Mathematics

Decimal Equivalent Find Fraction



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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

2. By long division: Knowing we will divide the numerator by the denominator we automatically know that we will divide with 5 as the dividend and 8 as the divisor. Draw the table and place 8 on the outside with 5 on the inside. Immediately you will see that you cannot simply divide 5 by 8 until you add a decimal point to the right of 5, making it (5.0). Place the decimal point ON the table exactly above where it is placed IN the table. Remember, when you first place a zero IN the table, you must place the decimal place ON the table in the same place. Now you are ready to do your division. 5.0 divided by 8 equals (0.6). Place 6 to the right of the decimal point on the table. Enter the product of 6 x 8 = 48 below the 50. Subtract to find a remainder of 2. You can see that if you added another zero into the hundreds place and brought down your zero to the 2, that you would have 20 which is also divisible by 8. Twenty divided by 8 equals 2. Write the 2 next to the 6 for a quotient of (0.62). Multiply the 2 by 8 (equals 16) and subtract the 16 from the 20, leaving 4. Place another zero in the thousandths place and bring down the zero to the 4, making 40 and divide again. 40 divided by 8 equals 5. Enter 5 above the zero. The answer is 0.625 with no remainder. Remember that you have moved to the right of the decimal point and added zeros. No matter how many zeros you add to the right of 5.0, the number 5 stays as 5 and does not increase. Every zero added to the right of the 5 only increases the number of tens places in the answer. Your first zero started the answer in the tens place: 6 tenths. The second zero increased the answer into the hundredths place: 62 hundredths. The last zero increased the answer into the thousandths place: 625 thousandths. The quotient by long division is (0.625). Using long division to find a decimal will NEVER give you a remainder. You can keep adding zeroes in the tens places and go on dividing almost to infinity! Generally, adding the total number of numerals in the problem will be equal to the number of decimal places in the answer. Here we begin with 8 and 5.0, which will give us three decimal places.

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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