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

$1 \ cm$