These NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers InText Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers InText Questions
NCERT Intext Question Page No. 194
Question 1.
Find the multiplicative inverse of the following:
(i) 2-4
(ii) 105
(iii) 7-2
(iv) 5-3
(v) 10-100
Answer:
(i) The multiplicative inverse of 2-4 = 24
(ii) The multiplicative inverse of 10-5 = 105
(iii) The multiplicative inverse of 7-2 = 72
(iv) The multiplicative inverse of 5-3 = 53
(v) The multiplicative inverse of 10-100 = 10100
Question 2.
Expand the following numbers using exponents.
(i) 1025.63
(ii) 1256.249
Answer:
| Number | Expanded form |
| (i) 1025.63 | 1 x 1000 + 0 x 100 + 2 x 10 + 5 x 1 \(\frac{6}{10}+\frac{3}{100}\) or 1 x 103 + 2 x 101 + 5 x 10° + 6 x 10-1 + 3 x 10-2 |
| (ii) 1025.249 | 1 x 1000 +2 x 100 +5 x 10 + 6 x 1 + \(\frac{2}{10}+\frac{4}{100}+\frac{9}{1000}\) or 1 x 103 + 2 x 102 + 5 x 101 + 6 x 10° + 2 x 10-1 + 9 x 10-3 |
NCERT Intext Question Page No. 195
Question 1.
Simplify and write in exponential form.
(i) (-2)-3 x (-2)-4
(ii) p3 x p-10
(iii) 32 x 3-5 x 36
Answer:
(i) (-2)-3 x (-2)-4 = (-2)3-4
[am x an = am+n]
= (-2)-7 = \(\frac{1}{(-2)^{7}}\)
(ii) p3 x p-10 = p3 + (-10) = p3 – 10 = p7 or \(\frac{1}{\mathrm{p}^{7}}\)
(iii) 32 x 3-5 x 36 = 32 + (- 5) + 6 = 32 – 5 + 6 = 38-5 = 33
NCERT Intext Question Page No. 199
Question 1.
Write the following numbers in standard form.
(i) 0.000000564
(ii) 0.0000021
(iii) 15240000
Answer:
(i) 0.000000564 = \(\frac{564}{1000000000}=\frac{564}{10^{9}}\)
= \(\frac{5.64 \times 10^{2}}{10^{9}}\) = 5.64 x 10-7
(ii) 0.0000021 = \(\frac{21}{10000000}=\frac{21}{10^{7}}\)
= \(\frac{2.1 \times 10}{10^{7}}\) = 2.1 x 101-7 = 2.1 x 10-6
(iii) 15240000 = 1524 x 10000
= 1.524 x 1000 x 10000 = 1.524 x 107
∴ 15240000 = 1.524 x 107
Question 2.
Write all the facts give in the standard form.
Answer:
A number is said to be in the standard form when it is written as k x 10n, Where 1 ≤ k < 10 and ‘n’ is an integer. A number expressed as the product of a number between 1 and 10 and an integral power of 10.
Example: Compare the size of a red blood cell which is 0.000007m to that of a plant cell which is 0.0000129m.
Size of red blood cell = 0.000007 m
= \(\frac{7}{1000000}\) x 10-6 m
Size of the plant cell = \(\frac{7}{10000000} \mathrm{~m}=\frac{1.29 \times 10^{2}}{10000000} \mathrm{~m}\)
= 1.29 x 10-5 m
Now = \(\frac{7 \times 10^{-6}}{1.29 \times 10^{-5}}=\frac{7 \times 10^{-1}}{1.29}\)
= \(\frac{7 \times 10^{-1}}{1.3}=\frac{0.7}{1.3}=\frac{1}{2}\) (approx)
Thus, the size of a red blood cell is half of the plant cell size.