### 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.