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Find decimal to fraction 0.3535

Solution:
Your problem `->` decimal to fraction 0.3535


1. Convert a Repeating Decimal to a Fraction

`0.3535... = 35/99`



Step by step solution :
Step-1 : let `x` equals the decimal number

`x = 0.3535... ->(1)`

Step-2 : Here repeating digits is 2, So create a second equation by multiplying both sides by `10^2 = 100`

`100 x = 35.353535... ->(2)`

Subtract equation (1) from equation (2)
`100 x`=`35.353535...`
`x`=`0.3535...`

`99 x`=`35`


`:. x = 35/99`


`:. 0.3535... = 35/99`




2. Convert a Decimal to a Fraction (Non Repeating)

`0.3535 = 3535/10000=(3535 -: 5)/(10000 -: 5) = 707/2000`



Step by step solution :
Step-1 : write the decimal number as a fraction (by dividing 1)
`0.3535=0.3535/1`

Step-2 : To eliminate 4 decimal places, multiply both numerator and denominator by `10^4 = 10000`

`0.3535/1 xx 10000/10000=3535/10000`

Step-3 : Find the Greatest Common Factor (GCF) of `3535` and `10000`, and reduce the fraction by dividing both numerator and denominator by GCF = 5

`=(3535 -: 5)/(10000 -: 5)=707/2000`

So `0.3535 = 707/2000`






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