With just a few short calculations, 0.375 may be calculated as a fraction and reduced to its simplest form. The simplest form of the fraction obtained from 0.375 is 38, but first, consider how to convert the decimal to a fraction and then reduce the fraction to its simplest form.
The first step in converting a decimal to the simplest form of a fraction is to transform the decimal you’ve got into a fraction. For this first conversion, any fraction will suffice. It would be useful to understand some properties of decimals and fractions. If you understand the relationship between decimals and fractions, converting a decimal to a fraction should be simple.
Converting A Decimal To A Fraction
Consider the following example of converting a decimal to a fraction. It’s important to understand that decimals are essentially fractions of whole numbers. As a result, numerals after the decimal point have number places (columns) just like whole numbers. The tenth place is the first column following the decimal point, followed by the hundredths place, and so on.
The number 0.75 is not a whole number; it represents 75% of a whole number. To convert a decimal to a percentage, take the decimal in the hundredths place and move it two spaces to the right, then place the position of the last column under the new value.
If you have the decimal 0.412, you can convert it to a fraction by noting that the 2 column represents the thousandths column, therefore 0.412 equals 412/1000. We just count the number of columns behind the decimal point and then move the decimal point over that many spaces to convert the decimal to a fraction. The value of the last column (one thousand in the thousands column) was then added to the number as the denominator.
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The Greatest Common Factor
When it comes to fractions, 412/100 is a bit of a pain. It’s possible that it’ll be much smaller. How would one go about determining the fraction’s smallest, or simplest, form? Putting a fraction in its simplest terms, or decreasing the fraction, refers to finding the smallest/simplest form of a fraction. To do so, one must first determine what is known as the greatest common factor or greatest common divisor (GCF or GCD).
The greatest common factor is the highest number that splits the fraction evenly into the numerator and denominator. If you have the fraction 412/1000 and want to simplify it, you should know that the greatest common factor of 412/100 is 4. If we simplify this to its most basic form, we get 103/250.
Let’s take a look at a different scenario. Let’s say you have 0.875 as a decimal. Let’s count the columns, move the decimal place over three spaces, and add one thousand underneath it to convert it to a fraction. This gives us a score of 875 out of 1000. The greatest common factor of 875/1000 is 125, which equals 78% when divided into the numerator and denominator.
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Finding The GCF
We gave you the greatest common factor for the fraction in the two previous examples we looked at. When trying to figure out the GCF of a fraction, you’ll usually have to conduct some math. There are various techniques for determining the greatest common factor of a fraction. The Prime Factorization approach, which involves multiplying out the prime factors present in both numbers, is one method of finding the GCF.
Consider the fraction 18/24 as an example. Factors that can only be multiplied by one and themselves are known as prime factors.
The integers 2 and 3 are prime factors of 18 (2 x 3 x 3 = 18), or the fewest numbers that may be multiplied together to get 18.
2 and 3 are also prime factors in 24 (2 x 2 x 2 x 3 = 24). Multiplying 2 and 3 together yields 6, which is divided by 18/24 to provide 34.
You might also just make a list of the components that are common between two integers. If you had 180/210, for example, you could write out the factors of both 180 and 210 and use that to calculate the great common factor.
Other than one factor of 180: 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20
2, 3, 5, 6, 7, 10, 14, 15, 21, 210 factors (other than one)
The components 2, 3, 5, 6, 10, and 15 are shared by the two numbers. The highest common component stated above in this situation is 15, which when multiplied by two equals 30.
The GCF for 180/210 is 30, as it happens. (It’s worth noting that you might have gotten 30 by adding 2, 3, and 5 together.) You get 78% if you divide 30 by 180/210.
If you had kept continuing and enumerated all the factors, you would have ultimately discovered that 30 was the GCF, but this would have taken far longer than using the prime factorization approach. Another approach for determining the GCF is to use the Division Method.
To Sum Up
Remember how simple it is to convert a fraction to a decimal: simply shift the decimal point to the right until you reach zero. Then you must count how many columns the decimal point was shifted over. If the final number was in the thousandths column, the fraction’s denominator is 1000.
All you have to do to reduce a fraction to its simplest form is discover the GCF. You can find the GCF using one of the following methods:
The prime factors of the individual numbers are listed first, and then the common prime factors are multiplied together.
After listing all of the numbers’ variables, choose the two largest factors that the numbers have in common.
Divide the two numbers by common factors until there are no more common factors between them, then multiply the two numbers together.
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