# 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.