1. Powers and expanded notation
Index Notation
Powers and expanded notation

2. Index notation is a short way of writing a number being multiplied by itself several times.
For example – instead of writing 4 x 4 x 4
we can write 43
Index notation

3. The number that is being multiplied by itself is known as the 'base'.
The number written above the base is known as the 'index' or the 'power'.
The index is the number of times that the base must be multiplied by itself
Index notation

4. Powers of ten Place value and index notation
Indices can also be useful when writing large numbers. For example, each column of a value table can be expressed in powers of 10 by using index notation:
Powers of ten

5. Expanded notation
We can use the index notation above when writing numbers in expanded notation.
Writing a number in expanded notation means breaking that number up in relation to its value to the power of 10. For example:
In expanded notation, the number would be written as
3 X X X X X X X 1
Alternatively the number can be written using index notation:
(3X106) + (6X105) + (5X104) + (7X103) + (4X102) + (2X101) + (8X100)
Expanded notation

6. Expanded notation Expand these using powers of ten– 4 562 056 203 890
Expanded notation

7. Expanded notation Solve these –
(4X106) + (2X105) + (5X104) + (1X103) + (4X102) + (7X101) + (5X100)
2. (1X106) + (6X105) + (2X104) + (4X103) + (0X102) + (5X101) + (9X100)
Expanded notation