In this ParaPro study guide, you will learn about decimal numbers. Also, we will learn how to perform various operations like – addition, subtraction, multiplication, and division on decimal numbers. As an application, we will see the steps to convert fractions to decimals using division. At last, we have a 5-question quiz to test our understanding.
Decimal Numbers
Decimal numbers contain a whole part and a decimal part with a decimal point separating them.
For example, 28.20 contains 28 as the whole part and 20 as the decimal part with a decimal point (.) between them.
Adding/Subtracting Decimal Numbers
To add or subtract two decimal numbers, first align their decimal points. Then, write zeros before the whole part and after the decimal part if needed. Finally, add or subtract the numbers. We will see this with the help of two examples.
Example 1
Add 3.9 to 11.26.
First align the decimal points, as shown below.
Write zeros before the whole part and after the decimal part to match the place values of both the numbers.
(Note: Writing these additional zeros does not change the original number)
Add normally (as if there was no decimal point),
Thus, the sum of 3.9 with 11.26 is equal to 15.16.
Example 2
Subtract 3.99 from 12.02.
Using the first two steps we can write,
Now, subtract normally (as if there was no decimal point)
Thus, on subtracting 3.99 from 12.02, we get, 8.03.
Multiplying Decimal Numbers
To multiply two decimal numbers, multiply the numbers assuming there are no decimal points, and then insert the decimal point such that the number of decimal places in the answer is the same as the two numbers combined.
However, when we multiply 10, 100, 1000, etc., to decimal numbers, we shift the decimal point as many times to the right as there are 0’s in 10, 100, 1000, etc.
Let us understand this with the help of two examples.
Example 3
Multiply 0.34 by 100.
100 has two 0’s.
So, when we multiply it with 0.34, we need to shift the decimal point two places to the right.
Thus, 0.34 × 100 = 34
Example 4
Multiply 1.24 by 6.
Write the numbers without the decimal point.
So, first we multiply 124 by 6.
124 × 6 = 744
Since, 1.24 and 6 have 2 decimal places in all, the final answer must also have 2 decimal places.
→ 1.24 × 6 = 7.44
Dividing Decimal Numbers
To divide a decimal number by 10, 100, 1000, etc., we shift the decimal point as many times to the left as there are 0’s in 10, 100, 1000, etc.
To divide a decimal number by another, we multiply both numbers by 10 as many times as there are decimal places in the number we are dividing by. Then, we follow the rules of long division to work out the result. Let us understand this with the help of two examples.
Example 5
Divide 7620 by 1000.
1000 has three 0’s.
So, when we divide 7620 by 1000, we need to shift the decimal point three places to the left.
(In a whole number the decimal point is always to the right of the whole part, in this case it would be of the form 7620.0)
7620 ÷ 1000 = 7.620 or simply 7.62.
Example 6
Divide 0.85 by 0.2.
First, note the number of decimal places in the number by which we need to divide by, that is 0.2.
Since, 0.2 has only one decimal place we multiply by 10 to both 0.85 and 0.2
Now we divide 8.5 by 2 using the long division method as shown below.
(Note: We stop the division process when we get 0 as our remainder, or after 2 decimal places usually.)
→ 0.85 ÷ 0.2 = 4.25
Converting Fractions to Decimals
To convert fractions to decimals, convert the original fraction to have 10, 100, or 1000 in the denominator and then divide. If we cannot perform this conversion, then divide the numerator by the denominator and write the answer to 2 decimal places (or as many as needed).
Let us see an example.
Example 7
Convert the below list of fractions to decimals.
$\dfrac{3}{10}, \dfrac{38}{50}, \dfrac{4}{3}$
For $\dfrac{3}{10}$ :
When we divide $3$ by $10$, we get, $0.3$. So, $\dfrac{3}{10}$ = $0.3$
For $\dfrac{38}{50}$ :
First multiply both numerator and denominator by $2$ to get, $\dfrac{76}{100}$.
When we divide $76$ by $100$, we get, $0.76$. So, $\dfrac{3}{10}$ = $0.76$
For $\dfrac{4}{3}$ :
Divide $4$ by $3$ using the long division method to get, $1.33$.
$\dfrac{4}{3}$ = $1.33$
Now that we are familiar with the operations of addition, subtraction, multiplication, and division on decimals, we can take the below 5-question quiz to test our understanding of the content.