Dividing Decimals

What You’ll Learn

In this lesson you’ll learn how to divide decimals by converting the divisor to a whole number, then using long division to find the answer.

The Concept

Dividing decimals uses one key trick: move the decimal point in the divisor to make it a whole number, then move the decimal in the dividend the same number of places.

Example: $6.5 \div 0.5$

1. Move decimal 1 place right in both: $65 \div 5$
2. Divide:

$$\begin{array}{r} 13 \\ 5\overline{)65} \\ \underline{-5}\phantom{5} \\ 15 \\ \underline{-15} \\ 0 \end{array}$$

Result: $13$

Another: $4.56 \div 0.12$

1. Move decimal 2 places right in both: $456 \div 12$
2. Divide:

$$\begin{array}{r} 38 \\ 12\overline{)456} \\ \underline{-36}\phantom{6} \\ 96 \\ \underline{-96} \\ 0 \end{array}$$

Result: $38$

When dividing a decimal by a whole number, just divide normally and bring the decimal straight up into the quotient.

Example: $9.36 \div 4$

$$\begin{array}{r} 2.34 \\ 4\overline{)9.36} \\ \underline{-8}\phantom{.36} \\ 1\phantom{.}3\phantom{6} \\ \underline{-12}\phantom{6} \\ 16 \\ \underline{-16} \\ 0 \end{array}$$

Result: $2.34$

Worked Examples

Divide $7.2 \div 0.6$

1. Move decimal 1 place right in both: $72 \div 6$
2. Long division:

$$\begin{array}{r} 12 \\ 6\overline{)72} \\ \underline{-6}\phantom{2} \\ 12 \\ \underline{-12} \\ 0 \end{array}$$

Result: $12$

Divide $15.75 \div 2.5$

1. Move decimal 1 place right in both: $157.5 \div 25$
2. Long division:

$$\begin{array}{r} 6.3 \\ 25\overline{)157.5} \\ \underline{-150}\phantom{.5} \\ 7\phantom{.}5 \\ \underline{-75} \\ 0 \end{array}$$

Result: $6.3$

Divide $0.648 \div 0.08$

1. Move decimal 2 places right in both: $64.8 \div 8$
2. Long division:

$$\begin{array}{r} 8.1 \\ 8\overline{)64.8} \\ \underline{-64}\phantom{.8} \\ 0\phantom{.}8 \\ \underline{-8} \\ 0 \end{array}$$

Result: $8.1$

Real-World Applications

Dividing decimals helps split costs (a 47.50 dollar dinner split 5 ways = 9.50 dollars each), calculate unit prices (3.78 dollars for 1.5 pounds = 2.52 dollars per pound), or figure out mileage (325.5 miles on 12.5 gallons = 26.04 miles per gallon). Any time you need a rate or per-unit cost, you’re dividing decimals.

You’ve Got This

The trick is making the divisor a whole number first. Shift both decimals the same way and it’s just regular long division from there. Practice with prices and measurements, and always estimate first to check your answer makes sense.

Quiz

What is 8.4 ÷ 0.7?

• A.12
• B.1.2
• C.0.12
• D.7.7

Divide 15.6 ÷ 1.2.

• A.13
• B.12
• C.1.3
• D.14

A 22.50 dollar bill is split equally among 5 people. How much each?

• A.4.50 dollars
• B.4.25 dollars
• C.5.50 dollars
• D.4.00 dollars

What is 0.96 ÷ 0.04?

• A.24
• B.2.4
• C.0.24
• D.240

Gas costs 3.60 dollars per gallon. You spend 27.00 dollars. How many gallons?

• A.7.5 gallons
• B.7 gallons
• C.8 gallons
• D.6.5 gallons