What is 1.1666666666667 as a fraction?

Answer 1

7/6

To convert - 1.1666666667 to a fraction:

1. Let x = 1.1666666667

2. The repeating digit is 6.

3. Place the repeating digit to the left of the decimal point.

In this case, move the decimal point 1 place to the right by multiplying it by 10.

Thus,

(x = 1.666666667) * 100

100x = 116.6666667 - equation (1)

4. Place the repeating digit to the right of the decimal point.

In this case, move the decimal point 2 places to the right.

Thus,

(x = 1.1666666667) * 10

10x = 11.666666667 - equation (2)

5. Subtract Eq.(2) from Eq.(1)

100 x - 10x = 116.6666667 - 11.666666667

90x = 105

divide both sides by 90

x = 105/90 or 7/6

Answer 2

To convert the decimal 1.1666666666667 to a fraction, we first note that this recurring decimal can be expressed as 1.1 recurring. This can be represented as 1.1 with a bar over the 1. To convert this to a fraction, we set x = 1.1666666... and notice that 10x = 11.1666666... Subtracting the original equation from the second, we get 9x = 10, which simplifies to x = 10/9. Therefore, 1.1666666666667 as a fraction is 10/9.