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