Decimal as Fraction

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





4th Grade Math Activities

From Decimal as Fraction to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Relation between Diameter Radius and Circumference |Problems |Examples

    Apr 22, 24 05:19 PM

    Relation between Radius and Diameter of a Circle
    Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice

    Read More

  2. Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

    Apr 22, 24 01:35 PM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  3. Preschool Math Activities | Colorful Preschool Worksheets | Lesson

    Apr 21, 24 10:57 AM

    Preschool Math Activities
    Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging

    Read More

  4. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Apr 20, 24 05:39 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  5. What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

    Apr 20, 24 05:29 PM

    Examples of Parallel Lines
    In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

    Read More