shifts.2.5 ÷ 10 = 0.25, ÷ 10 = 0.025
- Again the 2 and 5 are intact. A zero holds the tenths place so the 2 can sit in hundredths.2.5 ÷ 10² = 0.025
Check it: Reverse each one: 2,500 ÷ 1,000 = 2.5 and 0.025 × 100 = 2.5. Both bring the digits back to where they started.
Common Mistakes with 5.NBT.2
Counting the zeros instead of the factors
10³ = 30, or 10³ = 10 × 3
Try this: Expand the exponent in writing every time at first, 10 × 10 × 10, and multiply it out before using it.
Adding zeros to a decimal
4.7 × 100 = 4.700
Try this: Shift the digits on a place value chart instead of appending zeros: the 4 moves two columns left into the hundreds, so 470.
Moving the point the wrong way when dividing
2.5 ÷ 10² = 250
Try this: Ask whether the answer should be bigger or smaller before writing anything. Dividing by 100 makes 2.5 much smaller, so 0.025.
Where 5.NBT.2 Fits
Practice 5.NBT.2
Quick Check
- Write 10 × 10 × 10 × 10 with an exponent, and as a whole number.
- 58 × 10³
- 6.3 ÷ 10²