What is this skill?
This skill is about what happens to a number when it is multiplied or divided by 10, 100 or 1,000. Each time you multiply by 10, every digit moves one place to the left and is worth ten times as much. Each time you divide by 10, every digit moves one place to the right and is worth one tenth as much. So 4.5 × 10 = 45, 4.5 × 100 = 450, and 36 ÷ 1,000 = 0.036.
Fifth graders usually describe this as moving the decimal point, but the idea underneath is that the digits move, and the decimal point stays put. Seeing it that way avoids a common trap. Students also meet the exponent notation for these numbers: 10 squared is 100 and 10 cubed is 1,000, which is just a short way of writing how many tens are multiplied together.
Why it matters
Powers of ten are the structure of our number system, and a firm grip on them makes a lot of later work easier. Metric conversions (meters to centimeters, kilometers to meters) are multiplications and divisions by powers of ten. Decimal multiplication relies on it: 0.3 × 0.2 is 3 × 2 with the decimal places counted afterward. Scientific notation in middle school depends on it directly.
It also makes mental math faster. A child who knows that 7,000 ÷ 100 is 70 can estimate with large numbers quickly and does not have to rely on written methods for everything.
Common mistakes
- The “add a zero” rule. It works for 35 × 10 = 350, but it breaks on decimals: 4.5 × 10 is 45, not 4.50. Children who learned the shortcut without the reason get stuck here.
- Moving the decimal point the wrong way, such as making a number smaller when multiplying. A quick check helps: multiplying by 100 should make the number bigger.
- Moving it the wrong number of places. Count the zeros in 10, 100 or 1,000: one, two, three.
- Forgetting to fill empty places with zeros, writing 36 ÷ 1,000 as 0.36 instead of 0.036.
- Mixing up the number of zeros in the answer and the number of places the digits moved. They are often not the same.
How to help at home
- Use money. $4.50 is 450 cents, so multiplying by 100 changes dollars into cents, and dividing by 100 changes them back.
- Make a place-value chart on a sheet of paper with columns from thousands down to thousandths. Write a number with one digit per column and slide the digits left or right.
- Ask for the direction first: “Will the answer be bigger or smaller?” Then ask how many places.
- Look for powers of ten around the house: a 1,000 mL bottle holds 1 liter, and a 100 cm ruler is 1 meter.
- Skip the tricks until the idea is clear. If your child can explain why the digits move, the shortcuts will follow on their own.
Worked examples
These are real questions from the Tutorsaurus powers of ten practice, with the answers worked out.
Example 1
4700 ÷ 100 = ?
Answer: 47. Dividing by 100 moves the decimal point 2 places left: 47.
Example 2
25 × 1000 = ?
Answer: 25000. Multiplying by 1000 moves the decimal point 3 places right: 25000.
Example 3
41 ÷ 100 = ?
Answer: 0.41. Dividing by 100 moves the decimal point 2 places left: 0.41.