Index notation Mathematicians have a special shorthand way of writing some multiplication calculations. The small numbers are called index numbers or powers.

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Presentation transcript:

Index notation Mathematicians have a special shorthand way of writing some multiplication calculations. The small numbers are called index numbers or powers 5x5 can be written as 52 We say 5 to the power of 2 5x5x5 can be written as 53 We say 5 to the power of 3

Checking answers

Squared and Cubed Sometimes to the power 2 is called squared, and to the power 3 is called cubed. So, 4 squared is 42 = 4x4 and has a value of 16 ( because 4x4 = 16) and 4 cubed is 43 = 4x4x4 and has a value of 64 (because 4x4x4 = 64)

Q3 Checking Answers (a) 6 squared is 62 = 6x6 and has a value of …… (b) 10 squared is …..2 = …x…. and has a value of …… (c) 2 cubed is 23 = ….x….x…..and has a value of 8 (d) 5 cubed is ….3 = ….x….x…. and has a value of …..

Powers of 10 Example 102 = 10 x 10 = 100 in words (One Hundred) Checking your Answers (a) 103 = 10 x 10x 10 = ……. in words (One ……………..) (b) 10? = 10 x 10 x 10 x10 = 10000 in words (…………………………) (c) …… = 10 x 10 x 10 x 10 x 10 x 10 = ………………. in words ( one ………...) (d) 105 = ……………………………… = 100000 in words (One Hundred ………...)

You can see from your previous work that Working Backwards Example What number do your square and get 16 ? You can see from your previous work that 42 = 16. So the answer is 4. To save on writing mathematicians use a symbol to stand for “what do you square to get” it looks like this √ or √ and is called the square root. So √16 is “ the square root of 16” and has a value of 4

Checking Answers

Cube roots The symbol 3√ is used for the cube root of a number. For example, 3√8 is the cube root of 8 and has a value of 2 (because 2x2x2 = 8)

Using a calculator Most scientific calculators will have a square root button and cube root button. For most modern calculators you key in the sequence in the order you think about it. For example, to find the value of √6 you would press √ then 6 then = And see 2.449489743

Calculations with numbers in index form 53 is a short way of writing 5x5x5. The calculation 53 x 52 = 5x5x5 x 5x5 = 55 1 If you look closely there is a quick way of finding the answer. 34 x 35 = 3? What number should (?) become ? 2 Explain why.

Division As division is the opposite of multiplication, what do you think the (?) should become in the example below. ? 38 ÷ 33 = 3?