We will discuss how to express decimal as fraction.

0.5 = \(\frac{5}{10}\)

0.05 = \(\frac{5}{100}\)

0.005 = \(\frac{5}{1000}\)

2.5 = \(\frac{25}{10}\)

2.25 = \(\frac{225}{100}\)

2.275 = \(\frac{2275}{1000}\)

**To convert a decimal into a fraction, remember the following
steps.**

**Step I:** Write the number as the numerator omitting the decimal
point.

**Step II:** Write 1 in the denominator and add zeroes to it equal to the
number of decimal places.

**Note:** When a decimal is read, each digit of the decimal part
is read separately.

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. |

**Express the following decimals in expanded form:**

3.62 = 3 × 1 + \(\frac{6}{10}\) + \(\frac{2}{10}\)

75.86 = 7 × 10 + 5 × 1 + \(\frac{8}{10}\) + \(\frac{6}{10}\)

216.894 = 2 × 100 + 1 × 10 + 6 × 1 + \(\frac{8}{10}\) + \(\frac{9}{100}\) + \(\frac{4}{1000}\)

0.562 = \(\frac{5}{10}\) + \(\frac{6}{100}\) + \(\frac{2}{1000}\)

**Express the following as decimal numbers:**

**For examples:**

\(\frac{6}{10}\) + \(\frac{3}{100}\) = 0.63

\(\frac{6}{10}\) + \(\frac{3}{100}\) + \(\frac{5}{1000}\) = 0.635

4 × 1 + \(\frac{3}{10}\) + \(\frac{2}{100}\) = 4.32

7 × 10 + 2 × 1 + \(\frac{8}{10}\) + \(\frac{9}{100}\) = 72.89

**Convert the following decimals to fractions in their lowest
terms.**

**For examples:**

0.36 = \(\frac{36}{100}\) = \(\frac{9}{25}\) [\(\frac{36 ÷ 4}{100 ÷ 4}\) = \(\frac{9}{25}\)]

5.65 = 5 + 0.65 = 5 + \(\frac{65}{100}\) = 5\(\frac{65}{100}\) = 5\(\frac{13}{20}\)]

14.05 = 14 + 0.05 = 14 + \(\frac{5}{100}\) = 14\(\frac{5}{100}\) = 14\(\frac{1}{20}\)]

3.004 = 3 + 0.004 = 3 + \(\frac{4}{1000}\) = 3\(\frac{4}{1000}\) = 3\(\frac{1}{250}\)]

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

**Questions and Answers on Conversion of a Decimals to a Fractions:**

**I. Convert the following decimals as fractions or mixed numerals:**

(i) 0.6

(ii) 0.09

(iii) 3.65

(iv) 12.132

(v) 16.5

(vi) 5.46

(vii) 12.29

(viii) 0.008

(ix) 8.08

(x) 162.434

**II. Express the following in the expanded form.**

(i) 46.25

(ii) 115.32

(iii) 14.568

(iv) 19.005

(v) 77.777

**III. Write as decimals:**

(i) 2 × 1 + \(\frac{7}{10}\) + \(\frac{4}{100}\)

(ii) 3 × 10 + 5 × 1 + \(\frac{8}{10}\) + \(\frac{3}{1000}\)

(iii) 7 × 100 + 4 × 10 + 5 × 1 + \(\frac{4}{1000}\)

(iv) 9 × 100 + \(\frac{7}{10}\)

(v) \(\frac{5}{100}\) + \(\frac{8}{1000}\)

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