.1515 repeat, I get 303/2000 and divide it to get the .1515 repeat, but in my book, it says the answer is 5/33, how is that
if
n = .15151515...
100n = 15.15151515...
so,
99n = 15
n = 15/99 = 5/33
Any group of n digits which repeats is the string of digits divided by a string of 9's of the same length:
.333333 = 3/9
.15151515 = 15/99
.67836783... = 6783/9999
and so on
how do you get the 99n? im sorry but I am really confused
the usual way
subtract n from 100n to get 99n
look above to see that
15.151515...
-0.151515...
= 15
To understand why your calculation may differ from the answer given in the book, let's break down the process of converting a repeating decimal to a fraction.
Let's start with the repeating decimal 0.1515...
Step 1: Assigning a variable
Let x represent the repeating decimal:
x = 0.1515...
Step 2: Multiply by an appropriate power of 10
Since the repeat starts immediately after the decimal point, we multiply x by 100 (10^2) to shift the repeating part two places to the left:
100x = 15.1515...
Step 3: Subtract the original equation to eliminate the repeating part
Now, we subtract x from 100x:
100x - x = 15.1515... - 0.1515...
This simplifies to:
99x = 15
Step 4: Solve for x
Divide both sides by 99 to get the value of x:
x = 15/99
Simplifying the fraction:
The fraction 15/99 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3:
15/99 = (15 ÷ 3) / (99 ÷ 3) = 5/33
Therefore, the correct fraction form of the repeating decimal 0.1515... is 5/33.
It seems like you may have made an error at some point during your calculation. Double-check your steps and be mindful of any potential mistakes such as a miscalculation or omission of a step in the process.