Question

Show that 1.83bar on 3 can be expressed in form of p/q where q is not equal to 0 ​

Answer 1

Answer:

55/30

Step-by-step explanation:

Let x = 1.833333333...

Multiplying both sides by 10

10x = 18.3333333... -(1)

Multiplying both sides by 10

100x = 183.3333333... -(2)

2-1

90x = 165

x = 165/90 = 55/30

Shortcut Way (will work for every question, only for checking answer)

(Leave this if you can't understand) ↓↓↓

For denominator value -

Let 9 denote the bar numbers and 0 denote the non bar numbers - (3)

See the number after decimal places

Since 8 is the only number after decimal place without a bar and 3 is the only number with a bar, we denote denominator by 90 (9 is written first and 0 is written later) (9 for 8 and 0 for 3) [From 3]

For numerator value -

Numerator value is the full number - number which doesn't have a bar

So for this question numerator value is 183-18 = 165

So the answer is numerator/denominator = 165/90 = 55/30

Answer 2

Thank you for the answer but we no need to multiply with 10 and 100.

Just with 10, it's enough