## Approximations and Estimations Exercise

1. Round off the following numbers to the number of significant figures shown in brackets:

(a) 4.362 (to 2 sig. fig.) (f) 0.619 (to 2 sig. fig.)

(b) 5.4 (to 1 sig. fig.) (g) 4.1357 (to 4 sig. fig.)

(c) 0.0037 (to 1 sig. fig.) (h) 91345 (to 3 sig. fig.)

(d) 815.3 (to 2 sig. fig.) (i) 2.69 × 10 2 (to 2 sig. fig.)

(e) 5.795 (to 3 sig. fig.) (j) 9.32 × 10 − 3 (to 1 sig. fig.)

2. (a) In the table below, round each number to 1 significant figure and give the answer correct to 1 significant figure.

(b) Calculate the answer accurately and round it to 3 significant figures.

 Calculation (a) Estimate (to 1 sig. fig.) (b) Accurate answer (rounded to 3 sig. fig.) 8.372 + 4.65 9.371 × 2.84 (8.51) 2 3.89 − (4.63 + 5.2)

3.Round off the following numbers to the number of decimal places (d.p.) shown:

(a) 5.69 (to 1 d.p.) (d) 327.2954 (to 3 d.p.)

(b) 4.397 (to 2 d.p.) (e) 40.09 (to 1 d.p.)

(c) 0.087 (to 2 d.p.) (f) 49.95 (to 1 d.p.)

4. Do not use your calculator. Assess the answer according to the numbers involved.

 Problem Select the best answer (a) 25.6 ÷ 4.8 0.533, 5.34, 53.4, 534 (b) 4.9 × 39 1.91, 19.1, 191, 1910 (c) 498 ÷ 0.49 1.016, 10.16, 101.6, 1016

5. Round the following to the degree of accuracy stated:

(a) 36645 people at a football match (to the nearest thousand people)

(b) A mass of 2.4 kg (to the nearest kg)

(c) A salary of \$21,352 (to the nearest hundred dollars)

(d) A cricket score of 374 (to the nearest ten runs)

6. Complete the table:

 Purchase Estimated cost (to 1 sig. fig.) Accurate cost 4 m of material at \$4.99 per metre 2 zips at 89c each 6 buttons at 11 cents each 2 reels of cotton at 55c each 3 patterns at \$2.25 each Totals

7. Give the limits of accuracy of the following measurements:

(a) A length of 4 cm (d) A length of 135 m

(b) A mass of 6.7 g (e) A mass of 0.5 kg

(c) A volume of 5.36 mL (f) A distance of 53 km