Number Toolkit

Number

Place value is the value a digit carries because of where it sits in a number
Each column is worth ten times the column immediately to its right
In 5 273, the digits are worth 5 thousands, 2 hundreds, 7 tens and 3 ones
The value of a digit is the digit itself multiplied by its column heading
- The 2 in 5 273 is worth 200, not 2
Large numbers are written with a thin space every three digits, counting leftwards from the ones column
- 41276309 is written 41 276 309
Reading in words follows the same grouping: 41 276 309 is forty-one million, two hundred and seventy-six thousand, three hundred and nine

The decimal point separates two parts: whole units sit to its left, and fractions of a unit to its right
The columns after the point are tenths, hundredths, thousandths, and so on
In 8.407, the 4 is worth 4 tenths, the 0 is worth 0 hundredths and the 7 is worth 7 thousandths
A decimal is read digit by digit after the point: 8.407 is read as eight point four zero seven
Zeros between the point and a non-zero digit are not optional, because they hold the later digits in their columns
- 0.07 and 0.7 differ by a factor of ten

Worked example

Reading a large number

Write 6 208 034 in words, and write down the value of the digit 2.

Solution:

Group the digits in threes from the right: 6 | 208 | 034
The groups are millions, thousands and ones
In words: six million, two hundred and eight thousand and thirty-four
The 2 sits in the hundred-thousands column, so its value is 200 000
The zeros are not optional: they hold the 8 in the thousands column and the 3 in the tens column