Question

How to change \[8.3\] to a fraction?

Answer 1

Hint: To convert a decimal into a fraction there is no need for decimal to fraction formula, you just need to follow some basic steps for conversion. First, we need to write the given decimal as a numerator and then write 1 in the denominator. Multiply the numerator and denominator both by taking 1 annexed with as many zeros as is the number of decimal places in the given decimal. Reduce the resultant fraction to its simplest form.

Complete step by step solution:
We have the given decimal, i.e. \[8\cdot 3\]. Write down the given decimal as a fraction of one: \[8.3=\dfrac{8.3}{1}\]
Multiply numerator and denominator both by 10, as there is only one decimal place in the given decimal, As we have 1 number after the decimal point, we multiply both numerator and denominator by 10. So,
\[\dfrac{8\cdot 3}{1}=\dfrac{8\cdot 3\times 10}{1\times 10}=\dfrac{83}{10}\]
Divide the numerator and denominator by the greatest common divisor i.e. 1. The greatest common divisor of 83 and 10 is 1. When we divide the numerator and denominator by 1, we get;
\[\therefore \dfrac{83}{10}\]
Hence, it is the required fraction of the given decimal.

Additional information:
We can solve this question in another way also:
We can rewrite \[8\cdot 3\] as \[8\cdot 0+0\cdot 3\].
\[8\cdot 0\] is \[80\] tenths or \[\dfrac{80}{10}\].
\[0\cdot 3\] is \[3\] tenths or \[\dfrac{3}{10}\].
\[\dfrac{80}{10}+\dfrac{3}{10}=\dfrac{83}{10}\].
Therefore, it is a required fraction of the given decimal.

Note: To solve the given decimal into fraction, first we need to get of the decimal point in the numerator, we count the numbers after the decimal point and multiply the numerator and denominator by 10 if the numbers after decimal point is 1, by 100 if it is two numbers, by 1000 if it is three decimal numbers after decimal point and so on.