Pre-Algebra
Numbers and operations
Scientific notation
20 practice questions
0 video lessons
Theory + worked examples
Scientific Notation
California Pre-Algebra • Standard 8.EE.3 • Numbers & Operations
Scientific Notation is a topic in Numbers & Operations in the California Common Core State Standards. It is aligned to Standard 8.EE.3, which requires students to express numbers in scientific notation and operate with them.
Scientific notation writes a number as \(a\times10^n\) with \(1\le a<10\), handling very large or small values.
Theory
Scientific notation writes a number as \(a\times10^n\) with \(1\le a<10\) and \(n\) an integer.
Positive \(n\) for large numbers, negative \(n\) for small ones.
The form of scientific notation.
Moving the decimal point.
The form:
\[a\times10^n,\quad 1\le a<10\]
The exponent counts decimal places moved.
How to write scientific notation
- Place the decimal after the first nonzero digit.
- Count how many places it moved.
- Large number: positive exponent; small: negative.
- Write \(a\times10^n\).
Example 1 — Large number
Write \(53{,}000\) in scientific notation.
Solution
Move the decimal \(4\) places left.
| \(53000\) | \(=\) | \(5.3\times10^4\) |
Example 2 — Small number
Write \(0.0007\) in scientific notation.
Solution
Move the decimal \(4\) places right (negative power).
| \(0.0007\) | \(=\) | \(7\times10^{-4}\) |
Example 3 — Back to standard
Write \(2.5\times10^3\) in standard form.
Solution
Move the decimal \(3\) places right.
| \(2.5\times10^3\) | \(=\) | \(2500\) |
Example 4 — Multiply
Find \((2\times10^3)(4\times10^2)\).
Solution
Multiply the fronts, add the exponents.
| \(8\times10^{5}\) | \(=\) | \(800000\) |
Common pitfalls
\(a\) must be between \(1\) and \(10\).
Small numbers use negative exponents.
Count the decimal moves carefully.
Frequently asked questions
What is scientific notation?
A number written as \(a\times10^n\) with \(1\le a<10\).
When is the exponent negative?
For numbers less than one.
Write \(53{,}000\).
\(5.3\times10^4\).
Write \(2.5\times10^3\) in standard form.
\(2500\).
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