Leo is correct.
When we have a decimal with repeating decimals, such as 2.55555555..., we can represent it as a fraction by using the following steps:
1. Let x be the decimal number.
2. Multiply x by 10^n, where n is the number of repeating decimals, to shift the decimal point n places to the right:
10^n * x = y.
3. Subtract x from y to eliminate the repeating decimals:
10^n * x - x = y - x.
4. Solve for x:
x = (y - x) / (10^n - 1).
In this case, x = 2.55555555..., and n = 1 (since there is only one repeating decimal 5).
Following the steps above:
x = (y - x) / (10^n - 1)
2.55555555... = (y - 2.55555555...) / (10^1 - 1)
2.55555555... = (y - 2.55555555...) / (10 - 1)
2.55555555... = (y - 2.55555555...) / 9
Multiplying both sides by 9:
22.9999999... = y - 2.55555555...
Adding 2.55555555... to both sides:
22.9999999... + 2.55555555... = y - 2.55555555... + 2.55555555...
25.5555555... = y
Therefore, the correct fraction representation for 2.55555555... is 25/9, which is equivalent to Leo's fraction of 2 55/99.
Di and Leo both write the decimal 2.55555555.. As a fraction.
Di’s fraction: 2 55/100
Leo’s fraction: 2 55/99
Who is correct and why?
1 answer
1 answer