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# Rounding Decimals – Definition, Types, & Examples

Sep 19, 2022

### Key Concepts

• Rounding decimals to the nearest whole number.
• Express fractions as a decimal.
• Express decimals as a fraction.
• Equivalent fractions.

## Rounding Decimals:

### Rounding decimals to the nearest whole number or tenth.

Rounding is a process to estimate a particular number in the context. We can round decimals to the nearest wholes, tenths, or hundredths.

Rules for rounding decimals to the nearest whole number:

• To round a decimal to the nearest whole number, analyze the digit at the first decimal place, i.e., tenths place.
• If the tenths place value is 5 or greater than 5, then the digit at the ones place is increased by 1, and the digit at the tenths place becomes zero.
• If the tenths place value is less than 5, then the digit at the ones place remains the same, but the digits at the tenths place become zero.

Example: Round off 24.77 to the nearest whole number.

Sol:

Example:

(a) Round off 51.7 to the nearest whole number.

Sol: 51.7

The digit at the tenths place is 7.

7 > 5

The whole number part of 51.7 is increased by one.

51.7 rounded off to the nearest whole number as 52.

(b) Round 11.04 to the nearest tenths

Sol: 11.04

The digit at hundredths place is 4, and:

4 < 5

11.04 rounded off to the nearest tenths is 11.

### Fractions and decimals

#### Express fraction as a decimal

To convert a fraction to a decimal, divide the numerator by the denominator.

Example: What is as a decimal.

Sol:  = 0.125

#### Express decimal as a fraction.

To convert a decimal to a fraction, place the decimal number over its place value.

Example:

Example: Express 0.9 as fraction

Sol:       0.9 =

### Equivalent fractions.

Equivalent fractions: Equivalent fractions can be defined as fractions that may have different numerators and denominators but represent the same value.

Example:  and  are equivalent because both are equal to

=

=

Therefore,  =

## Exercise:

1. Write 205.9 in the place value table.
2. Write seven-tenths as a decimal.
3. Write 3 + 7/10 as a decimal.
4. Write 2.5 as a fraction.
5. Write 4/5 as a decimal.
6. Write 2.34 in the lowest terms.
7. Write 50 + 1/10  + 6/10 in decimal form.
8. Compare 1.09 or 1.093. Which is greater?
9. Compare 1.23 or 1.2. Which is smaller?
10. Round 1.76 to the nearest whole number.
11. Round 1.42 to the nearest tenths.
12. Write the numbers from the smallest to the largest: 51.5, 59.0, 39.2, 84.4.
13. Write the numbers from the largest to the smallest: 60.9, 66.6, 96.2, 90.5.
14. Find the next two numbers in the pattern of 2.1, 2.4, 2.7, 3, 3.3, 3.6, 3.9.
15. Express 2/9  as a decimal.

### What have we learnt:

• Introduction of decimals.
• How the place value of a digit changes when we multiply or divide it by ten.
• How to read, write, and model fractions with 10 and 100 in the denominator.
• How to compare decimals from the least to the greatest and from the greatest to the least.
• Ordering of decimals.
• How to round decimals to the nearest whole numbers.
• How to express a fraction as a decimal and a decimal as a fraction.

### Concept Map

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