Question

express 2.4178 ( 8 is repeating) in p/q form

Answer 1

let the fraction be x

2.417888...=2.4178bar
x=2.4178bar
1000x=2417.8bar
10000x=24178.8bar
10000x-1000x=24178.8bar-2417.8bar
9000x=21761
x=21761/9000

Answer 2

The p/q form of the given number is 21761/9000.

Given:

A non-terminating number 2.417$\overline{8}$ = 2.4178888...

To Find:

The given number in p/q form.

Solution:

We have been given a non-terminating number 2.417$\overline{8}$ = 2.4178888...

To write this number in the form of a rational number (p/q form, where q is non-zero), we will follow the steps given below:

Step 1: Consider the given number to be 'x'.

⇒ x = 2.4178888...        

Step 2: We observe that after the first three digits in the decimal expansion, the numbers keep repeating. So, multiply the given number by 1000.

1000x = 2417.888...         ..............................(I)

Step 3: Multiply the given number by 100.

100x = 241.7888...           ..............................(II)

Step 4: Subtracting (I) from (II).

⇒ 1000x-100x = 2417.888... - 241.78888...

⇒ 900x = 2176.1

⇒ 900x = 21761/10

⇒ x = 21761/9000.

Hence, the p/q form of the given number is 21761/9000.

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