# Using Operations with Scientific Notations

- Operations with Scientific Notation or Standard Form
- Understanding Operations with Scientific Notation
- Multiplying Numbers in Scientific Notation – Steps
- Dividing Numbers in Scientific Notation – Steps
- Adjusting the Solution to Scientific Notation
- Operations with Scientific Notation – Guided Practice
- Operations with Scientific Notation – Real-World Application
- Operations with Scientific Notation – Summary
- Operations with Scientific Notation – Frequently Asked Questions

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Learning text on the topic
**Using Operations with Scientific Notations**

## Operations with Scientific Notation or Standard Form

In this text, we're going to explore how to perform operations like multiplication and division with numbers expressed in **scientific notation**. This is also known as **standard form**. This skill is essential for handling very large or small numbers efficiently in maths and science. We'll also touch on how to convert numbers to scientific notation, providing a comprehensive understanding of this useful mathematical tool.

For a refresher on the **scientific notation rules**, check out this text: **Standard and Scientific Notation**.

## Understanding Operations with Scientific Notation

**Scientific Notation** is a way of expressing numbers that are very large or very small. It's expressed as a product of a number between 1 and 10 and a power of ten and can look like this: $4.3 \times 10^2$.

In the following section, you will learn the steps to finding the product or quotient of numbers in scientific notation.

### Multiplying Numbers in Scientific Notation – Steps

- Multiply the decimal parts.
- Add the exponents of 10.

### Dividing Numbers in Scientific Notation – Steps

- Divide the decimal parts.
- Subtract the exponent of the divisor from the exponent of the dividend.

*Let’s check your understanding so far.*

### Adjusting the Solution to Scientific Notation

Don’t forget, according to the **scientific notation definition**, the decimal part should be greater than or equal to 1 and less than 10. Adjusting the decimal and the exponent accordingly will ensure your result is in the correct form of scientific notation.

Condition | Action | Example Before Adjustment | Example After Adjustment |
---|---|---|---|

Decimal is greater than or equal to 10 | Shift decimal left; Increase exponent | $10 × 10^5$ | $1.0 × 10^6$ |

Decimal is less than 1 | Shift decimal right; Decrease exponent | $0.4 × 10^3 $ | $4.0 × 10^2$ |

*Let’s check your understanding so far:*

## Operations with Scientific Notation – Guided Practice

Let’s walk through some examples of multiplying and dividing numbers in scientific notation:

## Operations with Scientific Notation – Real-World Application

Now that you have learnt how to multiply and divide numbers written in scientific notation, let’s try to complete a few real-world problems.

## Operations with Scientific Notation – Summary

**Key Points from This Text:**

- Scientific notation simplifies the process of working with very large or small numbers.
- Multiplication involves multiplying the decimal parts and adding the exponents.
- Division includes dividing the decimal parts and subtracting the exponents.
- Converting to and from scientific notation is an essential skill in these operations.

Explore more topics and practice problems on our website, including interactive exercises, videos and worksheets to further enhance your understanding of scientific notation and other math concepts!

If you are looking for more on scientific notation, this video is a great resource: **Choosing Appropriate Units with Scientific Notation**.