Question

0.5 + 0.163 (3 has a line over it) and i need to find it in a fraction

Answer 1

`\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{(199)/(300)}}`

Explanation:

`0.16\bar{3} = 0.16333333333\\`

the 3 repeats until infinity

Let's multiply this by 100 to move the non-repeating part to the left of the decimal point

0.1633333333...... x 100 = 16.333333333333333...

.333333 = 1/3

Therefore the recurring number multiplied by 100 is

`16 + (1)/(3) = (16 * 3 + 1)/(3)=(49)/(3)`

Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333

`(49)/(3) / 100`

To divide by a number, multiply by the reciprocal of that number

Reciprocal of 100 is 1/100:

`(49)/(3) / 100 = (49)/(3) * (1)/(100) = (49)/(300)`

(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring

We want to add 0.5 to this.

0.5 =
`(1)/(2)`

so
0.5 + 0.16333333 = 0.6633333

`= (1)/(2) + (49)/(300)`

We can write
`(1)/(2)` as
`(150)/(300)` by multiplying numerator and denominator by 150

So we get

`0.5 + 0.1633333 = (150)/(300) + (49)/(300) = (150+49)/(300) = (199)/(300)`

If you perform this division on a calculator you will get the answer as 0.663333 =
`0.66\bar{3}` which is what you get when you add 0.5 and
`0.16\bar{3}`