How to Solve Scientific Notation? (+FREE Worksheet!)
Learn how to solve mathematics problems containing scientific notation in a few simple and easy steps.
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Watch this practice video for additional examples and reinforcement:
Related Topics
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- How to Multiply Exponents
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- How to Solve Zero and Negative Exponents
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Step by step guide to solve scientific notation problems
- Scientific notation is used to write very big or very small numbers in decimal form.
- In scientific notation all numbers are written in the form of: \(m×10^n\)
For education statistics and research National Center for Education Statistics.
| Decimal notation | Scientific notation |
| \( 5 \) | \(5 \times 10^0 \) |
| \(-25,000\) | \(-2.5 \times 10^4\) |
| \(0.5\) | \(5 \times 10^{ \ -1} \) |
| \(2,122\) | \(2.122 \times 10^{\ 3}\) |
Scientific Notation – Example 1:
Write \(0.00015\) in scientific notation.
Solution:
First, move the decimal point to the right so that you have a number that is between \(1\) and \(10\). Then: \(N=1.5\)
Second, determine how many places the decimal moved in step \(1\) by the power of \(10\).
Then: \(10^{ \ -4} →\) When the decimal is moved to the right, the exponent is negative.
Then: \(0.00015=1.5×10^{ \ -4} \)
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Scientific Notation – Example 2:
Write \(9.5 \times 10^{\ -5}\) in standard notation.
Solution:
\(10^{-5} →\) When the decimal is moved to the right, the exponent is negative.
Then: \(9.5×10^{-5}=0.000095\)
Scientific Notation – Example 3:
Write \(0.00012\) in scientific notation.
Solution:
First, move the decimal point to the right so that you have a number that is between \(1\) and \(10\). Then: \(N=1.2\)
Second, determine how many places the decimal moved in step \(1\) by the power of \(10\).
Then: \(10^{-4}→ \) When the decimal is moved to the right, the exponent is negative.
Then: \(0.00012=1.2×10^{-4}\)
Scientific Notation – Example 4:
Write \(8.3×10^{-5}\) in standard notation.
Solution:
\(10^{-5} →\) When the decimal is moved to the right, the exponent is negative.
Then: \(8.3×10^{-5}=0.000083\)
Exercises for Solving Scientific Notation
Write each number in scientific notation.
- \(\color{blue}{91 × 10^3}\)
- \(\color{blue}{60}\)
- \(\color{blue}{2000000}\)
- \(\color{blue}{0.0000006}\)
- \(\color{blue}{354000}\)
- \(\color{blue}{0.000325}\)
Download Scientific Notation Worksheet
- \(\color{blue}{9.1 × 10^4}\)
- \(\color{blue}{6 × 10^1}\)
- \(\color{blue}{2 × 10^6}\)
- \(\color{blue}{6 × 10^{–7}}\)
- \(\color{blue}{3.54 × 10^5}\)
- \(\color{blue}{3.25 × 10^{–4}}\)
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