One decimal place
7.2 ÷ 0.3 = 72 ÷ 3 = 24
Before this page: know how to multiply by powers of ten, then divide with short division or long division.
An equivalent division
A decimal divisor can look awkward, but we can change the calculation without changing its answer. For 55.2 ÷ 0.46, multiply both numbers by 100. The divisor becomes 46 and the dividend becomes 5,520.
The quotient counts how many divisor-sized groups make the dividend. Multiplying both by the same scale factor, 100, makes every group 100 times larger and the total 100 times larger, so the number of groups does not change.
In 55.2 ÷ 0.46, 120 groups of 0.46 make 55.2. After both numbers are multiplied by 100, the same 120 groups of 46 make 5,520.
55.2 ÷ 0.46
The divisor 0.46 has two decimal places
One multiplication by 10 is not enough to make 0.46 an integer.
Making the divisor a whole number
Count the divisor's decimal places, ignoring trailing zeros, and multiply both numbers by 10 once for each place: one place needs ×10, two need ×100. The divisor is then an integer, and the equivalent division is ready for short or long division.
Two decimal places
1.8 ÷ 0.04 = 180 ÷ 4 = 45
The dividend may stay decimal
8.75 ÷ 2.5 = 87.5 ÷ 25 = 3.5
Ignore a trailing zero
6.4 ÷ 0.20 = 64 ÷ 2 = 32
0.20 is 0.2, so one multiplication by 10 is enough.Dividing by a number below one
55.2 metres cut into 0.46 metre lengths
Each length is under half a metre, so more than two fit into each metre, and exactly 120 fit into 55.2 m.
For positive numbers, dividing by a positive number below 1 makes the quotient larger than the dividend: 55.2 ÷ 0.46 = 120. Multiplying by a positive number below 1 has the opposite effect, explained on numbers below one.
Explore equivalent divisions
Multiply both by 100
12.6 ÷ 0.35 = 36
0.35 has two decimal places, so both numbers are multiplied by 100.
Key points
- Multiply both dividend and divisor by the same power of ten. The quotient stays the same.
- Choose a scale that makes the divisor an integer, then divide as usual.
- Dividing a positive number by a positive number below one makes the quotient larger than the dividend.