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# Write each decimal as fraction in simplest form

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.Write each decimal as fraction in simplest form 1.0.222 2.2.0.1515 3.0242424 4.0.5555 5.-0.124124124

Jul 30, 2017

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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.

 $$0.222$$ 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!

Jul 30, 2017