## Converting Scientific Notation to Decimal Form

Contents

How can we convert from scientific notation to decimal form? Let’s look at two numbers written in scientific notation and see.

If we look at the location of the decimal point, we can see an easy method to convert a number from scientific notation to decimal form.

In both cases the decimal point moved 4 places. When the exponent was positive, the decimal moved to the right. When the exponent was negative, the decimal point moved to the left.

## Example

Convert to decimal form: \(6.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}.\)

### Solution

Step 1: Determine the exponent, \(n\), on the factor 10. | \(6.2×{10}^{3}\) |

Step 2: Move the decimal point \(n\) places, adding zeros if needed. | |

- If the exponent is positive, move the decimal point \(n\) places to the right.
- If the exponent is negative, move the decimal point \(|n|\) places to the left.
| 6,200 |

Step 3: Check to see if your answer makes sense. | |

\({10}^{3}\) is 1000 and 1000 times 6.2 will be 6,200. | \(6.2×{10}^{3}=6,200\) |

### How to Convert scientific notation to decimal form.

- Determine the exponent, \(n,\) on the factor \(10.\)
- Move the decimal \(n\) places, adding zeros if needed.
- If the exponent is positive, move the decimal point \(n\) places to the right.
- If the exponent is negative, move the decimal point \(|n|\) places to the left.

- Check.

## Example

Convert to decimal form: \(8.9\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}.\)

### Solution

\(8.9×{10}^{-2}\) | |

Determine the exponent \(n\), on the factor 10. | The exponent is −2. |

Move the decimal point 2 places to the left. | |

Add zeros as needed for placeholders. | 0.089 |

\(8.9×{10}^{-2}=0.089\) | |

The Check is left to you. |

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