Lesson 49: Dividing by a Decimal Number

New Concept

When the divisor of a division problem is a decimal number, we change the problem so that the divisor is a whole number. This is done by forming an equivalent division problem.

What’s next

This card introduces the core strategy. Next, you'll master this method through worked examples and tackle challenge problems involving decimal division.

Property

When the divisor of a division problem is a decimal number, we change the problem so that the divisor is a whole number. We do this by multiplying the divisor and the dividend by the same power of 10, creating an equivalent problem:

Examples

$1.44 \div 0.6$ is equivalent to $14.4 \div 6 = 2.4$.
$0.24 \div 0.4$ is equivalent to $2.4 \div 4 = 0.6$.
$9 \div 0.3$ is equivalent to $90 \div 3 = 30$.

Explanation

Tired of dividing by tricky decimals? Just give them a shove! We multiply both the number being divided (dividend) and the number we are dividing by (divisor) by 10, 100, or more, until the divisor is a happy whole number. This clever trick makes the problem much easier to solve without changing the final answer.

Property

To multiply a decimal number by 10, we shift the decimal point one place to the right. To multiply by 100, we shift the decimal point two places to the right.

Examples

To multiply $3.75$ by $10$, shift the decimal one place right: $3.75 \rightarrow 37.5$.
To multiply $0.543$ by $100$, shift the decimal two places right: $0.543 \rightarrow 54.3$.
To multiply $1.2$ by $1000$, shift the decimal three places right: $1.2 \rightarrow 1200$.

Explanation

Want to multiply a decimal by 10, 100, or 1000 in a flash? It is like a magic trick! Just count the zeros in the number you are multiplying by (like 100 has two zeros), and shift the decimal point that many places to the right. Abracadabra, you have got your answer in an instant!

Property

We can use division to model real-world situations, like finding out how many smaller units fit into a larger amount. For example, to find the number of quarters in three dollars, we can set up the division problem: $3.00 \div 0.25$.

Examples

To find quarters in 3 dollars, solve $3.00 \div 0.25$. This becomes $300 \div 25 = 12$.
To find nickels in 3.25 dollars, solve $3.25 \div 0.05$. This becomes $325 \div 5 = 65$.
A pencil costs 0.50 dollars. With 4 dollars, you can buy $4.00 \div 0.50$, or $400 \div 50 = 8$ pencils.

Explanation

Math is not just numbers on a page; it helps solve real-life puzzles! You can use decimal division to figure out practical things, like how many quarters are in a pile of money or how many items you can buy. Just turn the word problem into a division problem, make the divisor a whole number, and solve!