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

## 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: \(m×10^n\)

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.

- \(\color{blue}{91 × 10^3}\)
- \(\color{blue}{60}\)
- \(\color{blue}{2000000}\)
- \(\color{blue}{0.0000006}\)
- \(\color{blue}{354000}\)
- \(\color{blue}{0.000325}\)

### Download Scientific Notation Worksheet

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