### 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:**

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