Question

How do you convert \[\dfrac{3}{8}\] into a decimal?

Answer 1

Hint: In this problem, we have to convert the given fraction into a decimal form. We are given a fraction, on analysing it we can see that as the only prime factor of denominator is 2, in fact there are three twos. We can convert the fraction by multiplying the numerator and the denominator by \[5\times 5\times 5\].

Complete step by step answer:
We know that the given fraction to be converted into decimal is \[\dfrac{3}{8}\].
Now we can see that the only prime factor of the denominator is 2, in fact there are three twos \[2\times 2\times 2\] we can convert the fraction by multiplying the numerator and the denominator by \[5\times 5\times 5\].
Here we can multiply \[5\times 5\times 5\]on numerator and the denominator, we get
\[\Rightarrow \dfrac{3\times 5\times 5\times 5}{8\times 5\times 5\times 5}=\dfrac{375}{1000}\]
 Now we can move the decimal point three point to the left, to get a decimal value, we get
\[\Rightarrow \dfrac{375}{1000}=0.375\]
We should know that this is always possible if only prime factors of denominator are 2’s and 5’s just multiplying as many 5’s and 2’s.

Therefore, the decimal form of the fraction \[\dfrac{3}{8}\] is 0.375.

Note: We can also convert this in another method.
We know that the given fraction to be converted into decimal is \[\dfrac{3}{8}\].
We know that,
\[\dfrac{1}{8}=0.125\]
We can just multiply 3 in the decimal value above, as the given numerator is 3, we get
\[\Rightarrow 3\times \dfrac{1}{8}=0.125\times 3=0.375\]
Therefore, the decimal form of the fraction \[\dfrac{3}{8}\] is 0.375.
Students make mistakes while moving the decimal points, we should know that when we multiply with power of ten we should move the decimal point to the write for the given number in power and when we divide, we have to move the decimal point.