Question

express in the form of p/q 4.3 bar and2.37bar

Answer 1

Solution 1.)

Let a = 4.3 ( bar on 3) ------(1)

10a = 43.3 (bar on 3) ------(2)

On subtracting equation 1 from 2, we get

9a = 39

=> a = 39 / 9

=> a = 13/3

Solution 2.)

Let a = 2.37 (bar on 37) ------(1)

100a = 237.37 (bar on 37) ------(2)

On subtracting equation 1 from 2, we get

99a = 235

=> a = 235 / 99

Answer 2

Answer:

$4.\overline{3}=\frac{39}{9}$

$2.\overline{37}=\frac{2.35}{99}$

Step-by-step explanation:

Given:

$4.\overline{3}\:\:and\:\:2.\overline{37}$

We need to express given repeated decimal expansion in p/q form.

first,

let x = 4.333...    ...............(1)

multiply both sides by 10.

10x = 43.333...   .....................(2)

subtract (1) from (2)

10x - x = 43.333... - 4.333...

9x = 39

x = 39/9

Therefore, $4.\overline{3}=\frac{39}{9}$

Secondly,

let y = 2.3737...    ...............(3)

multiply both sides by 100.

100x = 237.3737...   .....................(4)

subtract (3) from (4)

100x - x = 237.3737... - 2.3737...

99x = 235

x = 235/99

Therefore, $2.\overline{37}=\frac{2.35}{99}$