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

Solution:

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

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 digit/digits 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

Thus, (a) 0.45 = 9/20, (b)1.3 (bar on 3) = 1⅓, (c) 2.45 (bar on 45) = 27/11 = 2(5/11) and (d) 3.33 = 333/100 = 3(33/100).

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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

Summary:

Each decimal as a fraction or mixed number in the simplest form: (a) 0.45 = 9/20, (b)1.3 (bar on 3) = 1 1/3 (c) 2.45 (bar on 45) = 27/11 = 2(5/11) and (d) 3.33 = 333/100 = 3(33/100).