Fractions and decimals are equivalent representations of the part of a whole. A decimal number has ten as its base and a fraction tell us how many parts of a certain size can be. Decimals and fractions represent the same thing (A number that is exactly not a whole number).
To convert a decimal to a fraction consider the steps below:

Step 1: Divide the decimal by 1, like: $\frac{Decimal}{1}$.
Step 2: Multiply both numerator and the denominator by the numbers after the decimal point in the range of $10^{n}$, where n = No of digits after the decimal.
For example, if there are two numbers after the decimal point use 100, if there are three then use 1000,etc.)
Step 3: Reduce the fraction to its lowest terms.

## Decimal to Fraction Chart

Above is the decimal chart to fraction chart conversion where, in first column the numbers are in decimals which are converted into fractions in the second column.

## Convert Repeating Decimal to Fraction

Repeating decimals are converted into fractions by the use of simultaneous equations, where we identify how many numbers are involved in the 'repeating part' of the repeating decimal.
Given below are the steps to be followed:
1. Firstly set the fraction X equal to the repeating decimal.
2. Multiply the first equation by $10^{n}$, where n = the number of digits in the 'repeating part' of the repeating decimal.
3. Now solve the simultaneous equation and reduce the fraction

## Converting Decimals into Fractions Problems

### Solved Examples

Question 1: Convert 4.28 to fractions.
Solution:

Step 1: The decimal 4.28 can be multiplied and divided by 1 as the value will remain same.

$\frac{4.28}{1}$ $\times$ 1

= $\frac{4.28}{1}$ $\times$ $\frac{100}{100}$  (There are two digits after the decimal so multiply and divide by 100)

= $\frac{428}{100}$

Step 2: Now to reduce fractions
Consider,
$\frac{428}{100}$ = $\frac{4 \times 107}{4 \times 25}$

= $\frac{107}{25}$

Step 3: $\frac{107}{25}$ can also be expressed in terms of mixed fraction.

$\frac{107}{25}$ = $\frac{100+7}{25}$

= $\frac{100}{25}$ + $\frac{7}{25}$ = 4 + $\frac{7}{25}$

So now the mixed fraction is 4$\frac{7}{25}$

Question 2: Express 0.75 as a fraction
Solution:

Divide 0.75 by 1.

$\frac{0.75}{1}$

Since there are two digits after the decimal we multiply and divide the numerator and denominator  by 100.

= $\frac{0.75}{1}$ $\times$ $\frac{100}{100}$

= $\frac{75}{100}$

= $\frac{75}{100}$ can be expressed as

= $\frac{75}{100}$ = $\frac{25 \times 3}{25 \times 4}$ = $\frac{3}{4}$

Therefore, the answer is $\frac{3}{4}$

Question 3: Convert 0.47474747 to fractions.
Solution:

We see that there are two digits which repeats 4 and 7.
As we need to set up two equations to solve the equations simultaneously, consider the first equation as X = 0.47474747                     -----(1)
As two digits are repeating, we move the decimal two place by multiplying that whole equation by $10^{2}$ which is 100.

X = 0.47474747.... $\times$ 100

100X = 47.474747                          ...... (2)

100X = 47.474747

Subtract equation (1) from (2)

(100X - X) = (47.474747 - 0.47474747)

99X = 47

X = $\frac{47}{99}$

As 47 is a prime number we can't reduce this fraction.

### Dividing Decimals

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