Question

Express the number 0.1375 in the simplest $\frac {p}{q}$ form.

Answer 1

Answer:

11/80

Step-by-step explanation:

Hi,

Given number, x = 0.1375

Multiplying and dividing the number with 10000, we get

x = 1375/10000

If we factorize both 1375 and 10000 into its prime factors, we get

1375 = 5³*11

10000 = 2⁴*5⁴

x = 5³*11/2⁴*5⁴

x = 11/2⁴*5

x = 11/80 which is in the simplest form.

Hope, it helps !

Answer 2

Solution :

Given Terminating decimal 0.1375

= 0.1375 × ( 10000/10000 )

= 1375/10000

= ( 5×5×3×17 )/( 2 × 5 )⁴

= ( 5×5×5 ×11 )/( 2⁴ × 5⁴ )

After cancellation, we get

= ( 11 )/( 16 × 5 )

= 11/80

Therefore ,

0.1375 = 11/80 [ p/q form ]

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