Dividing Decimals by Decimals
Every question with a fully worked solution.
- Dividing Decimals by Decimals - Video - How to Divide a Decimal by a Decimal Watch
Theory
Dividing by a decimal asks how many of that decimal fit into the number. To work it out, multiply both numbers by the same power of 10 so that you divide by a whole number. This Year 7 maths page shows why this keeps the answer the same, how to choose the power of \(10\), and why dividing by a number less than \(1\) gives a bigger answer.
\(0.9 \div 0.3\) asks how many groups of \(0.3\) are in \(0.9\). There are \(3\).
The divisor is the number you divide by. We cannot easily divide by a decimal, so make the divisor a whole number by multiplying it by \(10\), \(100\) or \(1000\), that is, moving its point to the right.
Move the point in the other number the same number of places. Both numbers change in the same way, so the answer stays the same: \(1.44 \div 0.3 = 14.4 \div 3 = 4.8\).
Dividing a positive number by a number between \(0\) and \(1\) gives a bigger answer. The smaller the divisor, the bigger the answer.
Multiply both numbers by the same power of 10:
| Division | Answer | Compared with 8 |
|---|---|---|
| \(8 \div 2\) | \(4\) | smaller |
| \(8 \div 1\) | \(8\) | the same |
| \(8 \div 0.5\) | \(16\) | bigger |
| \(8 \div 0.1\) | \(80\) | bigger |
How to divide by a decimal
- Count the decimal places in the divisor.
- Multiply both numbers by \(10\), \(100\) or \(1000\) so the divisor is a whole number.
- Divide by short division, point above point.
- Check by multiplying the answer by the original divisor.
| \(1.6 \div 0.4\) | \(=\) | \(16 \div 4\) |
| \(\) | \(=\) | \(4\) |
\(0, 0.4, 0.8, 1.2, 1.6\): there are \(4\) jumps. Check: \(4 \times 0.4 = 1.6\).
| \(0.8 \div 0.002\) | \(=\) | \(800 \div 2\) |
| \(\) | \(=\) | \(400\) |
Both numbers \(\times 1000\). Check: \(400 \times 0.002 = 0.8\).
(i) \(1.45 \div 0.5\)
(ii) \(7.25 \div 0.5\)
| \(1.45 \div 0.5\) | \(=\) | \(14.5 \div 5 = 2.9\) |
| \(7.25 \div 0.5\) | \(=\) | \(72.5 \div 5 = 14.5\) |
(i) \(2.9\)
(ii) \(14.5\)
| \(0.042 \div 0.07\) | \(=\) | \(4.2 \div 7\) |
| \(\) | \(=\) | \(0.6\) |
Both \(\times 100\). Check: \(0.6 \times 0.07 = 0.042\).
| \(9.90 \div 0.45\) | \(=\) | \(990 \div 45\) |
| \(\) | \(=\) | \(22\) |
\(45 \times 20 = 900\) and \(45 \times 2 = 90\), so \(990 \div 45 = 22\). Mei can buy \(22\) apples.
| \(0.84 \div 0.004\) | \(=\) | \(840 \div 4\) |
| \(\) | \(=\) | \(210\) |
\(210\) beads. Check: \(210 \times 0.004 = 0.840\).
Common pitfalls
Frequently asked questions
How do you divide by a decimal?
Multiply both numbers by the same power of \(10\) so the divisor is a whole number, then divide. \(1.45 \div 0.5 = 14.5 \div 5 = 2.9\).
Why does multiplying both numbers keep the answer the same?
Both change in the same way. \(1.6 \div 0.4\) and \(16 \div 4\) both ask how many groups fit, and both give \(4\).
Can dividing make a number bigger?
Yes. Dividing by a number between \(0\) and \(1\) gives a bigger answer: \(8 \div 0.5 = 16\).
How do you know what to multiply by?
Count the decimal places in the divisor. \(0.004\) has \(3\), so multiply both by \(1000\).
How do you check?
Multiply the answer by the original divisor. \(2.9 \times 0.5 = 1.45\).