Indices Learning Outcomes

Transcription

1 1 Indices Learning Outcomes Use and apply rules for indices: a p a q = a p+q ap aq = ap q a p q = a pq Use the notation a 1 2 Express rational numbers 1 in the form a 10 n, where a is a decimal and n is a natural number. (Use Scientific notation).

2 2 2 is the base 5 is the power or exponent Recall that multiplication represents repeated addition. e.g = 5 2 Indices are used to show repeated multiplication: e.g = 2 5 e.g. write the following numbers using indices: a) b) c) d) e) 5

3 3 e.g. Write out the following indices as numbers multiplied by themselves: a) 2 3 b) 7 2 c) 8 5 d) 9 4 e) 4 1 f) 5 10

4 4 Recall that adding and subtracting are opposites, and that multiplying and dividing are opposites. The opposite of an index is a root. e.g. 7 2 is seven squared, 7 is the square root of seven. e.g. Use a calculator to find the values of the following: a) 4 b) 9 c) 36 d) e) 5 2 f) g) h) i)

5 5 What happens when numbers in index form are multiplied? e.g. What is in index form? e.g. What is in index form? In general, what do you do to the power when multiplying numbers in index form? a p a q = a p+q

6 6 a p a q = a p+q Write the following in index form using the rule for adding powers: a) b) c) d) e) f) y 4 y 2 g) z 3 z 10 z 3

7 OL P1 Q3 The table shows the values when 2 is raised to certain powers. Complete the table. Maria wins a lottery and is given two options: Option A: 1000 today Option B: 2 today, 4 tomorrow, 8 the next day, doubling every day for 9 days. Which is the better option? Power of 2 Expanded Power of 2 Answer

8 8 What happens when numbers in index form are divided? e.g. What is in index form? e.g. What is in index form? In general, what do you do to the power when dividing numbers in index form? ap aq = ap q

9 a p 9 = ap q aq Write the following in index form using the rule for subtracting powers: a) b) c) d) e) f) y 4 y 2 z 3 z 10 g) h) i) j) k) l) y 3 y 8 y 5 z 4 z 2 z 9 z 3 z 4

10 OL P1 Q OL P1 Q2 Simplify a7 a 4 n N. Simplify a9 a 5 n N. a 3 a 2, giving your answer in the form an, where a 6 a 2, giving your answer in the form an, where

11 11 What happens when numbers in index form are raised to a power? e.g. What is in index form? e.g. What is in index form? In general, what do you do to the power when raising a number in index form to a power? a p q = a p q

12 12 a p q = a p q Write the following in index form using the rule for multiplying powers: a) b) c) d) e) f) y 4 2 g) z

13 OL P1 Q2 Using a calculator or otherwise, find the exact value of OL P1 Q2 i. Write a 3 2 in the form a n, n N. ii. Using your answer from (i) or otherwise, evaluate (S) LC OL P1 Q2 Show that a a 3 a 4 simplifies to a

14 14 Use Scientific Notation Scientific notation splits up the size of a number from its digits. It is used to show very large and very small numbers. e.g is a very long number. Scientific notation takes its first few digits (123 ) and makes it a decimal (1.23) It also takes its size (16 digits long) and makes it a power of ten (10 15 ) the power is 1 less than the number of digits. So is written in scientific notation, which is shorter.

15 15 Use Scientific Notation To enter scientific notation mode on a CASIO, press [SHIFT], [SET UP], [7:Sci], [3] (the last one is how many digits you want). To leave scientific notation mode on a CASIO, press [SHIFT], [SET UP], [8:Norm], [1]. e.g. enter scientific notation mode on your calculator and write the following numbers in scientific notation: a) 300 b) c) d) e) 0.2 f) g) h) 2

16 16 Use Scientific Notation

17 OL P1 Q OL P1 Q OL P1 Q2 2011(S) LC OL P1 Q2 Use Scientific Notation Using a calculator or otherwise, multiply 65.5 by 40 and express your answer in the form a 10 n, where 1 a < 10 and n Z. Using a calculator or otherwise, multiply 54.5 by 60 and express your answer in the form a 10 n, where 1 a < 10 and n Z. Using a calculator or otherwise, divide 1120 by and express your answer in the form a 10 n, where 1 a < 10 and n Z. Express 2 24 the form a 10 n, where 1 a < 10 and n Z.