You can divide a decimal by a whole number, and you know that multiplying by 10 shifts every digit. To divide by a decimal, turn the divisor into a whole number first.
Key idea
Multiply the divisor and the dividend by the same power of 10, enough to make the divisor a whole number. The quotient does not change. Then divide: $4.8 \div 0.6 = 48 \div 6 = 8$.
Why it works
Division asks how many times one amount fits in another. If both amounts get 10 times bigger, the answer stays the same: $6 \div 2 = 3$ and $60 \div 20 = 3$. In tenths: $4.8 \div 0.6$ asks how many 6 tenths fit in 48 tenths, which is the same as $48 \div 6$.
Worked examples
Worked example: A tenths divisor
Find $4.8 \div 0.6$.
- Multiply both by 10: $48 \div 6$.
- $48 \div 6 = 8$.
- Check: $8 \times 0.6 = 4.8$.
Answer: $8$
Worked example: A decimal answer
Find $2.56 \div 0.8$.
- Multiply both by 10: $25.6 \div 8$.
- $25.6 \div 8 = 3.2$ (256 tenths $\div 8 = 32$ tenths).
- Check: $3.2 \times 0.8 = 2.56$.
Answer: $3.2$
Worked example: Write zeros in the dividend
Find $9 \div 0.25$.
- The divisor has 2 decimal places, so multiply both by 100.
- $9 \times 100 = 900$ and $0.25 \times 100 = 25$.
- $900 \div 25 = 36$.
Answer: $36$
Common mistake
Moving the point in the divisor only: $4.8 \div 0.6$ becomes $4.8 \div 6 = 0.8$. Multiplying just one number changes the problem. Check: dividing by a number less than 1 gives an answer bigger than the dividend, and $8 \times 0.6 = 4.8$ confirms 8.