Multiplying and Dividing Decimals
Multiplying and Dividing Decimals
Multiplying and dividing decimals are skills you will use constantly — every time you calculate tax, convert units, or compute a GPA, decimal multiplication or division is involved.
The trick to multiplying decimals is to ignore the decimal points at first, multiply as if both numbers were whole numbers, and then place the point in the product by counting the total number of decimal places in the factors.
Division of decimals relies on a neat technique: move the decimal point in the divisor to make it a whole number, move it the same number of places in the dividend, and then divide normally. This lesson covers both operations with clear, step-by-step examples.
Multiplying
- Multiply ignoring decimal points.
- Count total decimal places in both factors.
- Place the decimal in the product with that many places.
$2.5 \times 0.34$
$25 \times 34 = 850$. Places: $1 + 2 = 3$. Answer: $0.850 = 0.85$
$0.07 \times 0.003$
$7 \times 3 = 21$. Places: $2 + 3 = 5$. Answer: $0.00021$
Dividing
Move the decimal right in both divisor and dividend to make the divisor a whole number.
$7.2 \div 0.4$
Move 1 place: $72 \div 4 = 18$
$15.6 \div 1.2$
Move 1 place: $156 \div 12 = 13$
Powers of 10 Shortcut
| Operation | Move Decimal | Example |
|---|---|---|
| $\times 10$ | 1 right | $3.47 \times 10 = 34.7$ |
| $\times 100$ | 2 right | $3.47 \times 100 = 347$ |
| $\div 10$ | 1 left | $3.47 \div 10 = 0.347$ |
| $\div 100$ | 2 left | $3.47 \div 100 = 0.0347$ |
Practice Problems
Show Answer Key
1. $1.8$
2. $24$
3. $0.01$
4. $130$
5. $650$
6. $6$
7. $11.55$
8. $91$
9. $0.003$
10. $50$
11. $15.624$
12. $0.3$
13. $0.0456$
14. $10$ gal
15. $\$16.63$