Question

Express each of the following in decimal form:
A. \[\dfrac{17}{3}\]
B. \[\dfrac{12}{18}\]

Answer 1

Hint: We can also do this using basic simplification techniques. For simplifying it first we find GCF (greatest common factor) of both numbers. After finding the greatest common factor of the numbers in the numerator and denominator, we will reduce the fraction into the simplest form. After getting the simplest form, we will need to divide the numerator by denominator and we will get the given fraction in the decimal form.

Complete step-by-step answer:
A. \[\dfrac{17}{3}\]
We have given the rational number i.e. fraction = \[\dfrac{17}{3}\]
As we can observe that,
The numerator and the denominator have no common factor.
Therefore,
Converting the given fraction to a decimal by dividing the numerator by the denominator is given by;
 \[\Rightarrow \dfrac{17}{3}=5.66\]
Hence, the decimal form of \[\dfrac{17}{3}\] is equal to \[5.66\] .

B. \[\dfrac{12}{18}\]
We have given the rational number i.e. fraction = \[\dfrac{12}{18}\]
Factors of numerator and denominator;
 \[\Rightarrow 12=1,2,3,4,6,12\]
 \[\Rightarrow 18=1,2,3,6,9,18\]
Therefore,
We can observe that,
The greatest common factor of numerator and denominator is 6.
Now,
Dividing the numerator and denominator by 6, we will get
 \[\Rightarrow \dfrac{12\div 6}{18\div 6}=\dfrac{2}{3}\]
Now,
The reduced fraction we get is,
 \[\Rightarrow \dfrac{2}{3}\]
Now,
As we can observe that,
The numerator and the denominator have no common factor.
Therefore,
Converting the given fraction to a decimal by dividing the numerator by the denominator is given by;
 \[\Rightarrow \dfrac{2}{3}=0.666\]
Therefore,
 \[\Rightarrow \dfrac{12}{18}=0.666\]
Hence, the decimal form of \[\dfrac{12}{18}\] is equal to \[0.666\] .

Note: We can also do this in a simple way without calculating the GCF. We can directly divide the numerator with the denominator. If the denominator is multiple of 10 we can directly convert the numerator into decimal according to the 0′s in the denominator. As our denominator is multiple of 10 we can also directly the decimal form based upon zeros in the denominator. If the denominator is not a multiple of 10 we can also convert the denominator into multiples of 10 by multiplying the numerator and denominator with the same number, it will make the fraction easier to convert into decimal form.