Converting Decimal to Fraction

Rational numbers - these are numbers that can be written in a fraction form \( \frac{a}{b}\), where b ≠ 0.

Finite decimals (eg. 1.23, 1.2569, 0.245, ...) are rational numbers and can be written in fraction form. Infinite repeating or recurring decimals(eg. 1.33333... , 0.66666...) are rational numbers but infinite and non-recurring decimals are irrational numbers..

Convert Finite Decimals to Fraction

1. Separate the whole part and the decimal part.
2. Divide the decimal part by 100xx. The number of zeroes depends on the number of digits on the decimal part.
3. Add the whole part to the fraction (2).
Examples:
• 1. Convert 1.25 into fraction
• 1 is the whole part and 0.25 the decimal part.
• Since there are 2 digits(25) on the decimal part add 2 zeroes to 1, then \( \frac{25}{100}\).
• 1.25 = \( 1 + \frac{25}{100}\)
• 1.25 = \( 1 + \frac{1}{4}\) = \(1 \frac{1}{4}\)
• 1.25 = \(\frac{5}{4}\)
• 2. Convert 3.645 into fraction

3.645 = 3 +\( \frac{645}{1000}\)

3.645 = 3 +\( \frac{129}{200}\)

3.645 = \( 3 \frac{129}{200}\)

3.645 = \( \frac{729}{200}\)

Convert Recurring Decimals to Fraction

1. Separate the whole part and the decimal part.
2. Divide the decimal part by 9xx. The number of 9's depends on the number of recurring digits on the decimal part.
3. Add the whole part to the fraction (2).
Examples:
• 1. Convert 1.3333... into fraction
• 1 is the whole part and 3 is the recurring decimal part.
• Since there is 1 recurring digit(3) on the decimal part use one 9's, then \( \frac{3}{9}\).
• 1.333... = \( 1 + \frac{3}{9}\)
• 1.333... = \( 1\frac{1}{3}\)
• 1.333... = \( \frac{4}{3}\)
• 2. Convert 0.52525252... into fraction

0.52525252... = 0 +\( \frac{52}{99}\)

3.645 = \( \frac{52}{99}\)

Convert Finite and Recurring Decimals to Fraction

1. Separate the whole part, the finite part and the reccuring decimal part.
2. Divide the finite part by 100xx, the number of zeroes depends on the number of digits on the finite decimal part. Divide the decimal part by 99yy00xx. The number of 9's(y's) depends on the number of recurring digits on the decimal part and the number of zeroes (x's) depends of the number of digits on the finite decimal part.
3. Add the whole part to the fraction (based on finite and recurring decimals).
Examples:
• 1. Convert 5.013333333... into fraction
• 5 is the whole part, 3 is the recurring decimal part and 0.01 is the finite part.
• There are 2 digits on the finte part then use \( \frac{01}{100}\) and there is 1 recurring digit(3) on the decimal part use one 9's then add two zeroes, thus \( \frac{3}{900}\).
• 5.013333333... = \( 5 + \frac{01}{100} + \frac{3}{900}\)
• 5.013333333... = \( 5 + \frac{1}{100} + \frac{1}{300}\)
• 5.013333333... = \( 5 \frac{1}{75}\)
• 5.013333333... = \( \frac{376}{75}\)
• 2. Convert 0.1353636363636... into fraction

0.1353636363636...= 0 +\( \frac{135}{1000} + \frac{36}{99000}\)

0.1353636363636...= 0 +\( \frac{27}{200} + \frac{1}{2750}\)

0.1353636363636...= \( \frac{1489}{11000}\)