What is Standard Form

This document introduces the idea of standard form with some examples and non examples. All numbers used are large numbers.

What is Standard Form in Maths? A Simple Guide

In mathematics, the term ‘Standard Form’ can be explained as the way of writing either very large or very small numbers in a compact and easy-to-read format. Usually, this method is largely used in the case of scientific notation, making the idea a lot easier to work with numbers in different subjects like physics, chemistry, as well as engineering.

Standard Form (Scientific Notation)

Standard Form is also known as Scientific Notation. This expresses numbers as:

A × 10ⁿ

Where:

• A is a number between 1 and 10 (not including 10).
• n is an integer exponent that shows how many places the decimal point has moved.

Example of Standard Form:

1.9 × 10⁷ = 19,000,000

Here, 1.9 is between 1 and 10, and the exponent 7 tells us to move the decimal 7 places to the right.

Why Use Standard Form in Maths?

• Simplifies very large or small numbers

Example:

5,600,000,000 can be written as 5.6 × 10⁹.
0.000042 can be written as 4.2 × 10^-5.

• Easier calculations in multiplication and division
• Used in scientific and engineering fields for precision

How to Write a Number in Standard Form?

Step 1: Place the Decimal

Find a number between 1 and 10 by moving the decimal point.

Example:
28,300,000,000,000,000 → 2.83 × 10¹⁶
(The decimal moves 16 places left)

Step 2: Count the Decimal Places Moved

Moving left increases the power of 10.
Moving right makes the exponent negative.

Example:
0.00028 → 2.8 × 10^-4
(The decimal moves 4 places right)

Common Mistakes in Standard Form

Incorrect: 28.3 × 10¹³ (Not between 1 and 10)
Correct: 2.83 × 10¹⁴

Incorrect: 0.283 × 10¹⁵
Correct: 2.83 × 10¹⁴

Always make sure the first number is between 1 and 10!