# Write each decimal as a fraction or mixed number in the simplest form:

## (a) 0.45 (b)1.3 (bar on 3) (c) 2.45 (bar on 45) (d) 3.33

The decimal to fraction conversion is one of the most frequently carried out steps in arithmetic.

## Answer: (a) 0.45 = 9/20

## (b)1.3 (bar on 3) = 1⅓

## (c) 2.45 (bar on 45) = 27/11 = 2(5/11)

## (d) 3.33 = 333/100 = 3(33/100)

Let's learn about each case in detail.

**Explanation:**

To convert a terminating decimal to a fraction, we follow three basic steps mentioned below:

- Rewrite the number by ignoring the decimal point.
- Divide the number by the place value of the last digit in the fractional part of the number.
- Simplify the fraction.

Now,

- 0.45 = 45/100 = 9/20
- 3.33 = 333/100 = 3(33/100)

To convert a non-terminating but repeating decimal into a fraction we follow a slightly different process:

- 1.333333..... = 1.3(bar on 3)

let x = 1.33333....

⇒ 10x = 13.333333....

10x - x = (13.33333....) - (1.33333...)

9x = 12

x = 12/9 = 4/3 = 1 + (1/3)

Therefore, 1.333333..... = 1.3(bar on 3) = 4/3 = 1⅓

- 0.2454545... is a non-terminating but repeating decimal, it is denoted by \(0.2\bar{45}\).

let x = 0.2454545...

100x = 245.454545...

100x - x = (245.454545...) - (2.454545...)

99x = 243

x = 243/99 = 27/11

Therefore, 0.2454545... = 0.245 (bar on 45)... can be expressed in the rational form as 243/99