# 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.