
Place value
Place value is the basis of our number system. The position of
a digit gives it its value.
The digits further to the left have larger values than those to
the right.
E.g. 234
The 2 is in the 'hundreds' column, and has the value of 200.
The 3 is in the 'tens' column, and has the value of 30.
The 4 is in the 'units' column, and has the value of 4.
Decimals
Decimals are a continuation of the number system, and the decimal
point marks the change from whole numbers to fractions.
E.g. 6.49
6 is in the 'units' column, and has a value of 6.
4 is in the 'tenths' column, and has a value of 4/10.
9 is in the 'hundredths' column, and has a value of 9/100.
Placing
numbers in order of size
When comparing the size of two numbers, we always look at the
digits furthest to the left.
E.g. Which is bigger, 135 or 137?
| hundreds |
tens |
units |
| 1 |
3 |
5 |
| 1 |
3 |
7 |
The numbers in the 'hundreds' and 'tens' columns are the same,
but when we compare the 'units' column, we see that 7 is bigger
than 5. Therefore, 137 is bigger than 135.
E.g. Which is bigger, 4.2 or 4.07?
| units |
|
tenths |
hundredths |
| 4 |
. |
2 |
|
| 4 |
. |
0 |
7 |
The numbers in the 'units' columns are the same, but when we compare
the 'tenths' column, we see that 2 is bigger than 0. Therefore,
4.2 is bigger than 4.07.
Negative Numbers
Positive numbers are greater than 0.
Negative numbers are less than 0.
-6 -5 -4 -3 -2 -1 0
1 2 3 4 5 6
We
always count away from 0, so 6 is greater than 4, but -6 is less
than -4.
E.g. Place the numbers 5, -7, -2, -5, 1 in order of size, smallest
first.
-7, -5, -2, 1, 5
|