Scientific Notation
Scientific notation (standard form) is a way of writing very large or very small numbers compactly using powers of 10. For example, 3,500,000 = 3.5 x 10^6 and 0.000045 = 4.5 x 10^-5.
What You Need to Know
Key Concept Diagram
Scientific notation: a number written as a x 10^n where 1 <= a < 10 and n is an integer
Large numbers have positive indices: 6,400,000 = 6.4 x 10^6
Small numbers (between 0 and 1) have negative indices: 0.00032 = 3.2 x 10^-4
To convert to standard form, count how many places the decimal point moves
Moving the decimal left increases the index; moving right decreases it
Key Vocabulary
Scientific Notation
A way of writing numbers as a x 10^n where 1 <= a < 10
Index
The power (exponent) in scientific notation, showing the number of places the decimal moves
Coefficient
The number a in a x 10^n; must satisfy 1 <= a < 10
Order of Magnitude
An estimate of size based on the power of 10 in scientific notation
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Write 45,000 in scientific notation.
Question 2
Write 2.3 x 10^-3 as an ordinary number.
Question 3
The distance from Earth to the Sun is approximately 150,000,000 km. In scientific notation this is:
Key Concepts Summary
- ●Scientific notation: a number written as a x 10^n where 1 <= a < 10 and n is an integer
- ●Large numbers have positive indices: 6,400,000 = 6.4 x 10^6
- ●Small numbers (between 0 and 1) have negative indices: 0.00032 = 3.2 x 10^-4
- ●To convert to standard form, count how many places the decimal point moves
- ●Moving the decimal left increases the index; moving right decreases it