How to Solve Scientific Notation? (+FREE Worksheet!)

Related Topics

• How to Solve Powers of Products and Quotients
• How to Multiply Exponents
• How to Divide Exponents
• How to Solve Zero and Negative Exponents
• How to Solve Negative Exponents and Negative Bases

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: \(m×10^n\)

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: \(0.00015=1.5×10^{ \ -4} \)

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.

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. \(\color{blue}{3.25 × 10^{–4}}\)