Standard Form

By Ultimate Maths

Introduction

Standard form (also called scientific notation) is a special way of writing very large or small numbers. It is used by scientists, mathematicians and engineers.

Standard Form is used for representing:

Distances to galaxies, solar systems and planets.

Diameters and circumferences of planets.

Mass of planets or stars

Size of an atom

Mass of a proton

Mass of an electron

Converting: Normal > Standard Form

To convert a normal number to standard form:

1. Transform the number into a decimal so that the first digit is in front of the decimal point. (eg: 3,200,000 > 3.2). The decimal should be between 1 and <10.

2. Multiply the decimal by , where x is the digits that you have to move the decimal point left or right to get the original number. For the example above, this would be as we have to move the decimal point 6 digits to the right to get the original number.

Moving the decimal point:

Right: x is positive (very large numbers - >10)

Left: x is negative (very small numbers - <1)

Converting: Standard Form > Normal

When converting standard form numbers to normal numbers, you simply move the decimal point by the number of times indicated by . This can be a bit complicated for larger numbers.

Examples:

Conversion (Calculator)

With a calculator, converting standard form is a lot easier.

When converting standard form to normal numbers simply type in the standard form expression into your calculator. If you press enter, it will show you the normal number.

To convert normal numbers to standard form use the scientific notation function on your calculator. Type in the original number and the calculator should transform it into .Where n is equal to the decimal, E to 10 and x to the exponent of 10.

Multiplying & Dividing Standard Form

Multiplying

Multiply the decimals of both standard form numbers

Add the exponents of both standard form number

Put the results together to get the answer

Dividing

Divide the first decimal by the second one

Subtract the first standard form exponent from the second

Put the results together to get the answer

Adding & Subtracting

To add/subtract:

Convert the standard form numbers into normal numbers

Add or subtract the normal numbers

Convert the answer back into standard form (optional)

You can also do standard form calculations using a calculator by simply typing in the expression.

Learn More!

Learn More on Ultimate Maths

Standard Form Lessons