Albert Teen
powered by
Albert logo


Standard Form: Basics

Standard Form: Basics

Standard Form: Basics

When numbers get really big or really small, standard form helps us to make numbers shorter and easier to understand by using indices with a base of 10.

Standard form makes it easier to write really big or really small numbers.

Why do we use standard form?

The speed of light is approximately 299,792,458299,792,458 metres per second, which is close to 300,000,000300,000,000 m/s (the unit for metres per second).

As you can see, this number is quite long and difficult to read!

However, when we use standard form, the speed of light looks like this:

3×108 3 \times 10^8

Standard form always looks roughly the same:

a×10xa \times 10^x

aa and xx can change, and aa is a number between 0.99 and 10.

Which of the following is in correct standard form?

Let's try expressing the number 560,000560,000 in standard form.


The new format should be a×10xa \times 10^x

aa must be a number between 11 and 1010.


We need to convert 560,000560,000 to a number between 11 and 1010

560,000560,000 is the same as 560,000.00560,000.00.

Let's move the decimal point to the left, so the number is between 11 and 1010.


How many places to the left should we move?


We've moved 5 places to the left

Therefore, we've divided the original number by 100,000100,000.

Notice that 100,000100,000 is the same as 10510^5.


By moving 5 places, we divide by 10510^5

Therefore, the number of places we move is the same as the index.


Now we can express in standard form

560,000=5.6×105560,000 = 5.6 \times 10^5

What is 56,88056,880 in standard form to 3 significant figures?

Let's have a go at expressing 45,67845,678 in the form a×10xa \times 10^x to 3 significant figures


aa must be between 11 and 1010

Divide 4567845678 by 1000010000. This leaves 4.56784.5678


Round 4.56784.5678 to 3 significant figure

4.56784.57(3sf)4.5678 \rightarrow 4.57 (3sf) as the 77 means we need to round up.


Express 10,00010,000 as a power of 1010


Now express this in standard form

45678=4.57×104(3sf)45678 = 4.57 \times 10^4 (3sf)

What is 7.23×1067.23 \times 10^6 as an ordinary number?

Small numbers can also be written in standard form, but the number of places the decimal point needs to move is written as a negative power.

0.00000375 can be written as:

3.75×1063.75 \times 10^{-6}

Let's convert 0.00007450.0000745 to standard form (3 significant figures)


Now we have a really small number

This time, we need to move the decimal place to the right, to get a number between 11 and 1010.


What is the first part of this standard form?


Find the power of 10

We moved the decimal point 5 places to the right, which means that the power of 10 is 5-5.


Express in standard form

0.0000745=7.45×1050.0000745=7.45 \times 10^{-5}

What is 0.00000045790.0000004579 in standard form to 3 significant figures?

What is 1.44×1071.44 \times 10^{-7} as an ordinary number?