Dividing Decimals – Meaning With Examples

Consider a situation where you buy 24 cans of water bottles at $\$$3.99. How would you find the price of one can? By dividing $\$$3.99 by 24! Dividing decimals is very much like dividing whole numbers. You just have to understand where the decimal point must be placed. Let’s explore the process of dividing decimals in more detail. But before that, let’s understand what decimals are.

What Is a Decimal Number?

A decimal number is a number that has a whole number part and the fractional part separated by a dot. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one.

In the decimal number 17.48, 17 is the whole number part and 48 is known as the decimal part or fractional part.

How to Divide Decimals?

Dividing Decimal numbers is similar to dividing whole numbers. We just have to take care of the correct position of the decimal point. Let’s discuss three different examples related to division of decimals.

Dividing Decimals Examples 

Take a look at the following examples.

Example 1: Dividing $\$$25.5 dollars among 5 friends.

Examples 2: Dividing the decimal 1.21 by the decimal number 1.1 

Example 3: Dividing the decimal number 23.56 by 1000.

So, we can see that there can be three types:

• Dividing decimals by whole numbers.
• Division of a decimal number by another decimal number.
• Division of decimals by 10, 100, and 1000. 

Dividing Decimals by Whole Numbers 

Let’s understand dividing decimals by whole numbers through an example. 

Consider 120.6 24. 

The following are the steps to divide 120.6 by 24:

The dividend is the number that is getting divided and the divisor is the number that divides the dividend. Here, 120.6 is the dividend and 24 is the divisor. 

So, $120.6 24 = 5.025$

Dividing a Decimal Number by Another Decimal Number 

Let’s understand dividing decimals by another decimal number using an example. Let’s divide 4.88 by 0.4. Here, 4.88 is the dividend and 0.4 is the divisor. 

The following are the steps he will use for the division: 

• Step 1: Since we already know how to divide a decimal number by a whole number, convert the divisor into a whole number. In this example, we convert 0.4 into 4 by moving the decimal point one position to the right. In this example, 0.4 will become 4. 

• Step 2: Move the decimal point in the dividend the same number of places as in the divisor. Moving the decimal point one position to the right in 4.88 gives 48.8.

• Step 3: Now divide the decimal number 48.8 by the whole number 4. This is equivalent to dividing the decimal 4.88 by 0.4.

Dividing Decimals by 10, 100, and 1000 

The division of a decimal number by 10, 100, and 1000 is quite simple. Let’s discuss each type. 

Division by 10 

Consider $82.5 \div 10$.

Dividing a decimal by 10 simply changes the position of the decimal point one place to the left.

$8251010=82510110=825100=8.25$

Division by 100 

Consider $98.6 \div 100$.

Dividing the decimal number by 100 shifts the decimal point two positions to the left. 

Also, $98610100=986101100=9861000=0.986$

Division by 1000 

Consider $8.725 \div 1000$.

Now since the decimal number is divided by 1000, the decimal point will shift three places towards the left in the quotient. 

Also, $872510001000=8725100011000=87251000000=0.008725$

Fun Facts

While dividing a decimal number by a whole number or by another decimal number,  there are cases when we end up with a remainder of 0. Such decimal numbers are called Terminating Decimals.

For example: $62.35 \div 5 = 12.47$

However, there can also be a case when the remainder never becomes 0 and the long division process goes on. Such decimal numbers are called Non-terminating Decimals.

Non-terminating decimals can be of two types:

a. Recurring/Repeating decimals like 0.2666666666 . . .

b. Non-recurring/Non-repeating decimals like 1.7320508 . . .

Solved Examples

1. Divide 67.25 by 10. 

Solution: On dividing 67.25 by 10, we shift the decimal point one position to the left. 

We get 

$67.25 \div 10 = 6.725$.

2. If the total weight of 3 oatmeal cookies is 31.5 grams, then what will be the total weight of 5 oatmeal cookies?

Solution: Total weight of 3 oatmeal cookies $= 31.5$ g

Weight of 1 oatmeal cookie $= 31.5 \div 3 = 10.5$ g

Total weight of 5 oatmeal cookies $= 10.5 \times 5 = 52.5$ g

3. A wooden plank of length 3.5 feet is divided into small pieces of length 0.07 foot. How many small pieces will be formed?

Solution: Length of wooden plank $= 3.5$ feet

Length of each small piece $= 0.07$ feet

Since we are dividing the plank into small pieces of equal length, we divide 3.5 by 0.07.

Shift the decimal point two positions to the right in both 0.07 and 3.5 to perform the division.

Number of small pieces $= 3.5 \div 0.07$ 

      $= 350 \div 7$ 

      $= 50$ 

4. George has $24.5 of his monthly allowance left with him. He spends it over the course of a week such that his daily expenses stay the same. How much money does he spend every day?

Solution: Money George has with him $= $\$$24.5$

This amount is equally spent in a week or 7 days.

Amount spent by George every day $= 24.5 \div 7 = $\$$3.5$

5. Amanda made two trips to visit her parents. She drove 432.78 miles in total. How far did Amanda drive on each trip?

Solution: Total distance Amanda drove $= 432.78$ miles

Number of trips she took $= 2$

Distance traveled on each trip $= 432.78 \div 2 = 216.39$ miles

Practice Problems

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