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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 299,792,458 metres per second, which is close to 300,000,000 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:
Standard form always looks roughly the same:
a and x can change, and a is a number between 0.99 and 10.
Which of the following is in correct standard form?
Let's try expressing the number 560,000 in standard form.
The new format should be a×10x
a must be a number between 1 and 10.
We need to convert 560,000 to a number between 1 and 10
560,000 is the same as 560,000.00.
Let's move the decimal point to the left, so the number is between 1 and 10.
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 100,000.
Notice that 100,000 is the same as 105.
By moving 5 places, we divide by 105
Therefore, the number of places we move is the same as the index.
Now we can express in standard form
What is 56,880 in standard form to 3 significant figures?
Let's have a go at expressing 45,678 in the form a×10x to 3 significant figures
a must be between 1 and 10
Divide 45678 by 10000. This leaves 4.5678
Round 4.5678 to 3 significant figure
4.5678→4.57(3sf) as the 7 means we need to round up.
Express 10,000 as a power of 10
Now express this in standard form
What is 7.23×106 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:
Let's convert 0.0000745 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 1 and 10.
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.
Express in standard form
What is 0.0000004579 in standard form to 3 significant figures?
What is 1.44×10−7 as an ordinary number?