These NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers 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

Answer:

(i) 0.0000000000085 = \(\frac{85}{10^{13}}=\frac{8.5 \times 10}{10^{13}}\)

= 8.5 × 10 × 10^{-13} = 8.5 × 10^{-12}

(ii) 0.00000000000942 = \(\frac{942}{10^{14}}\)

= \(\frac{9.42 \times 100}{10^{14}}=\frac{9.42 \times 10^{2}}{10^{14}}\)

= 9.42 × 10^{2} × 10^{-14} = 9.42 × 10^{-12}

(iii) 6020000000000000 = 602 × 10^{13}

= 6.02 × 10^{2} × 10^{13} = 6.02 × 10^{15}

(iv) 0.00000000837 = \(\frac{837}{10^{11}}=\frac{8.37 \times 10^{2}}{10^{11}}\)

= 8.37 × 10^{2 -11} = 8.37 × 10^{-9}

(v) 31860000000 = 3186 × 10^{7}

= 3.186 × 10^{3} × 10^{7}

= 3.186 × 10^{3} + 10^{3+7}

= 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}

Answer:

(i) 3.02 × 10^{-6} = 302 x 10^{-2} × 10^{-6}

= 302 × 10^{-8} = 0.00000302

(ii) 4.5 × 10^{4} = \(\frac{45}{10}\) × 10000 = 45000

(iii) 3 × 10^{-5} = \(\frac{3}{10^{8}}\) = 0.00000003

(iv) 1.0001 × 10^{9} = \(\frac{10001 \times 10^{9}}{10^{4}}\)

= 10001 × 10^{9-4} = 10001 × 10^{5}

= 1000100000

(v) 5.8 × 10^{12} = \(\frac{58}{10}\) × 10^{12} = 58 × 10^{12-1}

= 58 × 10^{12-1} = 58 × 10^{11}

= 5800000000000

(vi) 3.61492 x 10^{6} = \(\frac{361492}{10^{5}}\) × 10^{6}

= 361492 × 10^{6-5} = 361492 × 10

= 36149200

Question 3.

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

(i) 1 micron is equal to \(\frac{1}{1000000}\) 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

Answer:

(i) \(\frac{1}{1000000}=\frac{1}{10^{6}}\) = 1 × 10^{-6}

1 micron = 1 × 10^{-6}

(ii) 0.000,000,000,000,000,000,16 = \(\frac{16}{10^{20}}\)

= \(\frac{1.6 \times 10}{10^{20}}\) = 1.6 × 10^{1-20} = 1.6 × 10^{-19}

.’. Charge on an electron is 1.6 × 10^{-19} coulomb.

(iii) 0.0000005 = \(\frac{5}{10^{7}}\) = 5 × 10^{-7}

Size of a bacteria = 5 × 10^{-7} m

(iv) 0.00001275 = \(\frac{1275}{10^{8}}=\frac{1.275 \times 10^{3}}{10^{8}}\)

= 1.275 × 10^{3-8} = 1.275 × 10^{-5}

Size of a plant cell is 1.275 × 10^{-5}m

(v) 0.07 = \(\frac{7}{10^{2}}\) = 7 × 10^{-2}

.’. Thickness of a thick paper is 7 × 10^{-2}mm

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.

Answer:

Thickness of one book = 20 mm

Thickness of 5 books = 5 × 20 mm = 100 mm

Again, Thickness of one paper sheet = 0.016 mm

.’. Thickness of 5 paper sheets = 5× 0.016 mm

= 0.080 m

Total thickness =100 mm + 0.080 mm = 100.08 mm

\(\frac{10008}{10^{2}}=\frac{1.0008 \times 10^{4}}{10^{2}}\)

= 1.0008 × 10^{2} mm