Decimals

Working with decimal numbers is no different than working with whole numbers.

Addition and Subtraction:

1. 13.020 + 6.105

   line up the decimal points then add:

   13.020

    6.105

   --------

   19.125

    

2. 105.1 - 76.9

   line up the decimal points then subtract, borrowing as needed

   105.1

   -76.9

   ------

    28.2

    

3. 26.54 + 1.0034

   25.5400             “spaces imply zeros”

     1.0034

   ---------

   26.5434

    

4. 14.9 – 254.164

   254.164             “as with integers,

   - 14.900             “subtract magnitudes then take sign of larger”

   ---------

   239.264 ----> - 239.264

Multiplication:

Ignore the decimals, carry out the multiplication, then count the number of decimal places in the original numbers and move that many places from the right in the result to place its decimal point.

Examples:

1. 3.2 * 4.12                  “ 1 + 2 decimal places = 3 decimal places”

   32 * 412 = 13184         Now moving from the right to the left we get:

   13.184

   This makes sense, ignoring the fractional parts of the original numbers, multiplying gives 3 * 4 = 12, which is slightly less than 13.184. If we rounded each up 4 and 5 respectively, then

   4 * 5 = 20.

   We then expect the result to lie between 12 and 20, and since the fractional parts of each are small (2/10 and 12/100) the answer must be closer to 12 then 20.

    

2. 0.00092 * 2.09

   92 * 209 = 19228 we have, 5 + 2 decimal places --> 7 decimal places

   so we need to 0s in front to give us 7 digits .0019228, and it is customary to write this result as 0.0019228 (perhaps, just to make the decimal point easier to see.)

Division:

Convert the divisor into an integer by moving its decimal point to the right of its last digit. Now move the dividend's decimal point the same number of places, then carry out the division. The decimal point in the quotient will be directly above the decimal point in the dividend.

Let's have a look at an example.

Example: