Question

How do you find fractional notation for the ratio 1.6 to 9.8?

Answer 1

`8 / 49`

Explanation:

We can immediately get a "technically correct" answer by placing the first term over the second: `1.6 / 9.8`. This is not, however, a desirable fraction.

To get rid of the decimals, we can multiply the top and bottom by 10. This shifts the decimal places one to the right without changing the value of our fraction: `16/98`.

Now we have a proper fraction, but it is not fully reduced. To fully reduce a fraction, you need to get the top and bottom to have no common denominator greater than 1. In other words, when fully reduced, there should not exist an integer greater than 1 which evenly divides the top any bottom.

We see that 16 and 98 are divisible by 2, so we divide the top and bottom by 2 to get: `8 / 49`. This cannot be reduced any further, so it is our final answer.