how do you convert a decimal to a fraction? 5.9 that repeats?
.999999 = 1
so, 5.99999 = 6
any repeating digit .nnnnn... is n/9
sorry but I am still confused; I was taught one way in class but still don't understand how to do it. So would the answer be 5 9/10?
no, 5.9 = 5 9/10
5.99 = 5 99/100
5.9999999... = 5 9/9 = 5+1 = 6
consider n=5.999999
10n = 59.999999
10n-n = 9n
59.99999999...
-5.99999999...
---------------
54.00000000...
9n=54
so, n=6
probably ought t google repeating decimals to see other takes on the topic.
To convert a decimal to a fraction, follow these steps:
Step 1: Determine the decimal part that repeats. In this case, the decimal part is 9, which repeats.
Step 2: Assign a variable to the repeating decimal part. Let's assign "x" to the repeating decimal part: x = 0.9(repeating).
Step 3: Multiply both sides of the equation by 10 to eliminate the decimal point from x: 10x = 9.9(repeating).
Step 4: Subtract the original equation from the new equation: 10x - x = 9.9(repeating) - 0.9(repeating). This simplifies to 9x = 9.
Step 5: Solve for x: Divide both sides of the equation by 9: x = 1.
Step 6: Write the fraction using the variable x: Since x represents 0.9(repeating), we can write the fraction as 0.9(repeating) = 1.
Therefore, the decimal 0.9(repeating) can be simplified to the fraction 1.
Note: Any repeating decimal can be converted to a fraction following a similar approach.