Multiplying decimals · Usually met around P5
Powers of 10
The small number on 10 = how many 0s after the 1.
How to do it
Method
The small number on 10 = how many 0s after the 1
3.6 × 10² = 3.6 × 100 = 360
Another way
Times 10, again and again
3.6 → 36 → 360
In full
Several 10s multiplied can be written as a power of 10: 10² = 10 × 10 = 100, 10³ = 10 × 10 × 10 = 1000, 10⁴ = 10000. The small number up on the right says how many 10s are multiplied, which is how many 0s follow the 1: 10³ is 1 followed by 3 zeros. Careful: 10³ is not 10 × 3 = 30. To multiply by a power of 10, × 10² is × 100: every digit moves up two places, and the decimal point two places right: 3.6 × 10² = 360; 47 × 10³ = 47000. Another way: multiply by 10 again and again, as many times as the small number says: 3.6 × 10 = 36, 36 × 10 = 360.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Which power of 10 is 100?
- A. 10³
- B. 10⁴
- C. 10²
- D. 10⁵
Choose the right answer
Show the answer and working
Answer: C. 10²
Count the 0s after the 1 in 100: that is the small number on the 10.
Example 2
10⁴ = 10 × 10 × 10 × 10 = □; 8.5 × 10⁴ = □
Fill in each box
Show the answer and working
Answer: 10000，85000
Four 10s multiplied make 10000, 1 and four 0s; 8.5 × 10000 moves the point four places right: 85000.
Example 3
□ × 10² = 240
Show the answer and working
Answer: 2.4
10² = 100. Think backwards: 240 ÷ 100 = 2.4, the point two places left.
Practise it in the game →Multiplying decimals · Free to start, unlimited questions, no download