The fractional form of the rational number 0.1515... is:
15/99
<h3>
How to write 0.1515... as the quotient of two integer numbers?</h3>
I will do all the steps, not only the one in the picture.
First, we identify that we have a number where the decimals do a repeating pattern.
That number in our case is 0.1515...
That repeating pattern is "15".
First we need to identify the number of digits in the pattern, and we can see that is 2, thus we define n = 2
Now we multiply our number by 10^n (10^2 in this case).
0.1515...*10^2 = 0.1515...*100 = 15.1515...
Notice that we still have the pattern, so we can subtract the original number to remove it:
15.1515... - 0.1515... = 15
Ok, now we can rewrite the left side as:
15.1515... - 0.1515... = 100*0.1515... - 0.1515...
= (100 - 1)*0.1515... = 99*0.1515...
And we know that is equal to 15, then we can write:
99*0.1515... = 15
If we isolate the original number in the left side we will get:
0.1515... = 15/99
That is the fractional form of the rational number.
If you want to learn more about rational numbers:
brainly.com/question/12088221
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