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Approximations

1. Find the number of significant Figures in each of the following measurements:

    1. 8.4 cm has two significant figures
    2. 173.5 m has four significant figures
    3. 405 g has three significant figures
    4. 4.56 m has three significant figures
    5. 6.005 kg has four significant figures
    6. 0.035 km has two significant figures
    7. 0.00123 l has six significant figures
    8. 71.040 mg has five significant figures
    9. 10.010100 g has eight significant figures
    10. 20.00 km has four significant figures
    11. 4.500 ml has four significant figures
    12. 101.101 cm has six significant figures

2. Round off each of the following measurements correct to four significant figures:

i) 67.6519 g

The measurement 67.6519 g has 6 significant figures.

To round it off to 4 significant figures, we require rounding it off to 2 places after the decimal.

Therefore 67.6519 g = 67.65 kg rounded off to 4 significant figures.

ii) 5.30854 kg

The measurement 5.30854 kg has 6 significant figures.

To round it off to 4 significant figures, we require rounding it off to 3 places after the decimal.

Therefore 5.30854 kg = 5.309 kg rounded off to 4 significant figures.

iii) 22.211 km

The measurement 22.211 km has 5 significant figures.

To round it off to 4 significant figures, we require rounding it off to 2 places after the decimal.

Therefore 22.211 km = 22.21 km rounded off to 4 significant figures.

iv) 70.001 cm

The measurement 70.001 cm has 5 significant figures.

To round it off to 4 significant figures, we require rounding it off to 2 places after the decimal.

Therefore 70.001 cm = 70.00 km rounded off to 4 significant figures.

v) 0.0013795 m

The measurement 0.0013795 m has 7 significant figures.

To round it off to 4 significant figures, we require rounding it off to 4 places after the decimal.

Therefore 0.0013795 m = 0.001380 km rounded off to 4 significant figures.

vi) 0.0024060 l

The measurement 0.0024060 l has 7 significant figures.

To round it off to 4 significant figures, we require rounding it off to 4 places after the decimal.

Therefore 0.0024060 l = 0.002406 l rounded off to 4 significant figures.

3. Round off:

i) 17.354 g correct to three significant figures.

17.4 g

ii) 18.303 mm correct to four significant figures.

18.30 mm

iii) 5.0811 kg correct to two significant figures.

5.1 kg

iv) 22.0005 g correct to three significant figures.

22.0 g

v) 0.008507 g correct to one significant figure.

0.009 g

vi) 0.00195 mg correct to two significant figures.

0.002 g

4. Round off:

i) Rs. 69.51 to the nearest rupee

70 Rs

ii) 18.0555 kg to the nearest gram

18006 g

iii) Rs.4059.995 to the nearest paisa

406000 paisa

iv) 0.00949 m to the nearest cm

1cm

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