express 15.7121212... in the form p/q where p and q are integers and q not equal to 0.
Let a=15.7121212
then 100a=1571.21212
Calculate
100a-a=99a
=1571.2121212...-15.7121212...
=1555.5
therefore
a=1555.5/99
=15555/990
=1037/66
so p=1037, q=66
Wrong answer
To express the repeating decimal 15.7121212... as a fraction in the form p/q, we need to identify a pattern in the repeating part of the decimal. Let's start by defining a variable to represent the repeating part of the decimal.
Let x = 15.7121212...
Now, let's multiply both sides of the equation by 100 to shift the decimal point two places to the right:
100x = 1571.2121212...
Now, we'll subtract the original equation from the multiplied equation to eliminate the repeating part:
100x - x = 1571.2121212... - 15.7121212...
Simplifying the equation:
99x = 1555
Dividing both sides by 99:
x = 1555/99
Therefore, the fraction form of the repeating decimal 15.7121212... is 1555/99.
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