Maths⏱ 5 min read
What Is Scientific Notation and How Do You Use It?
Scientific notation makes enormous and tiny numbers manageable. Here's how to convert between standard and scientific notation, how to calculate with it, and why it's used in science and finance.
Scientific notation is a way of writing very large or very small numbers concisely — essential in science, engineering, and any field dealing with quantities that span many orders of magnitude.
The Standard Form
a × 10^n
Where:
1 ≤ a < 10 (a number between 1 and 10)
n = integer (positive for large numbers, negative for small)
Examples:
3,000,000 = 3 × 10^6
0.000045 = 4.5 × 10^-5
6,374,000 (Earth's radius in metres) = 6.374 × 10^6
0.00000000167 (mass of proton in kg) = 1.67 × 10^-27
Converting Standard Number → Scientific Notation
Step 1: Place decimal after first non-zero digit
Step 2: Count moves to original decimal position = n
Example: 425,000,000
= 4.25000000 × 10^?
Moved decimal 8 places left → n = 8
= 4.25 × 10^8
Example: 0.000372
= 3.72 × 10^?
Moved decimal 4 places right → n = −4
= 3.72 × 10^-4
Converting Scientific → Standard Number
Positive exponent: move decimal right
2.5 × 10^4 = 2.5000 → 25,000
Negative exponent: move decimal left
8.1 × 10^-3 = 0008.1 → 0.0081
Multiplying in Scientific Notation
Rule: multiply the coefficients, add the exponents
(3 × 10^4) × (2 × 10^3)
= (3 × 2) × 10^(4+3)
= 6 × 10^7
(4.5 × 10^-2) × (3 × 10^6)
= 13.5 × 10^4
= 1.35 × 10^5 (adjust so coefficient is between 1 and 10)
Dividing in Scientific Notation
Rule: divide the coefficients, subtract the exponents
(8 × 10^6) ÷ (2 × 10^2)
= (8 ÷ 2) × 10^(6-2)
= 4 × 10^4
(6 × 10^-3) ÷ (3 × 10^4)
= 2 × 10^(-3-4)
= 2 × 10^-7
Real-World Scale Examples
QuantityScientific Notation
Distance Earth to Sun1.5 × 10^11 metres
UK national debt (approx)£2.7 × 10^12
Diameter of a human hair7 × 10^-5 metres
Wavelength of visible light5 × 10^-7 metres
Number of cells in human body~3.7 × 10^13
Mass of Earth5.97 × 10^24 kg
Adding and Subtracting (Same Exponent Required)
To add/subtract, first make exponents equal:
(3.2 × 10^5) + (4.1 × 10^4)
Convert: 3.2 × 10^5 = 32 × 10^4
= (32 + 4.1) × 10^4
= 36.1 × 10^4
= 3.61 × 10^5