Example 1 · Two decimal places in the divisor
19.72 ÷ 0.85
- Multiply both numbers by 100: 1,972 ÷ 85.
- 85 × 23 = 1,955. Subtract: 1,972 − 1,955 = 17.
- Add a decimal point and a zero: 170 ÷ 85 = 2.
Answer: 23.2. Check: 23.2 × 0.85 = 19.72.
Mathematics · Decimals · Topic 10 · 3 of 5
Dividing Decimals by Decimals
Use equivalent division, add zeros, and round quotients when needed.
Keep the quotient the same
Multiplying both the dividend and divisor by the same nonzero number does not change the quotient. Use 10, 100, or 1,000 to make the divisor a whole number.
Example 2 · Add a zero when needed
0.774 ÷ 0.36 = 77.4 ÷ 36.
- 36 × 2 = 72; subtract from 77 to get 5.
- Bring down 4: 54 ÷ 36 gives 1 tenth, remainder 18.
- Write 77.40 and bring down 0: 180 ÷ 36 gives 5 hundredths.
Answer: 2.15. Check: 2.15 × 0.36 = 0.774.
Example 3 · Round to hundredths
6.292 ÷ 2.08 = 629.2 ÷ 208 = 3.025…
The hundredths digit is 2 and the next digit is 5, so round up: 3.03.
Use ≈ for an approximation: 6.292 ÷ 2.08 ≈ 3.03.
Common mistake: Moving only the divisor’s decimal point changes the problem. Always multiply BOTH numbers by the same power of 10.