Scientific Notation

Scientific Notation

Learn how to solve mathematics problems containing scientific notation in few simple and easy steps.

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: \(m×10^n\)
Decimal notation Scientific notation
\( 5 \) \(5 \times 10^0 \)
\(-25,000\)\(-2.5 \times 10^4\)
\(0.5\)\(5 \times 10^{ \ -1} \)
\(2,122\)\(2.122 \times 10^{\ 3}\)

Example 2:

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 moved to the right, the exponent is negative.
Then: \(0.00015=1.5×10^{ \ -4} \)

Example 2:

Write \(9.5 \times 10^{\ -5}\) in standard notation.

Solution:

\(10^{-5} →\) When the decimal moved to the right, the exponent is negative.
Then: \(9.5×10^{-5}=0.000095\)

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 moved to the right, the exponent is negative.
Then: \(0.00012=1.2×10^{-4}\)

Example 4:

Write \(8.3×10^{-5}\) in standard notation.

Solution:

\(10^{-5} →\) When the decimal moved to the right, the exponent is negative.
Then: \(8.3×10^{-5}=0.000083\)

Exercises

Write each number in scientific notation.

  1. \(\color{blue}{91 × 10^3}\)
  2. \(\color{blue}{60}\)
  3. \(\color{blue}{2000000}\)
  4. \(\color{blue}{0.0000006}\)
  5. \(\color{blue}{354000}\)
  6. \(\color{blue}{0.000325}\)

Download Scientific Notation Worksheet

  1. \(\color{blue}{9.1 × 10^4}\)
  2. \(\color{blue}{6 × 10^1}\)
  3. \(\color{blue}{2 × 10^6}\)
  4. \(\color{blue}{6 × 10^{–7}}\)
  5. \(\color{blue}{3.54 × 10^5}\)
  6. \(\color{blue}{3.25 × 10^{–4}}\)

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