# Standard and Scientific Notation

- Understanding Scientific Notation and Standard Notation
- Scientific Notation – Real-World Application
- Converting from Standard to Scientific Notation – Steps
- Converting from Scientific to Standard Notation – Steps
- Standard and Scientific Notation – Exercises
- Standard and Scientific Notation – Summary
- Standard and Scientific Notation – Frequently Asked Questions

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Learning text on the topic
**Standard and Scientific Notation**

## Understanding Scientific Notation and Standard Notation

Welcome to the intriguing world of **Scientific Notation**. This math concept is a game-changer when dealing with super large numbers like the number of stars in the universe or really tiny ones like the size of molecules in chemistry. It’s a helpful tool that makes working with these extreme numbers much simpler. Ready to learn how **scientific notation** makes big and small numbers a breeze to handle? Let’s get started!

**Scientific Notation** is a way of expressing large or small numbers as a product of a number between 1 and 10 and a power of ten. **Standard Notation** is our regular way of writing numbers.

## Scientific Notation – Real-World Application

Here's a table with real-world examples, illustrating their sizes in both standard form and scientific notation:

Item | Standard Form | Scientific Notation |
---|---|---|

Distance from Earth to Sun | 149,600,000 km | 1.496 × 10^{8} km |

Size of a Red Blood Cell | 0.000007 m | 7 × 10^{-6} m |

The first row represents the vast distance from the Earth to the Sun, while the second row shows the minuscule size of a red blood cell, each expressed in a form that best suits their scale.

## Converting from Standard to Scientific Notation – Steps

Converting numbers from standard to scientific notation can be done by following these steps:

Step | Direction | Example |
---|---|---|

1 | Move the decimal point to get a number between 1 and 10, with only one non-zero digit to its left. |
For 1,2345, move the decimal between the 1 and 2. 1.2345 |

2 | Count how many places you moved the decimal. | Decimal moved 4 places to the left. |

3 | Write the exponent based on your count. Positive for left moves (large numbers), negative for right (small numbers). | 12345 in scientific notation is 1.2345 × 10 ^{4} |

## Converting from Scientific to Standard Notation – Steps

Converting numbers from scientific to standard notation is the reverse process, with the following steps.

Step | Direction | Example |
---|---|---|

1 | Start with the number in scientific notation. | For 3.16 × 10^{4}, start with 3.16 |

2 | Move the decimal point based on the exponent. Right for positive exponents, left for negative. | Move decimal 4 places to the right. |

3 | Fill in with zeros if needed, to match the number of places you moved the decimal. | 3.16 becomes 31,600 (standard notation) |

*Check your understanding of these two conversions.*

### Converting from Scientific to Standard Notation – Examples

## Standard and Scientific Notation – Exercises

## Standard and Scientific Notation – Summary

**Key Points from This Text:**

- Standard notation is the regular form of a number we typically see in the world. For example: 50,800,000.
- Scientific notation makes it easier to work with very large or small numbers.
- Scientific notation is written as a product of a decimal between 1 and 10, and a power of ten, for example: 5.08 × 10
^{7}. - The or exponent shows how many times the decimal moves, with positive for large and negative for small numbers.

Conversion Type | Process |
---|---|

Standard to Scientific Notation | Move decimal to get a number between 1-10, count moves, times 10 to the power of moves. |

Scientific to Standard Notation | Start with scientific notation number, move decimal based on exponent (right for positive, left for negative). |

For more practice with this topic, this video is helpful for learning how to compare numbers written in scientific notation - **Comparing Numbers Written in Scientific Notation**

For more exciting math topics, explore our interactive problems, videos, and worksheets on our website!

## Standard and Scientific Notation – Frequently Asked Questions

Variables

Simplifying Variable Expressions

Evaluating Expressions

How to do Order of Operations?

Distributive Property

Adding Integers

Subtracting Integers

Multiplying and Dividing Integers

Types of Numbers

Transforming Terminating Decimals to Fractions and Vice Versa

Transforming Simple Repeating Decimals to Fractions and Vice Versa

Rational Numbers on the Number Line

Standard and Scientific Notation

Using Operations with Scientific Notations