Maths⏱ 4 min read
How to Write Numbers in Standard Form (Scientific Notation)
Standard form lets you write very large or very small numbers compactly. Here is how to convert to and from standard form, do calculations in standard form, and avoid the common errors.
Standard form (scientific notation) is used in science, engineering, and finance whenever numbers become unwieldy. The rules are simple once you see the pattern.
What Standard Form Looks Like
Standard form: A x 10^n
Where: 1 <= A < 10 (A is between 1 and 10, not including 10)
And: n is an integer (whole number, positive or negative)
Large number: 6,700,000 = 6.7 x 10^6
Small number: 0.00042 = 4.2 x 10^-4
Normal number: 350 = 3.5 x 10^2
Tiny number: 0.000000089 = 8.9 x 10^-8
Converting TO Standard Form
Step 1: Move the decimal point until one non-zero digit is to the left
Step 2: Count how many places you moved
Step 3: If you moved left (large number): positive power
If you moved right (small number): negative power
Example: 47,600,000
Move decimal 7 places left: 4.76
Power: 10^7
Answer: 4.76 x 10^7
Example: 0.0000321
Move decimal 5 places right: 3.21
Power: 10^-5 (moved right = negative)
Answer: 3.21 x 10^-5
Check: 3.21 x 10^-5 = 3.21 / 100,000 = 0.0000321 ✓
Converting FROM Standard Form
Positive power: move decimal right (makes number bigger)
Negative power: move decimal left (makes number smaller)
8.4 x 10^5: move decimal 5 places right
= 840,000
3.6 x 10^-3: move decimal 3 places left
= 0.0036
If you run out of digits, add zeros:
2.5 x 10^6 = 2,500,000 (add 5 zeros after the 5)
Multiplying and Dividing in Standard Form
Multiply: multiply the A values, ADD the powers
(3 x 10^4) x (2 x 10^3) = (3 x 2) x 10^(4+3) = 6 x 10^7
Divide: divide the A values, SUBTRACT the powers
(8 x 10^6) / (4 x 10^2) = (8/4) x 10^(6-2) = 2 x 10^4
If result A is not between 1 and 10, adjust:
(5 x 10^3) x (4 x 10^2) = 20 x 10^5
Adjust: 2 x 10^6 (move decimal left, increase power by 1)
Adding in standard form: convert to same power first
(3 x 10^5) + (4 x 10^4)
= (30 x 10^4) + (4 x 10^4) = 34 x 10^4 = 3.4 x 10^5
Real-World Standard Form Examples
QuantityValueStandard Form
World population8,100,000,0008.1 x 10^9
UK national debt£2,700,000,000,0002.7 x 10^12
Width of a human hair0.00007 m7 x 10^-5 m
Speed of light300,000,000 m/s3 x 10^8 m/s
Size of a virus0.0000001 m1 x 10^-7 m