Algebra
Exponents and scientific notation
Scientific notation
20 practice questions
1 video lesson
Theory + worked examples
Practice
20 questions
Practice questions
Every question with a fully worked solution.
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1 video(s)
- Introduction video Watch
Theory
Scientific notation writes a number as
\[a\times10^n,\qquad 1\le a<10,\]
- Large numbers use a positive exponent.
- Small numbers use a negative exponent.
The exponent counts how many places the decimal moves.
Scientific notation form.
Worked examples.
The form:
\[a\times10^n,\quad 1\le a<10\]
Multiply: multiply the \(a\)'s and add the exponents.
How to use scientific notation
- Place the decimal after the first nonzero digit.
- Count how many places it moved for \(n\).
- Positive \(n\) for large, negative for small.
- Multiply by multiplying \(a\)'s and adding exponents.
Example 1 — To standard form
Write \(3.2\times10^4\) in standard form.
Solution
Move the decimal \(4\) places right.
| \(3.2\times10^4\) | \(=\) | \(32{,}000\) |
Example 2 — To scientific notation
Write \(0.00056\) in scientific notation.
Solution
Move the decimal to just after the first nonzero digit.
| \(0.00056\) | \(=\) | \(5.6\times10^{-4}\) |
Example 3 — Multiply
Multiply \((2\times10^3)(3\times10^2)\).
Solution
Multiply the numbers, add the exponents.
| \((2\cdot3)\times10^{3+2}\) | \(=\) | \(6\times10^5\) |
Example 4 — Why use it
Why is scientific notation useful?
Solution
It writes very large or very small numbers compactly.
Common pitfalls
\(a\) must be between 1 and 10.
Negative exponent for small numbers.
Add exponents when multiplying.
Frequently asked questions
What is scientific notation?
Writing a number as \(a\times10^n\) with \(1\le a<10\).
What is \(5.6\times10^{-4}\) in standard form?
\(0.00056\).
When is the exponent negative?
For numbers smaller than 1.
How do you multiply in scientific notation?
Multiply the \(a\)'s and add the exponents.
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