How To Make Mathematica Give You Decimal Answer

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Fractions and decimal numbers are simply two different ways of representing numbers that are less than one. ^[1] Since any number below one can be represented with either a fraction or a decimal, there are specific mathematic equations that allow you to figure out what the equivalent of a fraction would be in decimal form, and vice versa.

1
Understand the parts of a fraction and what they represent. The fraction consists of three parts: the numerator, which is the top part of the fraction,^[2] the slash, which goes between the numbers, and the denominator, which is the bottom part.^[3]
- The denominator represents how many equal parts there are in the whole. For example, a pizza might be cut into 8 pieces. The denominator for the pizza would then be "8". If you cut the same pizza into 12 slices, then the denominator would be 12. Either way they represent the same whole, just cut up differently.^[4]
- The numerator represents a part, or parts, of the whole. One slice of the whole pizza would be represented by the numerator "1". Four slices would be represented by the numerator "4".
2
Understand what a decimal number represents. Decimals do not use a slash to indicate what part of the whole they represent. Instead, the decimal point to the left of the numbers signifies that the numbers are below one. With a decimal, the whole is considered to be based on 10, 100, 1000, etc, depending on how many spaces to the right of the decimal the number goes.
- Decimals are also often read in a way that demonstrates their similarity to fractions. For example, 0.05 would commonly be read aloud as "five-hundredths," the same as 5/100. The fraction is represented by the numbers placed to the right of the decimal point.
3

Understand how the fractions and decimals are related. Fractions and decimals are only differing representations of any value that is less than one. The fact that both are used for many of the same things means that you will often need to convert them in order to add, subtract, or compare them.

1
Think of a fraction as a math problem. The easiest way to convert a fraction to a decimal is to read the fraction as if it were a division problem, with the number on the top being divided by the number on the bottom.^[5]
- The fraction 2/3, for example, can also be stated as 2 divided by 3.
2
Divide the numerator of the fraction by the denominator of the fraction. You can do this math problem in your head, especially if the numerator and denominator are multiples of each other, with a calculator, or with long division.
- A simple way to do this is to simply put the divisor (for example, 2 is the divisor in 1 divided by 2) on the bottom and the dividend (1 is the dividend in 1 divided by 2) on top. So, 1 divided by 2 would equal one half (1/2)
3

Double check your math. Multiply the decimal equivalent you got by the denominator of the fraction you started with. You should come up with the numerator of the fraction you started with.

1

Try another way of converting a fraction into a decimal. This will help you to understand the relationship between fractions and decimals, as well as improving your other basic math skills.^[6]
2

Understand power of 10 denominators. A "power of 10" denominator is a denominator consisting of any positive number that can be multiplied to make a multiple of 10. The numbers 1,000 or 1,000,000 are powers of 10, but in most practical applications of this method, you will probably only be using numbers such as 10 or 100.
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Learn to spot the easiest fractions that can be converted. Any fraction that has 5 as the denominator is an obvious candidate, but fractions that have denominators of 25 are just as easily converted. Any number that already has an exponent of 10 as a its denominator will be very easy to convert.
4
Multiply your fraction by another fraction. This second fraction will have a denominator that, when both denominators are multiplied together, creates a multiple of 10. The top of this second fraction (the numerator) will be the same as its denominator. This makes the second fraction equal one.
- It is a basic rule in math that multiplying anything by one does not change its value. This means that when we multiply the original fraction we had by a fraction that is equal to one we are not changing its value, we are simply changing how we represent that value.
- For example, the fraction 2/2 is really just 1 (because 2 divided by itself is equal to 1). If you are trying to convert 1/5 to a fraction with a denominator of 10, you would multiply it by 2/2. The result would be 2/10.^[7]
- To multiply two fractions, simply multiply straight across. Multiply both numerators together and make the result the numerator of the answer. Then multiply the denominators and make the result the denominator of the answer. You will be left with a new fraction.
5
Convert your "power of 10" fraction into a decimal. Take the numerator of this new fraction and rewrite it with a decimal point at the end. Now look at the denominator and count how many zeros are in the number. Next, move the decimal point on your rewritten numerator to the left the number of spaces that are equal to the number of zeros in the denominator.
- For instance, you have the number 2/10. The denominator has one zero. So we start by rewriting "2" as "2." (this doesn't change the value of the number) and then we move the decimal one space to the left. That gives us "0.2".
- You will quickly learn how to do this with all sorts of numbers with easy denominators. After a while, this process becomes pretty easy. You just look for a fraction with a power of 10 denominator (or one that can be readily made into one) and convert the top number into a decimal.

