Question

Express 1.62 bar in thr p/q form

Answer 1

The number $\bf 1. \overline{62}$can be expressed as 161/99.

Given:

• $1. \overline{62}$

To find:

• p/q form of given number.

Solution:

Concept to be used:

Any terminating decimal expansion and non-terminating recurring decimal expansion can be expressed in p/q form, where q≠0.

Step 1:

Let the given number is x.

$x = 1. \overline{62}$

it can be expressed as

$x = 1.626262... \: \: \: \: \: \: ...eq1$

Multiply eq1 by 100.

$100x = 162.626262... \: \: \: ...eq2$

Step 2:

Subtract eq2-eq1 .

$100x - x = 162.626262... - 1.626262...$

or

$99x = 161$

or

$\bf \red{ x = \frac{161}{99}}$

Thus,

The given number can be expressed as 161/99.

Learn more:

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2) Express 1.233333..... in p/qform where p and q are co-primes.

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