Question

How do you write \[0.38\] as a fraction in simplest form?

Answer 1

Hint: To convert the decimal into fraction that means we just need to remove the decimal then it will be in fractional form. And we know that to remove the decimals we use \[{{10}^{n}}\] which makes quite easier the calculations. So in this question as we see there are two digits after the decimal that means we have to move the decimal by two digits then if we multiply it with \[100\] then to make the number the same we will have to divide it with the same \[100\]. After this the decimal is removed as decimal after all the digits in a number have no significance now just simplify it then the number will be in fractional form.

Complete step by step solution:
It is given that a number in decimal form and that is \[0.38\]
Now to convert it into fractional form we have to remove this decimal so we multiply it with \[100\] but if we want to make the number same then we have to divide it with the same \[100\]
\[\Rightarrow 0.38\times \dfrac{100}{100}\]
Now in this multiply the numerator part
\[\Rightarrow \dfrac{38}{100}\]
Now simplifying this, for this divide the numerator and denominator both by \[2\]
As we know that when we multiply or divide the numerator and denominator with the same number then the initial and the obtained fractions are the same and said to be equivalent fractions.
\[\Rightarrow \dfrac{\dfrac{38}{2}}{\dfrac{100}{2}}\]
\[\Rightarrow \dfrac{19}{50}\]

Hence \[0.38\] in fractional form is \[\dfrac{19}{50}\].

Note:
To convert the decimal form into fraction form first remove the decimal by multiplying the numerator and denominator with \[{{10}^{n}}\] where \[n\] depends on the question. In simple words just remove the decimal divide with \[{{10}^{n}}\] that is \[10\] raised to power the number of non-zero digits after the decimal. Though the decimal and fractional both are the same but written in different forms.