Final answer:
To show that a number is rational, we need to express it as a ratio of two integers. In this case, the number is 52.4681168116811. By representing the repeating part as x, we can write the number as a ratio of two integers.
Step-by-step explanation:
To show that a number is rational, we need to express it as a ratio of two integers. In this case, the number is 52.4681168116811. To write it as a ratio, we can start by noticing that the number has a repeating pattern. We can represent it as 52.4681168116811... and let x represent the repeating part. So, we have:
52.4681168116811... = 52 + x
To eliminate the repeating part, we can multiply both sides of the equation by a power of 10 that is equal to the number of decimal places in x. In this case, x has 13 decimal places, so we multiply by 10^13:
10^13(52.4681168116811...) = 10^13(52 + x)
This gives us:
524681168116811.1... = 52000000000000 + 10^13x
Let n = 524681168116811 and m = 52000000000000. Now we have:
n = m + 10^13x
Simplifying further:
10^13x = n - m
Finally, we can express the number as a ratio:
52.4681168116811... = (n - m) / 10^13