1.2.1 Try some yourself
Activity 3
Without using your calculator, find the following:
(a) 102
(b) 1002
(c) 0.12
(d) 0.012
(e)
(f) (−3)2
(g) (−1)2
Answer
(a) 102 = 10 × 10 = 100
(b) 1002 = 100 × 100 = 10 000
(c) 0.12 = 0.1 × 0.1 = = 0.01
(d) 0.012 = 0.01 × 0.01 =
= 0.0001
(e)
(f) (−3)2 = −3 × −3 = 9
(g) (−1)2 = −1 × −1 = 1
Activity 4
Explain why brackets should be used when writing the expression (−1)2.
Answer
If you write −12 it is not clear whether you mean to square 1 first then make the answer negative, giving −1, or to square −1, giving 1. Many calculators would assume you meant −(1)2, and return the answer −1.
Activity 5
Use your calculator to find the following, using your answers to the appropriate parts of Question 1 as estimates.
(a) 962
(b) 10.652
Answer
(a) Rough check: 1002 = 10 000.
Calculator gives 962 = 9216.
(b) Rough check: 102 = 100.
Calculator gives 10.652 = 113.4225.