Approximations

Question 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

Question 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.

Question 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

Question 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

1 \ cm

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