Topics covered within this unit: 19.1 Index (scientifi c) notation
19.2 Multiplying variables with powers
19.3 Dividing variables with powers 19.4 A power on a power 19.5 Square root of a number
The Learning Outcomes covered in this unit are contained in the following sections:
N.1c.I N.1c.II N.1f
Key word Square root
An Base 10n Base Power Power
Indices
Something to think about …
Atoms are extremely small particles. The number of atoms of carbon in 12 grams of carbon is equal to 602 214 085 700 000 000 000 000
It’s diffi cult to write this number when doing calculations. Can you write this number in another way?
19.1 Index (scientifi c) notation
By the end of this section you should: ● be able to write numbers in index notation
In Section A of this book, we were introduced to indices.
Recall, 5 3
means 5 × 5 × 5 = 125
It means: 5 is used 3 times in the multiplication In words: 5 3
84 = 8 × 8 × 8 × 8 = 4 096 In words: 8 4 could be called ‘8 to the power 4’. Powers of 10
‘Powers of 10’ is a very useful way of writing down large or small numbers.
Instead of having lots of zeros, you show how many powers of 10 will make that many zeros. Example: 5 000 = 5 × 1 000 = 5 × 10 × 10 × 10 = 5 × 10 3
Scientists and engineers (who often use very big or very small numbers) like to write numbers this way. It is commonly called scientifi c notation, or index notation.
could be called ’5 cubed’ or ‘5 to the power 3’.
Recall from Section A: The exponent (or index or power) of a number says how many times to use the number in a multiplication.