 Mathematics

# Decimal Equivalent Find Fraction Elizabeth Pierce Ritz's image for:
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Image by: Converting a fraction into a decimal can be done in one of four ways. First there are a few easy rules about decimals to remember. As a refresher:

1. Any number to the right of a decimal is less than 1 (one). 2. To the right of the decimal, each place is a multiple of ten. 3. From the decimal point and moving right, the places are the tens, hundredths, thousandths, ten thousandths and so on. 4. Adding zeros to the right of any decimal neither increases nor decreases the number. 5. To the left of the decimal, any numbers are whole numbers. Increasing a number to the left of the decimal point increases the whole number. 6. A fraction is a numerator with a slash or bar under it and the denominator below the slash or bar. An easy way to remember that the denominator is under the numerator is to think of the denominator as a dominating number, usually larger than the number on top of it. 7. You will always divide the numerator by the denominator in converting a fraction into a decimal, unless you use the tens system. The tens system is logical and methodical. With easy memorization, it is a much simpler way to convert a fraction into a decimal.

Recall that a proper fraction is a number less than one. An improper fraction is a number greater than one, in fraction form. Both types of fractions can be converted to a decimal in the same ways.

Below are examples of the same proper fraction converted into a decimal, using four different techniques. We will use a simple fraction, 5/8, in each example.

1. By calculator: We know at first glance that 5/8 is less than one, so immediately we know to divide the numerator 5, by the denominator 8. Using the calculator simply enter 5, enter the divide sign, enter 8 then enter the equals sign. 5/8= (0.625). Again, what you have done on your calculator is divide the numerator by the denominator. The quotient found by calculator is 0.625

3. By working with the tens: Decimals work in equivalent to tens, because the first position after the decimal is the tens position, and multiples of tens follow each successive position. Working with tens, in step one you would do long division in the tens system. In this case you would use 100-a multiple of 10-as the dividend, with 8 as the divisor. Your quotient is (12.5). In step two, move the decimal to the left of the quotient according to the the number of zeroes in the dividend. (In this case the dividend is 100, which has two zeroes and requires two places to the left of the quotient). So 12.5 becomes (0.125). In step three, you multiply that quotient (0.125), by the numerator 5, to find the product (0.625). In this case, in step one, you will want to know how many times 100 can be divided by the divisor 8; dividing 100 by 8 equals (12.5). Since you have used two zeros in your division, in step two you will move your decimal in the quotient two spaces to the left. Now your answer is 0.125 for 1/8. You want to know 5/8, so in step three, you would multiply 0.125 by (5). By working with tens your product is (0.625).

4. By memory using tens: Converting fractions to decimals is easiest if you simply commit to memory how many times 100 can be divided by each number from 2 to 9. Then convert the quotient to a decimal by placing a decimal point two places to the left. Multiply this decimal by the numerator. Working by memory this way is the fastest way to reach your answer. It is the most methodical and orderly for the brain. For this reason, correctly done, it is the fastest way to find a decimal from a fraction.  Examples of 100 divided by units 2 through 9, with decimals placed to the left of the quotient are:

100 divided by 2= 0.50; 100 divided by 3= 0.33; by 4= 0.25; by 6= 0.166; by 7= 0.142; by 8= 0.125; by 9= 0.111  Using memory that 1/8 equals 0.125, then 5/8 is found by simply multiplying 0.125 by 5 for a product of (0.625).

What about 1,000 or 1,000,000 as divisors? It doesn't change! 1,000 divided by 2 equals 500. Then we move the decimal by how many places? Yes, we move the decimal three places because we have 3 zeroes! Move the decimal 3 places to the left and you have (0.500). And 0.500= 0.50= 0.5! So you see that memorizing using tens with 100 as the divisor is the easiest way, in the tens system, to find that decimal equivalent from a fraction. When you give it further thought, the case for working with tens, only requires memorizing eight divisions of 100: (2-9).

Converting fractions into decimals is fun and easy. Fractions to decimals can be used, for instance, to convert dollars into cents or driving time into increments of travel miles. It is a dynamic process that we use every day to provide clarity and understanding to the world around us.

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