- Chapter No.1 Introduction to Biology
- Chapter No. 2 Solving a Biological Problem
- Chapter No.3 Biodiversity
- Chapter No.4 Cells and Tissues
- Chapter No.5 Cell Cycle
Q.1 Express each of the following numbers in scientific notation.
(i) 5700
(iv) 416.9
(ii) 49,800,000
(iii) 96,000,000
(v) 83,000
(vi) 0.00643
(vii) 0.0074
(viii) 60,000,000
(ix) 0.00000000395
(x) 275,000/0.0025
Solution:
To express numbers in scientific notation, we write the number as a product of a coefficient and a power of 10, where the coefficient is greater than or equal to 1 and less than 10. The power of 10 indicates how many places the decimal point must be moved to get the original number. Here’s how to express each of the given numbers in scientific notation:
(i) 5700
5700 can be expressed as 5.7 × 10^3 in scientific notation. We move the decimal point three places to the left to get 5.7, and the exponent 3 indicates that the decimal point was moved three places.
(ii) 49,800,000
49,800,000 can be expressed as 4.98 × 10^7 in scientific notation. We move the decimal point seven places to the left to get 4.98, and the exponent 7 indicates that the decimal point was moved seven places.
(iii) 96,000,000
96,000,000 can be expressed as 9.6 × 10^7 in scientific notation. We move the decimal point seven places to the left to get 9.6, and the exponent 7 indicates that the decimal point was moved seven places.
(iv) 416.9
416.9 can be expressed as 4.169 × 10^2 in scientific notation. We move the decimal point two places to the left to get 4.169, and the exponent 2 indicates that the decimal point was moved two places.
(v) 83,000
83,000 can be expressed as 8.3 × 10^4 in scientific notation. We move the decimal point four places to the left to get 8.3, and the exponent 4 indicates that the decimal point was moved four places.
(vi) 0.00643
0.00643 can be expressed as 6.43 × 10^(-3) in scientific notation. We move the decimal point three places to the right to get 6.43, and the negative exponent -3 indicates that the decimal point was moved three places to the left.
(vii) 0.0074
0.0074 can be expressed as 7.4 × 10^(-3) in scientific notation. We move the decimal point three places to the right to get 7.4, and the negative exponent -3 indicates that the decimal point was moved three places to the left.
(viii) 60,000,000
60,000,000 can be expressed as 6.0 × 10^7 in scientific notation. We move the decimal point seven places to the left to get 6.0, and the exponent 7 indicates that the decimal point was moved seven places.
(ix) 0.00000000395
0.00000000395 can be expressed as 3.95 × 10^(-9) in scientific notation. We move the decimal point nine places to the right to get 3.95, and the negative exponent -9 indicates that the decimal point was moved nine places to the left.
(x) 275,000/0.0025
To express this in scientific notation, we need to divide 275,000 by 0.0025 first:
275,000 ÷ 0.0025 = 110,000,000
Now, 110,000,000 can be expressed as 1.1 × 10^8 in scientific notation. We move the decimal point eight places to the left to get 1.1, and the exponent 8 indicates that the decimal point was moved eight places.
Q.2 Express the following numbers in ordinary notation.
(i) 6 x 10^-4
(iii) 9.018 x 10^-6
(ii) 5.06 x 10^10
(iv) 7.865 x 10^8
Solution:
To express numbers in ordinary notation, we simply perform the operations indicated by the exponent of 10. Here’s how to convert each of the given numbers from scientific notation to ordinary notation:
(i) 6 x 10^(-4):
To convert this to ordinary notation, we move the decimal point four places to the left since the exponent is -4:
6 x 10^(-4) = 0.0006
(ii) 5.06 x 10^(10):
To convert this to ordinary notation, we move the decimal point ten places to the right since the exponent is 10:
5.06 x 10^(10) = 50,600,000,000
(iii) 9.018 x 10^(-6):
To convert this to ordinary notation, we move the decimal point six places to the left since the exponent is -6:
9.018 x 10^(-6) = 0.000009018
(iv) 7.865 x 10^(8):
To convert this to ordinary notation, we move the decimal point eight places to the right since the exponent is 8:
7.865 x 10^(8) = 786,500,000