1
Convert some common fractions you use regularly into decimals. You can do this by dividing the numerator by the denominator (the top number by the bottom number), as was done in the first part of this article.
- Some basic fraction to decimal conversions you should know by heart are 1/4 = .25, 1/2 = .5, and 3/4 = .75.
- If you want to convert the fraction really quickly, you can simply use a search engine on the internet to search for the answer. For example, you could type "1/4 decimal" or something similar.
2

Make flashcards with the fraction on one side and it's decimal equivalent on the other side. Practicing these will help you memorize these fraction and decimal equivalents.
3

Recall the decimal equivalents of a fraction from memory. This can be very useful for fractions you use regularly.

Add New Question

Question

How do you turn a mixed number into a decimal?

This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

wikiHow Staff Editor

Staff Answer

First, convert the mixed number into an improper fraction. Multiply the whole number by the denominator, then add the result to the numerator to get the new numerator (e.g., 2 2/3 = 8/3). Divide the numerator by the denominator to get the decimal.
Question

How can I convert a fraction to a percent?

This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

wikiHow Staff Editor

Staff Answer

To convert a fraction into a percent, first convert it into a decimal. For example, ½ = .5. Next, multiply the result by 100 to get a percent. Simply move the decimal point to the right 2 places. For example, .5 x 100 = 50%.
Question

Can you explain things in simpler terms?

To convert a fraction into a decimal, divide the top number by the bottom number.
Question

What about with denominators that don't divide into 10, 100 or 1000, such as 7?

You still divide the denominator into the numerator, no matter what the numbers are. It's likely you would wind up with a quotient consisting of a decimal number.
Question

What is the point of this?

There are many situations in which operating with a decimal number is easier than operating with a fraction.
Question

Can you explain ratios and unit rates?

A ratio is a comparison between two numbers. The ratio 1:2 compares 1 to 2. It is equivalent to the fraction ½. In this case the first number is half the second number (or the second number is twice the first number). A "rate" is a ratio that compares quantities expressed in different units (such as miles and hours). A "unit rate" is a rate in which the second number in the ratio is 1 (such as ten miles per (one) hour).
Question

How do I turn a fraction into a mixed number?

You can turn an improper fraction into a mixed number if the denominator does not divide evenly into the numerator. In this case, the quotient becomes the integer of the mixed number, and the remainder is the numerator of the mixed number. The original denominator remains unchanged. If the denominator divides evenly into the numerator so that there's no remainder, you're left only with a whole number (and thus no mixed number).
Question

What happens if I can't use a calculator, but the number doesn't go into 100 equally, e.g. 7?

You would have to do the division manually, carried out to as many decimal places as needed.
Question

How can I convert 0.625 to a fraction?

0.625 = 625/1000. That reduces to 25/40 and finally to 5/8.
Question

How do I turn 2.072 into a fraction?

That's the same as the mixed number 2 72/1,000, which reduces to 2 9/125.

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Article SummaryX

To convert fractions to decimals, look at the fraction as a division problem. Take the top number, or the numerator, of the fraction and divide it by the bottom number, or the denominator. You can do this in your head, by using a calculator, or by doing long division. For example, ¼ is just 1 divided by 4, or 0.25. After you divide, you can check your work by multiplying the decimal by the denominator to get the numerator. To learn how to convert fractions to decimals using power of 10 denominators, keep reading!

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