Scientific notation is a way of expressing very large or very small numbers in a compact form. It is especially useful in chemistry and physics, where precision is essential. The general form of scientific notation is:
N×10n
Where:
N is a number between 1 and 10.
n is an integer (positive or negative) that represents the exponent.
For example:
1.34×105 = 134,000
8.6×10−4 = 0.00086
Counting Significant Figures in Scientific Notation
The number of significant figures is determined by N, not by the exponent.
1.34×105 has 3 significant figures.
8.6×10−4 has 2 significant figures.
To express a number with a certain number of significant figures, zeros may be added after the decimal point:
1.34×105 with 6 significant figures = 1.34000×105
Rounding Off to Significant Figures
If a number has more digits than required, it is rounded appropriately.
Example: Express 46897 in two significant figures.
The first two digits are 46.
Since the next digit is 8 (greater than 5), we round up.
Final result: 4.7×104.
Operations in Scientific Notation
Addition and Subtraction
If the exponents are the same, simply add or subtract the coefficients.
Example: (2.65×103)+(6.4×103)
(2.65+6.4)×103=9.05×103
Rounded to one decimal place: 9.1 × 103
If the exponents are different, adjust one number to match the other.
Example: (9.578×103)−(5.326×102)
Convert to decimal: 9578 – 532.6 = 9045.4
Convert back to scientific notation: 9.045 × 103
Multiplication and Division
Multiplication: Multiply the coefficients and add the exponents.
Example: (3.4×10−6)×(2.5×104)
(3.4×2.5)×10−6+4 = 8.5×10−2
Division: Divide the coefficients and subtract the exponents.
Example: (6.0×105)÷(2.0×102)
(6.0÷2.0)×105−2 = 3.0×103
Conceptual Questions
Why do we use scientific notation?
To simplify the representation of very large or small numbers.
To avoid misplacing zeros.
What determines the number of significant figures in scientific notation?
The coefficient N (not the exponent).
Do You Know?
The speed of light in vacuum is approximately 3.00 × 10⁸ m/s.
Avogadro’s number is 6.022 × 10²³, representing the number of atoms in a mole.
The charge of an electron is 1.602 × 10⁻¹⁹ C.
Worksheet
Q1: Convert the following into scientific notation:
a) 0.000678
b) 123,400
c) 5,690,000
Q2: Perform the following calculations and express the result in scientific notation:
a) (2.5×104)×(3.6×10−2)
b) (5.7×106)÷(1.9×102)
Test Paper (Total: 10 Marks)
Q1: Convert into scientific notation: (2 Marks)
a) 0.00034
b) 789,000
Q2: Express with three significant figures: (2 Marks)
a) 12.347
b) 0.008659
Q3: Solve: (3 Marks)
(4.5×103)+(6.3×103)
Q4: Perform the following multiplication: (3 Marks)
(3.2×10−4)×(1.1×102)
Quick Revision Points
Scientific notation is N×10n, where N is between 1 and 10.
Significant figures are counted in the coefficient N, not in the exponent.
In addition/subtraction, make exponents the same before performing operations.
In multiplication, add exponents; in division, subtract them.
Always round answers to match the smallest number of significant figures.
