Question

How do you convert \[0.51\] as a fraction?

Answer 1

Hint: To solve this question, we will write the given number \[0.51\] in the form of an equation by equating it to some variable. Then, we will multiply the equation by \[10\] repeatedly until we remove the decimal point and convert the given number into the whole number. On solving this equation, we will obtain the required fractional form of \[0.51\].

Complete step-by-step solution:
According to the question, we have a number \[0.51\] which has to be converted as a fraction.
Let us suppose that it is equal to some variable, say \[n\]. So we can write the equation as
\[n = 0.51\]
Now, for converting the given number to a fraction, we need to multiply it by \[10\] repeatedly until we obtain zero after the decimal.
So multiplying both sides of the above equation with \[10\], we get
\[\begin{array}{l} \Rightarrow 10n = 0.51 \times 10\\ \Rightarrow 10n = 5.1\end{array}\]
As can be seen above, the decimal is still not removed, so we will again multiply the both sides by \[10\], we get
\[\begin{array}{l} \Rightarrow 100n = 5.1 \times 10\\ \Rightarrow 100n = 51\end{array}\]
We can see that there is no decimal point in the number.
Now, we will divide both sides of the above equation by \[100\]. Therefore, we get
\[ \Rightarrow n = \dfrac{{51}}{{100}}\]
As there is no common factor between the numerator and denominator, so we cannot simplify it further.

Hence, the number \[0.51\] is converted to a fraction as \[\dfrac{{51}}{{100}}\].

Note:
A decimal number is a number that contains a whole number part and a fractional part separated by a decimal point. When a number is divided by 100, the result can be obtained by shifting the decimal point 2 digits to the left from the last digit. For example, The number 43 can be written as 043. When 043 is divided by 100, the result is \[0.43\], which is simply obtained by shifting the decimal point two places to the left from the last digit 3.