Numbers
1. Numbers
1.2. Whole numbers and place value
Whole numbers are positive numbers (upwards from and including 0), which have no decimal or fractional elements. For example: 0, 5, 13, 128.
The number of digits used, and the place value of each, tells us the value of that number.
A table with appropriate headings can be a useful aid to understanding place values.
Starting on the right, and working from right to left, the headings in this table represent units (U), Tens (T), Hundreds (H), Thousands (Th), Ten-Thousands (TTh), Hundred-Thousands (HTh) and Millions (M).
| M | HTh | TTh | Th | H | T | U |
|---|---|---|---|---|---|---|
| 1 | 0 | |||||
| 2 | 6 | |||||
| 3 | 4 | |||||
| 1 | 0 | 0 | ||||
| 4 | 6 | 0 | ||||
| 1 | 0 | 2 | 2 | |||
| 4 | 2 | 6 | 5 | 0 | ||
| 3 | 4 | 0 | 5 | 4 | 6 | |
| 2 | 6 | 3 | 2 | 0 | 0 | 0 |
Units
A single digit is used to represent a value from 0 (zero) to 9 (nine).
Tens
Two digits are used to represent values from 10 (ten) to 99 (ninety-nine), with the digit on the right representing units and the digit to its left representing multiples of ten.
- 10 (ten): 1 ten and 0 units
- 26 (twenty-six): 2 tens and 6 units
- 34 (thirty-four): 3 tens and 4 units
Hundreds
Three digits are used to represent values from 100 (one hundred) to 999 (nine-hundred and ninety-nine), with the place values from left to right representing hundreds, tens and units.
- 100 (a hundred): 1 hundred, 0 tens and 0 units
- 460 (four hundred and sixty): 4 hundreds, 6 tens and 0 units
Larger numbers
Using further digits, we can represent increasingly larger values.
- 1 022 (One thousand and twenty-two): 1 thousand, 0 hundreds, 2 tens and 2 units
- 42 650 (forty-two thousand, six hundred and fifty): 4 ten-thousands, 2 thousands, 6 hundreds, 5 tens and 0 units
- 340 546 (three hundred and forty thousand, five hundred and forty-six): 3 hundred-thousands, 4 ten-thousands, 0 thousands, 5 hundreds, 4 tens and 6 units
- 2 632 000 (two million, 6 hundred and thirty-two thousand): 2 millions, 6 hundred-thousands, 3 ten-thousands, 2 thousands, 0 hundreds, 0 tens and 0 units
Note: Small spaces, or commas inserted between groups of three digits, working from right to left, aid the reading of larger numbers.
Rounding whole numbers
Rounding whole numbers involves simplifying them to the nearest defined place value, for example to the nearest Ten, Hundred, or Thousand.
This is useful for estimating, giving an approximate number, which can be easier to picture and quicker to work with.
For example, rounding 227 to the nearest 10, would make it 230. As 7 is closer to 10, it has been rounded up. If, however, the unit was less than 5, it would be rounded down. For example, 223 would become 220.
Rounding and estimating are covered in more detail in the final page of this book.