.397777777777 to vulgar fraction

Question

How to convert .3977777777 to vulgar fraction without using a scientific calculator

Answer 1

????????????????????????? "vulgar frakshun" ???????????????????

Answer 2

Here, we try to find a fraction equivalent to the given recurring decimal.    

Divide the decimal into 2 parts; a finite decimal (0.39), and recurring decimal (0.007777...),so

Sol.1: 0.397777...=0.39+0.007777...    While,

1/9=0.1111..., 1/90=0.01111..., 1/900=0.001111...    Thus,

0.007777...= 7x0.001111...=7x(1/900)=7/900    And,

0.39=39/100=(39x9)/900=351/900    Therefore,

0.397777...= 0.39+0.007777...=351/900 + 7/900=358/900=(2x179)/(2x450)=179/450

The answer is: 0.397777...=179/450 

Sol.2: 0.397777...=0.39+0.007777...    Let 0.39=A and 0.007777...=B, so 0.397777...=A+B

10B=0.07777.7.., so 10B-B=0.077777... - 0.007777...=0.07  

That is: 9B=0.07    We have: B=0.07/9=7/900   While,

A=0.39=39/100=351/900    Therefore,

0.397777...=A+B=351/900 + 7/900=358/900=179/450

The answer is: 0.397777...=179/450

Answer 3

Move the decimal point two places to the right by multiplying by 100: 39.77777... The recurring part is one digit, 7. Write this over one 9: 7/9, now we have the mixed number: 39 7/9. Convert this to a improper fraction: (39*9+7)/9=358/9. Finally divide by 100 to compensate for multiplying earlier: 358/900, which cancels down to 179/450.