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Decimal as Fraction | Convert From a Decimal to a Fraction |Changing


We’ll talk about find out how to specific 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 transform a decimal right into a fraction, bear in mind the next
steps.

Step I: Write the quantity because the numerator omitting the decimal
level.

Step II: Write 1 within the denominator and add zeroes to it equal to the
variety of decimal locations.

Notice: When a decimal is learn, every digit of the decimal half
is learn individually.

Allow us to think about a few of the following examples on expressing a decimal as a fraction.

1. Convert 2.12 right into a fraction.

Resolution:

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 worth of digits of decimal after which add as standard.


2. Convert 5.125 right into a fraction.

Resolution:

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 worth of digits of decimal after which add as standard.

Specific the next decimals in expanded type:

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})

Specific the next 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 next decimals to fractions of their lowest
phrases.

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})]

Notice: We at all times cut back the fraction transformed from a decimal
to its lowest type.

Questions and Solutions on Conversion of a Decimals to a Fractions:

I. Convert the next decimals as fractions or combined 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. Specific the next within the expanded type.

(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 Actions

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