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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Standard Form

Introduction

Standard form is a method of writing down very large or very small numbers easily. The method relies on using powers of ten to shorten the numbers. Consider the number

Therefore we can write which is writing it in standard form.

This idea can be used to write even larger numbers down easily in standard form.

Small numbers can also be written in standard form. However, instead of the index being positive (in the above example, the index was 3), it will be negative.

The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10^{(a number)}.

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On a calculator, you usually enter a number in standard form as follows: Type in the first number (the one between 1 and 10). Press EXP . Type in the power to which the 10 is risen.

Operations in Standard Form

Addition and Subtraction in Standard Form

When adding two numbers in standard form, it helps to have them both with the index of 10, so we remove one from standard form. Perform the operation (taking out the index of 10 as a common factor) and then convert back into standard form. Consider this example, adding

First we convert to the same exponent (I personally prefer to use the lower exponent)

Take out the common factor of

This isn't in standard form since 99 isn't between 1 and 10, therefore we put it into standard form

We follow an identical method for subtraction

Multiplication in Standard Form

Division in Standard Form

Exponentiation in Standard Form

Comments

More areas need to be covered - including converting to decimal standard form (eg 44511.7 = 4.45117 x10⁴), negative powers in standard form, adding and subtracting numbers in standard form and multiplying and dividing numbers in standard form.