Decimals · Technique guide
Multiplying Decimals in Your Head
By Robert Hansson, Kung Fu Math
Decimals look harder than whole numbers, but the digits multiply in exactly the same way. The only new skill is knowing where the decimal point ends up, and a quick estimate tells you that almost every time.
Treat every decimal problem as two small problems: a whole-number product, and a question of size. Get both right and you have the answer.
01
Ignore the point, then place it
Remove the decimal points and multiply the whole numbers. Then count the total number of decimal places in the factors; the answer has that many decimal places.
Worked example
0.6 × 0.7
- → 6 × 7 = 42
- → One decimal place in each factor: two in total
- → 0.42
Answer: 0.42
Practice: Try 0.3 × 0.9, 1.2 × 0.4 and 0.05 × 0.8.
02
Estimate first
Round each factor to a whole number and multiply. That tells you roughly how big the answer must be, so you cannot misplace the decimal point by a factor of ten.
Worked example
3.2 × 4.5
- → Estimate: about 3 × 5 = 15
- → 32 × 45 = 1 440
- → The answer must be near 15, so 14.4
Answer: 14.4
Practice: Try 2.5 × 6.4, 7.1 × 3 and 9.8 × 1.5.
03
Use fractions
Some decimals are friendly fractions: 0.5 is a half, 0.25 is a quarter, 0.2 is a fifth and 0.75 is three quarters. Multiplying by them is the same as dividing.
Worked example
48 × 0.25
- → 0.25 is a quarter
- → 48 ÷ 4 = 12
Answer: 12
Practice: Try 36 × 0.5, 45 × 0.2 and 80 × 0.75.
04
Shift by 0.1 and 0.01
Multiplying by 0.1 moves every digit one place to the right, which is the same as dividing by 10. Multiplying by 0.01 divides by 100. Combine this with whole-number products for numbers like 0.3 or 0.04.
Worked example
250 × 0.04
- → 250 × 4 = 1 000
- → × 0.01 means ÷ 100
- → 1 000 ÷ 100 = 10
Answer: 10
Practice: Try 70 × 0.3, 1 200 × 0.05 and 8.5 × 0.1.
05
Split the decimal
Split a decimal into its whole part and its decimal part, multiply each and add. 2.5 × 18 is 2 × 18 plus half of 18.
Worked example
2.5 × 18
- → 2 × 18 = 36
- → 0.5 × 18 = 9
- → 36 + 9 = 45
Answer: 45
Practice: Try 1.5 × 24, 3.2 × 15 and 4.25 × 8.
Common mistakes
- Counting decimal places in the answer instead of the factors.
- Thinking that multiplying always makes a number bigger. Multiplying by a number below 1 makes it smaller.
- Dropping trailing zeros too early. 0.5 × 0.4 = 0.20, which is 0.2.
Summary
- Multiply the digits as whole numbers, then place the point.
- Estimate with rounded numbers to check the size.
- Swap friendly decimals for fractions and divide instead.
Into the dojo
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