Scientific Notation

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Learning intentions:

Scientific Notation is a way of writing very large or very small numbers in a simplified form.

This makes it easier to work with these numbers in calculations, especially when using a calculator.

A number is in scientific notation when it is written in the form:

$\textbf{a} \times 10^{\textbf{n}}$

a is a number that is between 1 and 10.
n is an integer (it can be positive or negative) which tells you how many places to move the decimal point.

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Example 1: Large Number 3400 in scientific notation is written as 3.4 × 10³.

Here, a = 3.4 (which is between 1 and 10).
n = 3 because you would move the decimal point 3 places to the right to get back to 3400.

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Example 2: Small Number 0.004 in scientific notation is written as 4 × 10⁻³.

Here, a = 4 (which is between 1 and 10).
n = -3 because you would move the decimal point 3 places to the left to get back to 0.004.

Identify the most significant digit (the first non-zero digit) in the number.
Place the decimal point after this digit to make the number between 1 and 10.
Count the number of places you moved the decimal point:

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Example 3: Converting 25,000 to Scientific Notation

Example 4: Converting 0.00056 to Scientific Notation

If you are using a Casio calculator, you can enter numbers in scientific notation easily.

Button to Use:

How to Type in 7 × 10⁴: Press 7, then the × $10^x$ button, and then press 4.

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Exam Tip: Always double-check that the number a is between 1 and 10. If it's not, then your scientific notation is incorrect.

Scientific Notation Simplified Revision Notes for Junior Cycle Mathematics