# Standard and Scientific Notation

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## Understanding Scientific Notation and Standard Notation

Welcome to the intriguing world of Scientific Notation. This maths 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. It is also known as standard form. 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 × 108 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 12,345, 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). 12,345 in scientific notation is 1.2345 × 104

## 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
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 becomes 30,000 (standard notation)

Check your understanding of these two conversions.

How does the exponent change when converting a small number to scientific notation?

## Standard and Scientific Notation – Exercises

Convert $50,000$ to scientific notation.
Convert $0.0005$ to scientific notation.
Convert $6.7 × 10^{2}$ to standard notation.
Convert $2.1 × 10^{-3}$ to standard notation.
A scientist is measuring a very small bacteria colony that has a size of $0.00009$ metres in diameter. To report this measurement in a scientific paper, convert this size to scientific notation.

## 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 × 107.
• The 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 - Choosing Appropriate Units with Scientific Notation

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

## Standard and Scientific Notation – Frequently Asked Questions

What is the importance of understanding scientific notation?
What's a real-world example of a large number in scientific notation?
Is scientific notation only for positive exponents?
What is a real-world situation where scientific notation is used to represent very small numbers?
How do you identify if a number in scientific notation represents a large or a small number?
What is the difference between standard notation and scientific notation?
Why do we move the decimal point in scientific notation?
Is it possible to use scientific notation in everyday life, outside of science and maths?
What are some common mistakes to avoid when converting between standard and scientific notation?
How do you write a very small number, like $0.0003$, in scientific notation?
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