Question

Brianna asked 45 students if they would vote for her to be student council president. She used her calculator to compare the number of students who said yes with the total number of students. Her calculator showed the result as 0.6222.... Answer parts a and b.

Answer 1

Explanation:

In this problem, it is given that, the number shown by the calculator is 0.6222....

(a) We need to find the number as a fraction

Let x = 0.6222.... ...(1)(it is a recurring decimal at the digit '2')

Muliply both sides of equation (1) by 10.

10x=0.6222.. × 10

10x = 6.222..

Multiply both sides of equation (1) by 100.

100x = 0.6222.. × 100

100x = 62.222.. ...(2)

Subtract equation (2) by (1).

100x-10x = 62.2222... - 6.2222...

90x=56

x=(56/90)

⇒
`x=(28)/(45)`

This is the required fractional form of the given no i.e. "28/45"

(b) The fraction has 28 at numerator and 45 at denominator. Numerator shows the part of a denominator.

It would mean that 28 students vote for Brianna.