Try some yourself
Activity 40
Without using your calculator, find the following.
(a) 75.6 ÷ 0.6
(b) 75.6 × 0.6
(c) 100.001 + 75.6 ÷ 0.6
(d) (100.001 + 10.1) × 60
Answer
(a)
(b) 75.6 × 0.6 = 75.6 × = 7.56 × 6 = 45.36.
(c) Carrying out the division first, use the result of part (a) to give:
100.001 + 75.6 ÷ 0.6 = 100.001 + 126
= 226.001.
(d) Carry out the addition in brackets first:
(100.001 + 10.1) × 60 = 110.101 × 60 = 1101.01 × 6 = 6606.06.
Activity 41
Try dividing 10 by 3, first without using your calculator, and giving your answer as a decimal. What is the difficulty? What answer does the calculator give?
Answer
10 ÷ 3 gives
and so on.
Each time you divide by 3 you get a remainder 1, which gives 10 in the next column, so the decimal carries on forever. This is called a recurring decimal, because the 3 recurs repeatedly.
A scientific calculator gives 3.333333333 (it rounds to 10 digits).
Activity 42
Is the following statement true or false?
Multiplying one number by a second number always gives an answer greater than the first number.
Answer
False. For example, multiplying 7.9 × 0.8 in Activity 38(a) gave 6.32, which is less than 7.9. In general multiplying a positive number by a number less than one gives a smaller number.