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

(i)  8.4 \ cm       (ii)  173.5 \ m       (iii)  405 \ g       (iv)  4.56 \ m      (v)  6.005 \ kg       (vi)  0.035 \ km       (vii)  0.00123 \ l       (viii)  71.040 \ mg       (xi)  10.010100 \ g       (x)  20.00 \ km       (xi)  4.500 \ ml       (xii)  101.101 \ cm

Answer:

i)  8.4 \ cm has two significant figures

ii)  173.5 \ m has four significant figures

iii)  405 \ g has three significant figures

iv)  4.56 \ m has three significant figures

v)  6.005 \ kg has four significant figures

vi)  0.035 \ km has two significant figures

vii)  0.00123 \ l has six significant figures

viii)  71.040 \ mg has five significant figures

xi)  10.010100 \ g has eight significant figures

x)  20.00 \ km has four significant figures

xi)  4.500 \ ml has four significant figures

xii)  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      ii) 5.30854 \ kg      iii) 22.211 \ km

iv) 70.001 \ cm      v) 0.0013795 \ m      vi) 0.0024060 \ l

Answer:

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.

ii) 18.303 \ mm correct to four significant figures.

iii) 5.0811 \ kg correct to two significant figures.

iv) 22.0005 \ g correct to three significant figures.

v) 0.008507 \ g correct to one significant figure.

vi) 0.00195 \ mg correct to two significant figures.

Answer:

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     ii) 18.0555 \ kg to the nearest gram

iii) Rs. \ 4059.995 to the nearest paisa     iv) 0.00949 m to the nearest cm

Answer:

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