Decimal as Fraction

We will discuss how to express decimal as fraction.

Let us consider some of the following examples on expressing a decimal as a fraction.

1. Convert 2.12 into a fraction.

Solution:

2.12 = 2 + 1 tenth + 2 hundredths

       = 2 + \(\frac{1}{10}\) + \(\frac{2}{100}\)

       = 2 + \(\frac{1 × 10}{10 × 10}\) + \(\frac{2}{100}\)

       = 2 + \(\frac{10}{100}\) + \(\frac{2}{100}\)

       = 2 + \(\frac{10 + 2}{100}\)

       = 2 + \(\frac{12}{100}\)

       = 2 + \(\frac{3}{25}\)

       = 2\(\frac{3}{25}\)




We write the place value of digits of decimal and then add as usual.


2. Convert 5.125 into a fraction.

Solution:

5.125 = 5 + 1 tenth + 2 hundredths + 5 thousandths

        = 5 + \(\frac{1}{10}\) + \(\frac{2}{100}\) + \(\frac{5}{1000}\)

        = 5 + \(\frac{1 × 100}{10 × 100}\) + \(\frac{2 × 10}{100 × 10}\) + \(\frac{5}{1000}\)

        = 5 + \(\frac{1 × 100}{10 × 100}\) + \(\frac{2 × 10}{100 × 10}\) + \(\frac{5}{1000}\)

        = 5 + \(\frac{100}{1000}\) + \(\frac{20}{1000}\) + \(\frac{5}{1000}\)

        = 5 + \(\frac{100 + 20 + 5}{1000}\)

        = 5 + \(\frac{125}{1000}\)

        = 5 + \(\frac{1}{8}\)

        = 5\(\frac{1}{8}\)






We write the place value of digits of decimal and then add as usual.

Note: We always reduce the fraction converted from a decimal to its lowest form.





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