With just a few simple calculations you can convert 0.125 into a fraction and then put it into its simplest form. The simplest form of 0.125 as a fraction is ⅛, yet how would you do this calculation? Let’s take a look at the steps needed to convert 0.125 into a fraction and then to put that fraction into its simplest form.
The first part of converting any decimal into the simplest form of a fraction is to convert the decimal into a fraction. For this first conversion, any fraction will do, and knowing about the properties of fractions and decimals will help you make these conversions. A conversion between decimals and fractions can be made very easily if you know the secret behind their relationship to one another.
Converting A Decimal To A Fraction
Let’s take a quick look at how you can convert a decimal to a fraction. Always remember that decimals are just parts of a whole number. This property means that just as whole numbers have columns, like tens and hundreds, the numbers that come after the decimal point also have columns, and these columns represent what portion of a whole number the decimal is. The first column after the decimal point is the tenths place, while the second column is the hundredths place, and so on.
So if one is given the decimal 0.82, they know that 0.82 isn’t a whole number, just 82% of a whole number. The number 1 is equivalent to 100%, which means that converting a decimal to a percentage, and then to a fraction, is very easy. All you have to do is take the decimal in the hundredths place and push it over to the right by two spaces, then put the last column’s place value under the number. For example, 0.82 would become 82% or 82/100.
As another example, if you have the decimal 0.515, you can easily make this a fraction by noticing that the second five is in the thousandths place, which makes an equivalent to the fraction 515/1000. Converting the decimal into a fraction is done simply by counting the columns after the decimal point, then pushing the decimal that many spaces to the right. Finally, add the value of the final column (in this case, this thousandths column) to the fraction as its denominator.
Putting The Fraction In Simplest Form
Now that we have a fraction – 515/100 – we can go about reducing the fraction, or putting it in its simplest form. 515/1000 is pretty messy, so how would one go about finding the smallest, simplest version of the fraction? This can be done by finding what is known as the Greatest Common Factor or Greatest Common Divisor (GCF or GCD), and then using it to reduce a fraction to its simplest terms.
The greatest common factor is the largest, greatest number that you can divide evenly into both the denominator and numerator of the fraction. Let’s take the fraction 515/1000 and distill it to its simplest form. In this case, the greatest common factor is 5. Dividing 5 into 515 gives you 103/200.
Here’s a second example. If you have the decimal 0.875, you could convert it to a fraction (875/1000), and then find the greatest common factor. In this case the GCF is 125, so dividing 125 into both the numerator and denominator will get you ⅞.
In the two prior examples, we already knew what the GCF for the fractions was. However, you’ll usually have to do a bit of math to determine the GCF of a fraction. There are multiple ways to find a fraction’s GCF, including listing, prime factorization, and the division method. One of the main ways to determine the GCF of a fraction is to utilize the Prime Factorization method. In the prime factorization method, you will multiply out the prime factors common to both numerator and denominator.
Finding The GCF
Let’s take the fraction 18/24 for example. Prime factors that can only be multiplied by one and itself are prime factors, so with prime factorization, you’ll want to list out only the factors which are prime numbers. In this case, the prime factors of 18 are 2 and 3. These are also the smallest numbers which you could multiply together to get 18 (2 x 3 x 3 = 18). Meanwhile, the prime factors of 24 are also 2 and 3 (2 x 2 x 2 x 3 = 24). Multiplying 2 and 3 together gets you the number 6, which you can then divide into 18/24 to get ¾.
It’s also possible to find the greatest common factor by just listing out factors of the two numbers until you run out of possible factors and find the GCF. As an example, if you were given the fraction 180/210 you could look for the GCF by listing out the factors like so:
Factors of 180 (other than one): 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20
Factors of 210 (other than one): 2, 3, 5, 6, 7, 10, 14, 15, 21
Let’s stop here because we may have the GCF already, or a way to find it. The common factors between 180 and include, 2, 3, 5, 6, 10, and 15. In this case, the biggest factor listed here is 15, and if we try multiplying it by 2 we get 30, which is indeed the greatest common factor for the fraction.
Dividing 30 into 180/210 would get you the fraction ⅞. We could also have arrived at 30 for the GCF by multiplying together the numbers 2, 3, and 5. Another way to find the GCF would have been just to keep going and list out the factors until reaching 30, though as you can see this process can take quite a bit of time compared to prime factorization.
One other way of finding the GCF is the Division Method. The division method involves splitting the two numbers up into smaller chunks until you have numbers that can no longer be divided. As an example, let’s try finding the GCF of 144/280 using the division method.
Dividing 144 and 280 by 2 gives us: 72 and 140.
72 and 140 have more common factors, so we can attempt to divide the numbers by two once more.
Doing this will give us: 36 and 70.
Once more, 36 and 70 still have common factors between the two numbers, so let’s divide by 2 again to get 18 and 35. These two numbers don’t have any common factors besides one, so let’s stop here and see what we have.
Let’s multiply everything together: 2 x 2 x 2 = 8. Now we can divide 144/280 by 8 to get 18/35.
Now let’s apply everything we’ve learned to converting 0.125 into the simplest form of a fraction.
0.125 is just 125/1000 when expressed as a fraction. Let’s divide 125/1000 by the greatest common factor. The GCF in this instance is 5, and dividing 125/1000 gets us 25/200, which can be divided once more by 5 to get 5/40 and divided by 5 a final time to get ⅛.