Question

Express 6.03 as a mixed fraction.

Answer 1

Hint: The basic idea in this type of question is to write the given decimal form of the number to the form $\dfrac{a}{b}$ where a is the number obtained after removing the decimal from the given number and b is equal to ${10^n}$ where n is the number of digits after decimal point and finally the fraction is changed into mixed fraction.

Complete step-by-step solution:
The given decimal number is 6.03,
As it is known that to convert the decimal number into fraction, the numerator part is the number which is obtained when the decimal part is not there and the denominator part is obtained by raising the base 10 to the power n, where n is the number of digits after the decimal point.
$\Rightarrow $ 6.03 is equal to $\dfrac{{603}}{{{{10}^2}}}$ ,
In this the numerator 603 is obtained by writing the decimal number without decimal point and the denominator ${10^2}$ is obtained as the number of digits after decimal point in 6.03 is two. So, 10 raised to the power 2 is done.
$\Rightarrow {\text{ 6}}{\text{.03 = }}\dfrac{{603}}{{{{10}^2}}}$
Or,
$\Rightarrow {\text{ 6}}{\text{.03 = }}\dfrac{{603}}{{100}}$
Also the fraction is to be converted into a mixed fraction.
As it is known that the mixed fraction is of the form $a\dfrac{b}{c}$ , where a is the quotient, b is the remainder and c is the divisor.
On dividing 603 by 100,
$a = 6$
$b = 3$
$c = 100$
On rearranging,
$ \Rightarrow 6.03 = 6\dfrac{3}{{100}}$
$\therefore {\text{ 6}}{\text{.03 in mixed fraction is 6}}\dfrac{3}{{100}}$ .

Note: In this question the corresponding fraction of the given decimal number is in the simplest form so it cannot be reduced further. But if the changed fraction is not in simplified form then it must be simplified before changing it into mixed fraction. Calculations should be done carefully to avoid any mistake. Always try to solve step by step.