Fractions and decimal numbers are simply two ways of representing numbers below unity. Since numbers smaller than 1 can be expressed with both fractions and decimals, there are specific mathematical equations that allow you to calculate the fractional equivalent of a decimal and vice versa.
Steps
Part 1 of 4: Understanding Fractions and Decimals
Step 1. Know the parts that make up a fraction and what they represent
The fraction is made up of three parts: the numerator, which is located in the upper part, the fraction line which is interposed between the two numbers, and the denominator which is located in the lower part.
- The denominator represents how many equal parts there are in the whole. For example, a pizza can be divided into eight slices; the denominator of the pizza will then be "8". If you divide the same pizza into 12 slices, then the denominator will be 12. In both cases you expressed the whole, although divided into a different number of parts.
- The numerator represents the part, or parts, of a whole. A slice of our pizza would be represented with the numerator equal to "1". Four slices of pizza would be indicated with "4".
Step 2. Understand what a decimal number represents
This does not use the fraction line to indicate which part of the whole it represents. In its place, the decimal point is written to the left of all numbers under the unit. With a decimal number, the integer is considered in base 10, 100, 1000 and so on, depending on how many digits are written to the right of the comma.
Furthermore, decimals are often pronounced in a way that demonstrates their affinity with fractions; for example the value 0.05 is often pronounced as "five cents" just like 5/100. The fraction is represented by the numbers written to the right of the decimal point
Step 3. Understand how fractions and decimals relate to each other
Both are the expression of a value lower than unity. The fact that both are used to define the same concept makes it necessary to convert them in order to add, subtract or compare them.
Part 2 of 4: Converting Fractions to Decimals with Division
Step 1. Think of the fraction as a math problem
The simplest way to convert a fraction to a decimal number is to evaluate it as a division where the top number (numerator) must be divided by the one below (denominator).
The fraction 2/3, for example, can also be thought of as "2 divided by 3"
Step 2. Proceed to divide the numerator by the denominator
You can do this in mind, especially if the two numbers are a multiple of the other; alternatively you can use a calculator or proceed with a division by column.
Step 3. Always check your calculations
Multiply the equivalent decimal by the denominator of the starting fraction. You should get the numerator of the fraction.
Part 3 of 4: Converting Fractions with a "Power of 10" Denominator
Step 1. Try another method of converting fractions to decimals
This allows you to understand the relationship that exists between fractional and decimal numbers, as well as improve other basic math skills.
Step 2. Understand what a power denominator of 10 is
The term "power of 10" indicates a denominator represented by a positive number that can be multiplied to obtain a multiple of 10. The numbers 1000 and 1,000,000 are powers of 10, but in most practical applications of this method you will be dealing with values like 10 and 100.
Step 3. Learn to recognize the easiest fractions that can be converted with this technique
Obviously all those with the number 5 in the denominator are perfect candidates, but even those with a denominator equal to 25 are easily transformable. Furthermore, all fractions showing a value with exponent 10 as denominator are easy to convert.
Step 4. Multiply the starting fraction by another fraction
The second must have a denominator which, when multiplied by the denominator of the original fraction, generates a multiple product of 10. The numerator of this second fraction must be equal to the denominator. This "trick" makes the fraction equal to the value 1.
- Multiplying any number by 1 means obtaining a product equal to the starting number: it is a simple basic mathematical rule. This means that when you multiply the first fraction by the second (which is equivalent to 1) then you are simply changing the graphic expression by an identical value.
- For example, the fraction 2/2 is equivalent to 1 (because 2 divided by 2 gives 1). If you want to convert the fraction 1/5 to one with a denominator 10 then you need to multiply it by 2/2. The resulting product will be 2/10.
- To multiply two fractions, just perform the operation in a straight line. Multiply the numerators together and write the result as the numerator of the final fraction. Repeat the same process for the denominators and write the product as the denominator of the final fraction. At this point you have obtained a fraction equivalent to the starting one.
Step 5. Convert the "power of 10" fraction to a decimal value
Take the numerator of this new fraction and rewrite it with the decimal point at the bottom. Now look at the denominator and count how many zeros appear. At this point, move the decimal point of the numerator you have rewritten to the left by as many spaces as there are zeros in the denominator.
- For example, consider the fraction 2/10. The denominator shows only one zero. For this reason write the numerator "2" as "2," (this does not change the value of the number) and then move the comma one decimal space to the left. Eventually you will get "0, 2".
- You will learn very quickly to apply this method to all the fractions that have a “favorable” denominator; after a while you will find that it is a very easy mechanism. Look for a fraction that has a denominator as a power of 10 (or one that can be easily converted this way) and turn its numerator into a decimal value.
Part 4 of 4: Memorizing the Important Equivalent Decimals
Step 1. Convert some very common fractions that are regularly used as decimals
You can do this by dividing the numerator by the denominator (the number above the fraction line by the number below the fraction line), as described in the second part of this article.
- Some of the fraction to decimal conversions you should know by heart are: 1/4 = 0.25; 1/2 = 0.5; 3/4 = 0.75.
- If you want to transform fractions very quickly, you can use your internet search engine and find the solution. For example just type the words "1/4 to decimal" or something similar.
Step 2. Make flashcards with the fractional number on one side and the decimal equivalent on the other
Practice with these to memorize equivalences.
Step 3. Remember the decimal equivalents of fractions
It will be very useful for those fractions you use often.
