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Division Decimals and Rounding Off

Division using decimals is almost the same as Simple Division from an earlier lesson, only the remainder is shown in decimal form rather than a fraction. We will be rounding off the nearest one hundredth place, but you can carry out your division problem as far as you want using this method. Below is an illustration of the process of dividing 8 by 7.

8 divided by 7
  1. Draw out your long division problem adding a decimal in front of the whole number 8, and then putting a decimal on top of the long division sign directly above the decimal in front of the 8. Place 3 zeros in front of the decimal point that you put in front of the 8. We need these because we are going to round off to the nearest one hundredth place Ask yourself, how many times will 7 go into 8 without going over 8? 1 time because 1 x 7 = 7 and 2 x 7 = 14, so put a 1 directly over the 8.
  2. 7x1= 7 so place a 7 under the 8 and subtract.
  3. Bring a 0 down in front of the 1 left from subtracting 7 from 8. Find the number of times 7 will go into 10 without going over and place this number directly above the 0 you just brought down, on top of the long division symbol. 1x7=7, 2x7=14 so the number you want is 1.
  4. 7x1=7, so take 7 away from the 10 created when you brought the 0 down. Bring the next 0 down creating 30.
  5. How many times will 7 go into 30 without going over? 7x1=7, 7x2=14, 7x3=21, 7x4=28, 7x5=35, so 4 times. Put a 4 on top of the long division symbol directly over the last 0 you brought down.
  6. 4x7=28, So subtract 28 from 30 getting 2. Bring down your next 0.
  7. How many times will 7 go into 20 without going over? 7x1=7, 7x2=14, 7x3=21, so 2 times. Write a 2 directly over the last 0 you brought down. Since you are rounding to the nearest hundredths place and 4 is in the hundredths place, look at the number to its right,2. If this number is less than 5, just cross it of and your final answer is 1.14 . If the number to the right of the hundredth place digit would have been 5, 6, 7, 8, or 9 you would cross it off and add 1 to the 4 or hundredth place digit.

Rounding Off Numbers

When we say round off to the nearest hundredth place, only show your answer with 2 places past the decimal point. One place to the right of the decimal point is the tenths place. Two places to the right of the decimal point is the hundredth place. Three places past the decimal point is the thousandths place. Four places past the decimal point is the ten thousandths place and so on. Since we are rounding off to the nearest hundredth place, if the number in the thousandth place is 4 or less cross it off and leave the tenths and hundredth places as they are. If the thousandth place number is 5 or more, add one to the hundredth place.

You can round off to the nearest tenth by carrying your answers out to the hundredth place. If the hundredth place digit is larger than 4 add 1 to the tenth place and drop the hundredth place only showing your answer to the tenth place. If the number in the hundredth place is 4 or less just drop it and leave the tenth place number as it is.

If you want to show your answer rounded to the nearest thousandth place, carry out your problem to the ten thousandth place. If the number in the ten thousandth place is 5 or more add 1 to the thousandth place and drop the ten thousandth place from your answer. If the number in the ten thousandth place is 4 or less just drop it and leave your answer as it is.

Note that .1 is the same value as 1/10., .25 is equal to 25/100 and .789 is equal to 789/1000. You can check this using the method below.

Converting Fractions to Decimals

Many times you will want to know the decimal value of a fraction. To find the decimal value of a fraction, divide the numerator(top number) by the denominator(bottom number). Lets convert 3/5 to its decimal equivalent.

Decimal equivalent of 3/5
  1. 3/5 Means 3 divided by 5. Make your long division symbol. Put 3.000 in it and place a decimal point directly above the one in 3.000 on top of the symbol. Ask yourself how many times will 5 go into 3 without going over. It wont go into 3 so place a 0 over the 3.
  2. 5x0=0 so place a 0 under the 3 and take 0 from 3. Bring your next 0 down.
  3. How many times will 5 go into 30 without going over. 5x6=30. Place a 6 over the last 0 you brought down.
  4. 5x6=30 so place 30 under the 30 in the long division problem and then take it away. There isn't anything left over so your final answer is .6.

Sometimes you may want to convert a decimal to a fraction with a specific denominator. Tape measures usually have 1/16 and 1/8 inch graduations on them. When we calculate things to build we sometimes have decimal answers. Say you come up with .3125 inches. You can convert to 1/16 inches by simply multiplying 16 times .3125 and placing the product over 16. .1325 X 16 = 5, So .1325 inches is 5/16 of an inch. You can check it by converting 5/16 back to a decimal. The same thing works for eighth or any denominator you need.

The answer to a division problem is called the quotient. The number that you are dividing is called the dividend. The number that you divide the dividend by is called the divisor.

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  14. You are here. Division and Decimals and Rounding Off
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Copyright 2008 Robert Lee Thomas

18218 Fewins Rd. Interlochen, MI 49643

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