E Maths Revision Notes >>
Approximation and estimation
Significant figures
Rules:
1. Non-zero digits are significant, i.e. $25.39 \text{ (4 s.f.)}$
2. Zero(s) between non-zero digits are significant, i.e. $10 \phantom{.} 005 \text{ (4 s.f.)}$
3. Zero(s) before non-zero digits are not significant, i.e. $0.012 \text{ (2 s.f.)}$
4. Zero(s) following a non-zero digit after the decimal point are significant, i.e. $12.100 \text{ (5 s.f.)}$
5. In an integer, zero(s) after a non-zero digit may be significant, i.e. $1500 \text{ (2 or 3 or 4 s.f.)}$
$ 1499.8 \approx $$ 1500 $ $ \text{ (4 s.f.)}$
$ 1504 \approx $$ 1500 $ $ \text{ (3 s.f.)}$
$ 1532 \approx $$ 1500 $ $ \text{ (2 s.f.)}$
Questions
Approximation question
1(a) Use your calculator to evaluate the following expression:
$$ {45.8^2 \times \sqrt{940.5} \over 9.64 + 0.02} $$
Write down the first five digits on your calculator display.
Answer: $ 6 \phantom{.} 659.3 $
1(b) Round off your answer in part (a) to two significant figures.
Answer: $ 6 \phantom{.} 700 $
Estimation question
2. By first rounding each term in the following expression to 2 significant figures,
$$ {403.2 \times \sqrt{50.15} \over 1.95^2} $$
estimate the value of the expression, leaving your answer in 2 decimal places.
Answer: $ 707.11 $
Work backwards from approximation (Lower bound vs. Upper bound)
3. Hebe measures her height, rounds it to 3 significant figures and records her height. The recorded height is $1.60$ m.
(a) State the smallest possible value of Hebe's actual height.
Answer: $ 1.595 \text{ m} $
(b) State the largest possible value of Hebe's actual height.
Answer: $ 1.604 \phantom{.} 999… \approx 1.605 \text{ m} $
(c) Complete the following inequality to show the range of her actual height, $h$:
$$ \text{………} \le h < \text{………} $$
Answer: $ 1.604 \phantom{.} 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.
Previous topic: Prime factorisation → Next topic: Indices →