Question

How do you write \[\dfrac{5}{9}\] as a decimal?

Answer 1

Hint: To convert \[\dfrac{5}{9}\] to a decimal, we need to divide the numerator of a fraction by the denominator of a fraction and then see what kind of decimal expression we are getting. In fraction, the numerator is the number which is written above the fraction and denominator is the number which is written below the fraction.

Complete step by step answer:
The number which is given in the above problem of which we have to find the decimal expression is as follows:
\[\dfrac{5}{9}\]
As you can see that the above number is in the form of a fraction so to find the decimal expression of the above number we have to divide the numerator of the fraction by the denominator. The numerator of the above number is 5 and denominator is 9 so dividing 5 by 9 we get,
\[9\overset{0.55}{\overline{\left){50}\right.}}\]
     \[\dfrac{45}{50}\]
     \[\dfrac{45}{50}\]
In the above division, 5 are of repeating nature. Hence, the decimal representation of \[\dfrac{5}{9}\] is as follows:
0.5555555
Hence, from the above, we have converted the given fraction \[\dfrac{5}{9}\] into decimal and the decimal
representation is equal to 0.5555555.

Note:
You can check whether the decimal representation is correct or not in the following way:
From the above, we got:
\[\dfrac{5}{9}=0.55555\]
Now, multiplying 9 on the both sides we get,
\[\dfrac{5}{9}\times 9=0.55555\times 9\]
\[\Rightarrow 5=4.9995\]
Now, if we round off the R.H.S of the above equation we will get 5 which means that L.H.S is equal to R.H.S so the decimal representation that we have written in the solution is correct.
In this way, you can divide 5 by 0.55555 and see whether the answer is nearly equal to 9 or not.
\[\dfrac{5}{0.5555}=9\].