Dividing by Decimals

Dividing by a decimal might look tricky, but there is a simple trick to make it easy: change the divisor into a whole number!

The Golden Rule

When you have a problem like $6.4 \div 0.8$, the divisor (the number you are dividing by) is $0.8$. To make $0.8$ a whole number, you can multiply it by $10$, which moves the decimal point one place to the right.

But remember, whatever you do to the divisor, you must also do to the dividend (the number being divided). Multiply them both by the same power of ten (like $10$ or $100$) so the problem stays completely balanced.

Step-by-Step Examples

Let's look at how to solve a few different types of decimal division problems.

Example 1: $6.4 \div 0.8$

1. Look at the divisor: $0.8$. It has one decimal place.
2. Multiply both numbers by $10$ (move the decimal point one place to the right).
3. $0.8 \times 10 = 8$
4. $6.4 \times 10 = 64$
5. Now, divide normally: $64 \div 8 = 8$ So, $6.4 \div 0.8 = 8$.

Example 2: $12 \div 0.25$

1. The divisor is $0.25$. It has two decimal places.
2. Multiply both numbers by $100$ (move the decimal point two places to the right).
3. $0.25 \times 100 = 25$
4. $12 \times 100 = 1200$ (Since $12$ is a whole number, just add two zeros).
5. Divide normally: $1200 \div 25 = 48$ So, $12 \div 0.25 = 48$.

Example 3: $3.78 \div 0.6$

1. The divisor is $0.6$. It has one decimal place.
2. Multiply both numbers by $10$ to make the divisor a whole number.
3. $0.6 \times 10 = 6$
4. $3.78 \times 10 = 37.8$ (It is perfectly fine if the dividend is still a decimal!)
5. Divide normally: $37.8 \div 6 = 6.3$ So, $3.78 \div 0.6 = 6.3$.

Important Tips

• Always focus on the divisor. You only need to move the decimal enough times to make the divisor a whole number.
• If you run out of digits in the dividend when moving the decimal point, just add zeros to the end.