# Exercise 12.2

Question 1

Express the following numbers in standard form.

(i) 0.0000000000085 (ii) 0.00000000000942

(iii) 6020000000000000 (iv) 0.00000000837

(v) 31860000000

Sol :

(i) 0.0000000000085 = 8.5 × 10^{−12}

(ii) 0.00000000000942 = 9.42 × 10^{−12}

(iii) 6020000000000000 = 6.02 × 10^{15}

(iv) 0.00000000837 = 8.37 × 10^{−9}

(v) 31860000000 = 3.186 × 10^{10}

Question 2

Express the following numbers in usual form.

(i) 3.02 × 10^{−6} (ii) 4.5 × 10^{4}

(iii) 3 × 10^{−8} (iv) 1.0001 × 10^{9}

(v) 5.8 × 10^{12 }(vi) 3.61492 × 10^{6}

Sol :

(i) 3.02 × 10^{−6} = 0.00000302

(ii) 4.5 × 10^{4} = 45000

(iii) 3 × 10^{−8} = 0.00000003

(iv) 1.0001 × 10^{9} = 1000100000

(v) 5.8 × 10^{12} = 5800000000000

(vi) 3.61492 × 10^{6} = 3614920

Question 3

Express the number appearing in the following statements in standard form.

(i) 1 micron is equal to m.

(ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 coulomb.

(iii) Size of a bacteria is 0.0000005 m

(iv) Size of a plant cell is 0.00001275 m

(v) Thickness of a thick paper is 0.07 mm

Sol :

(i) = 1 × 10^{−6}

(ii) 0.000, 000, 000, 000, 000, 000, 16 = 1.6 × 10^{−19}

(iii) 0.0000005 = 5 × 10^{−7}

(iv) 0.00001275 = 1.275 × 10^{−5}

(v) 0.07 = 7 × 10^{−2}

Question 4

In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?

Sol :

Thickness of each book = 20 mm

Hence, thickness of 5 books = (5 × 20) mm = 100 mm

Thickness of each paper sheet = 0.016 mm

Hence, thickness of 5 paper sheets = (5 × 0.016) mm = 0.080 mm

Total thickness of the stack = Thickness of 5 books + Thickness of 5 paper sheets

= (100 + 0.080) mm

= 100.08 mm

= 1.0008 × 10^{2} mm

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