Decimals are numbers written using 10 as the
base. Each position of the decimal number represents a power of 10
and the decimal point, the period '.', is used to indicate how the
powers of ten advance as you move away from the decimal.
So, a decimal number is written like
this: +/- D---.d---
I used '-'s to indicate zero or more Ds or ds,
the '+' is normally omitted if the decimal is a positive number.
1034.9123, -0.15, -156.2
We speak of positions or place holders for
each number to the left or to the right of the decimal
point. I will use letters to name the position to which
I refer in what follows.
Consider the decimal
The decimal point is located between the
positions marked with the letters 'A' and 'a'.
The numbers 0,1,2,3,4,5,6,7,8,9 are used to
"fill" these positions and name the number of 1s, 10s, 100s, ..., 1/10s,
1/100s, 1/1000s, etc.
As we move left from the
decimal point, A represents the number of 1s, B the number of 10s, C the number
of 100s, D the number of 1,000s, and E the number of 10,000s.
As we move right from the
decimal point, a represents the number of 1/10s, b the number of 1/100s, c the
number of 1/1000s, d the number of 1/10,000s, and e the number of
Example: 325.16 means:
3 * 100 + 2 * 10 + 5 * 1 + 1 * 1/10
+ 6 * 1/100
0.125 means: 0 * 1 + 1*
1/10 + 2 * 1/100 + 5 * 1/1000
-2.93 means: -2 * 1 + -9 * 1/10 + -3
NOTE how the negative sign moves through the
When adding/subtracting decimals, write the
decimals one per line, lining up the decimal points and write zeros for
missing place values. Then perform the operations in the normal way.
Example: 3.56 + 206.1
Example: 0.0101 + 100.0
Example: 27.52 -
Example: 3.0025 - 27.52
In this example recall how to add
mixed-signed numbers when the negative number is larger in magnitude than
the positive number: Subtract the smaller magnitude from the larger
magnitude then add the negative sign to the result.
So we have:
24.5175 now add the negative sign and
as the answer!