1(a) Use your calculator to evaluate the following expression:

$$ {45.8^2 \times \sqrt{940.5} \over 9.64 + 0.02} $$

Write down the first five digits on your calculator display.

Answer: $ 6 \phantom{.} 659.3 $

1(b) Round off your answer in part (a) to two significant figures.

Answer: $ 6 \phantom{.} 700 $

2. By first rounding each term in the following expression to 2 significant figures,

$$ {403.2 \times \sqrt{50.15} \over 1.95^2} $$

estimate the value of the expression, leaving your answer in 2 decimal places.

Answer: $ 707.11 $

Solutions

3. Hebe measures her height, rounds it to 3 significant figures and records her height. The recorded height is $1.60$ m.

(a) State the smallest possible value of Hebe's actual height.

Answer: $ 1.595 \text{ m} $

(b) State the largest possible value of Hebe's actual height.

Answer: $ 1.605 \text{ m} $

(c) Complete the following inequality to show the range of her actual height, $h$:

$$ \text{………} \le h < \text{………} $$

Answer: $ 1.595 \le h < 1.605 $

4. Sarah is going to a trip to the United Kingdom. She has $ \$ 1200 $ in her savings account, rounded off to the nearest $ \$ 100 $. The exchange rate is fixed is $ \$ 1 = \text{£} 0.58 $.

A pre-booked tour in the United Kingdom costs $ \text{£} 670 $. Sarah says, "I have plenty of money because $1200 \times 0.58 = 696$." Explain, with calculations, why Sarah might actually be unable to afford the tour.

Solutions