Multiplying and dividing by 10, 100, and 1,000
In 5th grade, children learn why multiplying and dividing by 10, 100, and 1,000 shifts digits and moves the decimal point; and how to write those numbers as powers of 10, like 10³.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 5th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Amara's family packs rice for a food bank in bags of 1.5 kilograms. How many kilograms of rice are in 10 bags?
- 0.15 kilograms
- 15 kilograms
- 11.5 kilograms
Why this matters
Moving digits by tens is a skill your child will reach for again and again once decimals arrive. It is how 2.5 meters becomes 250 centimeters, how 10 items at $1.25 come to $12.50, and later how scientists write very large and very small numbers. A child who knows the digits move, rather than that you "add a zero," will not be thrown when 3.6 × 10 is 36.
Where kids can get stuck
- Using the "add a zero" rule on decimals, so 4.2 × 10 becomes 4.20, which is still 4.2, instead of 42.
- Moving the decimal point the wrong way when dividing, so 6.5 ÷ 10 becomes 65 instead of 0.65.
- Losing count of zeros when the number already ends in one, writing 50 × 100 as 500 instead of 5,000.
How you can help
- Use prices at the store: if one apple costs $0.45, ask your child what 10 apples and 100 apples would cost. Talk about why the digits moved and whether the answers, $4.50 and $45.00, feel sensible.
- Write 10, 100, 1,000, and 10,000 on a scrap of paper and have your child count the zeros in each. Show that 1,000 is 10 × 10 × 10, written 10³, then ask how they would write 10,000 the same way.
- Ask quick car-ride questions like "What is 7.2 divided by 10?" and "What is 7.2 times 100?" Have your child say whether the answer should be bigger or smaller before working it out.
Want a little more? Try Bobby's Math Club for free practice that adapts to your child.
Questions parents ask
Why is my child learning to multiply by 10 this way instead of adding a zero?
Adding a zero works for whole numbers but fails with decimals, and children who rely on it get stuck as soon as decimals appear. Teachers explain the pattern as digits moving to places worth ten times more. That one explanation covers 45 × 10 = 450 and 3.6 × 10 = 36 alike. It takes a little longer to learn but does not have to be unlearned later.
Is the decimal point moving or are the digits moving?
Strictly, the digits move to new places and the decimal point stays put. In 3.6 × 10 = 36, the 3 moves from the ones place to the tens place and the 6 moves from tenths to ones. Many people describe it as the point moving, and that is a fine shortcut, as long as your child can explain the place value reason underneath.
Where will my child use this pattern next?
Later in 5th grade, your child will convert metric measurements, such as 1.5 kilograms to 1,500 grams, which relies on exactly this pattern. It also helps with decimal multiplication and estimating. In middle school, the same idea supports scientific notation, where very large and very small numbers are written using powers of ten.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Free, unlimited practice for every child in your family
- A few minutes a day, at just the right level
- Level-ups, badges, and a cheer for every win
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 5.NBT.A.2: “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.” Learn how Bobby's Math Club can help your students grow. (Common Core 5.NBT.2)