Adding and Decimals

Adding with decimals works just like adding multiple digits in the Adding with Multiple Digits exercises except now there is a decimal point and place values to the right of the one's place value. The decimal point marks the point where the whole part of the number stops and the fractional part of the number beggins.

One place value to the right of the one's place value shows the number of tenths of one. Two place values to the right of the one's place shows the number of one hundredths. The place value of a digit to the right of the one's place value or decimal point can be found by counting how many places to the right of the decimal point it is then multiplying 10 times itself that many times and placing the digit you are looking at over the product in the form of a fraction. Check out the number 3.14159265. We have 3 ones plus the .14159265 part. .1 is one place value to the right of the decimal point and so is equal to 1/10X1 or 1 divided by 10 which is 1 tenth. the 4 is 2 places to the right of the decimal point and has a value of 4/10X10 or 4 one hundredths(4 divided by one hundred). The 1 that comes after the 4 is 3 places to the right of the one's place value or decimal point and is equal to 1/10X10X10 or 1 one thousandth(1 divided by 1000). The 5 is 4 places right of the decimal point so its value is 5/10X10X10X10 or 5/10,000 or 5 ten thousandths. The 9 is 5 places to the right of the decimal point and has a value of 5/10x10x10x10x10 or 5 hundred thousandths. You can see the pattern so i won't go through the rest of the number.

In Homemade Math's Adding Decimals exercises, i only go out to the hundredth place but you can solve any decimal addition problem with the same method. Put the numbers to be added one on top of the other making sure to line up the decimal points. Bring your decimal point down and place it directly under the decimal points in the numbers being added. Now add the numbers the same way you did in the Adding Multiple Digits exercises. If a number doesn't show a hundredth or tenth place value just use 0 for that value. Make sure and put your decimal point in the answer or sum directly in line wth the numbers you are adding. You can just ignore the decimal point until you have finished adding and then put it in. A stack of numbers to be added are called addends.

OK we should look at what is meant by 1/10 (one thenth) and 1/100 (one one hundredth) or .1 (point one) and .01 (point zero one). In the 1/10 value we have 1 broke up in 10 equal pieces and .1 represents one of those pieces.

Above 1.0 is shown graphically by a box made up of 10 equal boxes all colored in representing the 1 and a box of 10 empty boxes representing the .0. Next 1.1 is shown with the .1 part of the number represented by a box of 10 equal size boxes and one of them being colored in. .2 Is shown by a box of 10 equal size boxes and 2 of them are colored in. .3 Or point three would be shown by ten boxes and three of them being colored in. If we continue adding .1 to the box representing tenths we will eventually have 10 full boxes. At this point we have one full box and add 1 to the ones place and change the tenths box back to 10 empty boxes or 0(zero).

Now if we take one of the ten boxes that make up the tenths place and divide it up into 10 equal boxes, each of these little boxes will be a one hundredth. If we put 10 of these little boxes of 10 together we have a box of 100 little boxes and if all these are filled we have one. Now imagine we have the box that was one of the ten tenth place boxes and it is divided into 10 equal boxes like the middle picture above. Each one of these boxes is 1/100 of one and each of these little boxes is 1/10 of a one of the 10 boxes that make up the tenth place box. If we add .01 and color in a box representing hundredth's as the middle picture above and keep adding .01 until we have all the hundredth boxes filled in then we have one full tenth and add one to the tenth boxes and change the hundredth boxes all back to empty or 0. You should see the pattern .1 is one tenth of one. .01 is one tenth of .1. .001 is one tenth of .01 and so on. Each decimal place to the right represents a tenth the value to its left. This is why we can just line up our decimal points in a column of numbers to be added and start adding from the far right and each time we reach a value of 10 or greater in a column, put the one's part under that column and carry the higher place value or values to the next column of digits to the left. Note that i said to carry the higher place value or values to the next column of digits to the left. Most of the time you only have to carry the ten's part but if you add large columns of numbers like 99 added to itself 12 times you add the far right column of 9s and arrive at a sum of 108. Put the one's part, 8 under the far right column of 9s. Carry 10 to the top of the next column to the left add and arrive at a sum of 118. Since there are no more columns to add, 118 goes under the ten's place column for a final sum of 1188.

I had to throw this in in case you become an accountant or something.

You can use the Scrathpad in Hmemade Math to solve decimal addition problems like the screenshot from the game above.