Recognize Decimal Places: To express the decimal 0.1019 as a fraction, we first need to recognize how many places there are after the decimal point. There are four digits after the decimal point, which means the decimal can be expressed over 10,000 (since 104=10,000).
Write as Fraction: Now, we write 0.1019 as 1019 over 10,000. This gives us the fraction 100001019.
Simplify Fraction: The next step is to simplify the fraction. We need to find the greatest common divisor (GCD) of 1019 and 10000 to reduce the fraction to its simplest form. The GCD of 1019 and 10000 is 1, since 1019 is a prime number.
Check for Simplest Form: Since the GCD is 1, the fraction 100001019 is already in its simplest form. Therefore, we do not need to simplify it further.
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