.Write each decimal as fraction in simplest form 1.0.222 3.0242424 4.0.5555 5.-0.124124124

Guest Jul 30, 2017

If you are going to list decimals, I would highly advise separating them with commas, as opposed with a numbered list. The decimals are confusing to read. If you want to use a numbered list still, I would do what I did below.


This is how I would revise your question:

Write each decimal as a fraction in simplest form.


1) 0.222

2) 0.1515

3) .0242424

4) 0.5555

5) -0.124124124


This is what I perceive the intended decimals to be, but I am not entirely sure, so correct me if I am wrong. 


I will start with the first decimal, 0.222.


\(0.222\) First, identify what place the decimal extends until (in this case, it extends to the thousandths place) and set it equal to a fraction over 1000.
\(0.222=\frac{222}{1000}\) Now, identify the GCF of the fraction. It is harder with larger numbers, but both numbers are even, so we can, at least, divide by 2.
\(\frac{222}{1000} \div \frac{2}{2}=\frac{111}{500}\) 111 and 500 do not share any common factors, except for 1, so this fraction is in simplest form.


I will do the next decimal, 0.1515


\(0.1515\) Do the same process as above; the decimal extends until the ten thousandths place. Set it to a fraction over that amount, ten thousand.
\(0.1515=\frac{1515}{10000}\) Yet again, it can be hard to determine the GCF, but both numbers end in a 5 or 0, so both are divisible by 5. 
\(\frac{1515}{10000}\div \frac{5}{5}=\frac{303}{2000}\) Yet again, there are no common factors greater than 1, so this fraction is irreducible.


I will do the next decimal, as well.


\(0.0242424\) This extends to the ten millionth place, so put the number over a fraction over ten million.
\(0.0242424=\frac{242424}{10000000}\) The numerator and denominator's final two digits are divisible by 4, so we can divide them by, at least, 4.
\(\frac{242424}{10000000}\div\frac{4}{4}=\frac{60606}{2500000}\) We aren't done yet. The numerator and denominator are both even, so it is divisible by 2.
\(\frac{60606}{2500000}\div\frac{2}{2}=\frac{30303}{125000}\) The numerator and denominator are co-prime, so this fraction is in simplest form.


Here goes the next one:


\(0.5555\) The decimal extends to the ten thousandths place, so make a fraction over ten thousand.
\(0.5555=\frac{5555}{10000}\) Both the numerator and denominator are divisible by 5 because both of them end in a 5 or a 0.
\(\frac{5555}{10000}\div \frac{5}{5}=\frac{1111}{2000}\) 1111 and 2000 have no common factors, so the fraction is simplified completely. 


And, of course, here is the next one, -0.124124124.


\(-0.124124124\) This decimal extends to the billionth place, so set it over a billion. Just put the negative sign in front of the fraction.
\(-0.124124124=-\frac{124124124}{1000000000}\) Both the numerator and denominator's final 2 digits are divisible by 4, so the fraction can be simplified. 
\(-\frac{124124124}{1000000000}\div\frac{4}{4}=\frac{31031031}{250000000}\) There are no more common factors. 


You are done now!

TheXSquaredFactor  Jul 30, 2017

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