Index Notation Powers and expanded notation Index notation

Index Notation Powers and expanded notation

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

�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

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

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 3 657 428 would be written as 3 X 1 000 + 6 X 100 000 + 5 X 10 000 + 7 X 1 000 + 4 X 100 + 2 X 10 + 8 X 1 Alternatively the number can be written using index notation: (3 X 106) + (6 X 105) + (5 X 104) + (7 X 103) + (4 X 102) + (2 X 101) + (8 X 100) Expanded notation

Expand these using powers of ten– 4 562 056 2. 203 890 3. 1 222 118 1. Expanded notation

Solve these – 1. (4 X 106) + (2 X 105) + (5 X 104) + (1 X 103) + (4 X 102) + (7 X 101) + (5 X 100) 2. (1 X 106) + (6 X 105) + (2 X 104) + (4 X 103) + (0 X 102) + (5 X 101) + (9 X 100) Expanded notation