what is.196 with a bar on the 6 converted to a decimal, also how did you do it?

Question

i need help

wha is 55.7% as a decimal

77% as a decimal????

Answer 1

100x = 19.66...
100x = 19 + 0.66... = 19 + 2/3
so x = (19 + 2/3)/100

Answer 2

The bar implies that the 6 is repeated indefinitely
That means that it represents a rational number
That means that the entire number is equivalent to the ratio of two integers.
I assume that your instructor wants to have you specify the smallest pair of integers that have a ratio equivalent to .1966666...
This number is very close to ,2000
That is 20/100
The difference is 1/3 of 1/100=1/300
finding a common denominator we have
60/300-1/300=59/300

I am sure there is a slicker way that works but I don't remember it this evening.

Answer 3

.196666666666666666666666666667
repeated 6 is usually a form of 1/6 which = .16666666666667
1/60 = .016666666666666667 which would leave .18

= .18 + .016666666666666666666666666667
= 18/100 + 1/60 get a common denominator 600
= (18)(6) / (6)(100) + (1)(10) / (60)(10)
= 108/600 + 10/600
= 118/600 reduce
= 59/300
----------------------------------------------------------------------------

55.7%
= 55.7/100
= .557

77%
= 77/100
= .77

Answer 4

Let a = .1966...
10a = 1.966...
100a = 19.66...
1000a = 196.66...
1000a - 100a = 196.66...- 19.66...
900a = 177
a = 177/900 = 59/300

And to convert % to a decimal, divide by 100. I think you already have those answers.

Answer 5

.196666666 (that's what the bar means, the 6 repeats) IS a decimal...