Scientific notation:
Very large or very small numbers can be expressed in the simplest form by using scientific notation. In this notation any number can be written as the product of a number ‘x’ such that 1≤ x < 10 and a power of 10.
Example:
Note: (i) 100.08 mm =1.0008 ×10² mm
(ii) 0.00000000000942=9.42 ×10⁻¹²
1) when we move the decimal point towards right side then multiply with negative power (power=number of places we moved) of 10.
Example: 0.00000000000942=9.42 ×10⁻¹²
2) when we move the decimal point towards left side then multiply with positive power (power=number of places we moved) of 10.
Example: 100.08 mm =1.0008 ×10² mm
class 8 maths chapter 12 exercise 12.2 (1)
1. Express the following numbers in standard form.
(i) 0.0000000000085 (ii) 0.00000000000942
(iii) 6020000000000000 (iv) 0.00000000837
(v) 31860000000
Solution to class 8 maths chapter 12 exercise 12.2 (1)
(i) 0.0000000000085 =8.5 ×10⁻¹²
(ii) 0.00000000000942=9.42 ×10⁻¹²
(iii) 6020000000000000=6.02 ×10¹⁵
(iv) 0.00000000837=8.37 ×10⁻⁹
(v) 31860000000 =3.186 ×10¹⁰
class 8 maths chapter 12 exercise 12.2 (2)
2. Express the following numbers in usual form.
(i) 3.06 ×10⁻⁶ (ii) 4.5 ×10⁴ (iii) 3 ×10⁻⁸
(iv) 1.0001 ×10⁹ (v) 5.8 ×10¹²
(vi) 3.61492 ×10⁶
Solution to class 8 maths chapter 12 exercise 12.2 (2)
(i) 3.06 ×10⁻⁶ = ⁽³·⁰⁶⁾/₍₁₀₀₀₀₀₀₎ =0.00000302
(ii) 4.5 ×10⁴ =4.5 ×10000 =45000
(iii) 3 ×10⁻⁸ =³/₍₁₀₀₀₀₀₀₀₀₎ =0.00000003
(iv) 1.0001 ×10⁹ =1.0001 ×1000000000
=1000100000
(v) 5.8 ×10¹² =5.8 ×1000000000000
=5800000000000
(vi) 3.61492 ×10⁶ =3.61492 ×1000000
=3614920
class 8 maths chapter 12 exercise 12.2 (3)
3. Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to 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
Solution to class 8 maths chapter 12 exercise 12.2 (3)
(i)1 micron is equal to ¹/₍₁₀₀₀₀₀₀₎ m.=1 ×10⁻⁶ m
(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb
=1.6 ×10⁻¹⁹ coulomb.
(iii) Size of a bacteria is 0.0000005 m
=5.0 ×10⁻⁷ m
(iv) Size of a plant cell is 0.00001275 m
= 1.275 ×10⁻⁵ m
(v) Thickness of a thick paper is 0.07 mm
= 7.0 ×10⁻² mm
class 8 maths chapter 12 exercise 12.2 (4)
4. In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack.
Solution to class 8 maths chapter 12 exercise 12.2 (4)
Thickness of one book = 20 mm
Thickness of 5 books = 20 x 5 = 100 mm
Thickness of one paper = 0.016 mm
Thickness of 5 papers = 0.016 x 5 = 0.08 mm
Total thickness of a stack = 100 + 0.08
=100.08 mm =1.0008 ×10⁻² mm