How to Solve Scientific Notation

How to Solve Scientific Notation

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

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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: \(m×10^n\)
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 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: \(0.00015=1.5×10^{ \ -4} \)

Scientific Notation – 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: \(9.5×10^{-5}=0.000095\)

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 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 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.

  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. \(\color{blue}{3.25 × 10^{–4}}\)

Related to "How to Solve Scientific Notation"

How to Multiply and Divide in Scientific Notation
How to Multiply and Divide in Scientific Notation
How to Add and Subtract  in Scientific Notations
How to Add and Subtract in Scientific Notations

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