How to Round Off Decimals

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In mathematics, a decimal can be defined as a number which has two parts: a whole part and a fractional part, and these two parts are separated by a decimal point. The whole part always represents a number greater than one, while the fractional part, i.e., the part after the decimal, always represents a number less than one.

For example, let’s take the number \( 13.74 \). Now here the whole part is represented by \( 13 \), whereas the fractional part \( (\frac{74}{100} \ ) \) is represented by \(74\). Here \( 74 \) can also be denoted as the decimal part, as it lies after the decimal point.

The Concept of Preceding Powers of 10

Now, there’s a very interesting concept linked to decimal numbers. This concept is known as the preceding powers of \( 10 \). All decimal numbers are based on this concept. So, as we move from left to right in a decimal number, basically, the place value of every digit gets divided by \( 10 \). So, the first digit after a decimal could be represented as\(\frac{1}{10}\) , second as \(\frac{1}{100}\) and so on.
So, from this concept, we can easily find out the expanded form of a decimal.

For example, let’s take the decimal number \(12.457.\) The expanded form could be written as: \(10+2+ \frac{4}{10}+\frac{5}{100}+\frac{7}{1000}\)
Also, \(12.457\) can be represented as \(12\frac{457}{1000}\) in mixed fraction terms.

What is Rounding Off?

Rounding off is a process to estimate a number into its nearest accurate/approximate for. For example, \(12.395\) rounded to the nearest whole number would be \(12\), and \(12.678\) rounded to the nearest whole number would be \(13\).

How to Round Off Decimals

To round off a decimal, use the following steps:

Take note of your place value. This is the number which is considered while rounding off.
Now, look at the digit next to the place value. If this digit is greater than \(5\), add 1 to the place value and remove all succeeding digits. If less than 5 then no change and remove all succeeding digits.

For example, \(2.67\) becomes \(2.7\),\( 2.34\) becomes \(2.3\) and so on.

Free printable Worksheets

Exercises for Rounding Decimals

1) \(3\underline{4}.697 \ \Rightarrow \ \)

2) \(1\underline{4}.584 \ \Rightarrow \ \)

3) \(11.\underline{4}05 \ \Rightarrow \ \)

4) \(18.\underline{1}52 \ \Rightarrow \ \)

5) \(41.496 \ \Rightarrow \ \)

6) \(19.209 \ \Rightarrow \ \)

7) \(12.332 \ \Rightarrow \ \)

8) \(\underline{2}.971 \ \Rightarrow \ \)

9) \(50.\underline{9}22 \ \Rightarrow \ \)

10) \(57.\underline{1}25 \ \Rightarrow \ \)

Answers

1) \(3\underline{4}.697 \ \Rightarrow \ \color{red}{35} \ \)

First, look at the next place value to the right of the ones place. It’s \(6\) and it is greater than \(5\) , thus add \(1\) to the digit in the ones place.

2) \(1\underline{4}.584 \ \Rightarrow \ \color{red}{15} \ \)

First, look at the next place value to the right of the tenth place. It’s \(8\) and it is greater than \(5\) , thus add \(1\) to the digit in the tenth place.

3) \(11.\underline{4}05 \ \Rightarrow \ \color{red}{11.4} \ \)

First, look at the next place value to the right of the hundredth place. It’s \(0\) and it is less than \(5\) thus removing all the digits to the right. Then, the answer is \(11.4\).

4) \(18.\underline{1}52 \ \Rightarrow \ \color{red}{18.2} \ \)

5) \(41.496 \ \Rightarrow \ \color{red}{41} \ \)

6) \(19.209 \ \Rightarrow \ \color{red}{19} \ \)

7) \(12.332 \ \Rightarrow \ \color{red}{12} \ \)

8) \(\underline{2}.971 \ \Rightarrow \ \color{red}{3} \ \)

9) \(50.\underline{9}22 \ \Rightarrow \ \color{red}{50.9} \ \)

10) \(57.\underline{1}25 \ \Rightarrow \ \color{red}{57.1} \ \)

How to Round Off Decimals