Scientific notation is a way of writing numbers. It is often used by scientists and mathematicians to make it easier to write large and small numbers.
The basic idea of scientific notation is to express zero as a power of ten.
The notation for this can be written as: a × 10b where b is an integer or whole number that describes the number of times 10 is multiplied by itself and the letter 'a' any real number, called the significant or mantissa.
Example:
700 is written as 7 × 102 in scientific notation.
Both 700 and 7 × 102 have the same value, just shown in different ways.
Let’s see how it works.
4,900,000,000 is written as 4.9 × 109 in scientific notation.
1,000,000,000 = 109
Both 4,900,000,000 and 4.9 × 109 have the same value, just shown in different ways.
So the number is written in two parts:
(i.e. it shows how many places to move the decimal point)
5326.6 = 5.32366 × 103
In this example, 5326.6 is written as 5.3266 × 103
because 5326.6 = 5.3266 × 1000 = 5.3266 × 103
Others ways of writing it
We can use the ˄ symbol as it is easy to type: 3.1 ^ 108
For example, 3 × 10^4 is the same as 3 × 104
3 × 10^4 = 3 × 10 × 10 × 10 × 10 = 30,000
Calculators often use E or e like this:
For example, 6E + 5 is the same as 6 × 105
6E + 5 = 6 × 10 × 10 × 10 × 10 × 10 = 600,000
For example, 3.12E4 is the same as 312 × 104
3.12E4 = 3.12 × 10 × 10 × 10 × 10= 31,200
How to do it?
To figure out the power of 10, think “how many places do I move the decimal point?”
Example: 0.0055 is written 5.5 × 10-3
Because 0.0055 = 5.5 × 0.001 = 5.5 × 10-3
Example: 3.2 is written 3.2 × 100
We didn’t have to move the decimal point at all, so the power is 100
But it is now in scientific notation.
Check!
After putting the number in scientific notation, just check that:
The digits part is between 1 and 10 (it can be 1, but never 10)
The power part shows exactly how many places to move the decimal point.
Why use it?
Because it makes it easier when dealing with very big or very small numbers, which are common in scientific and engineering work.
Example: It is easier to write and read 1.3 × 10-9 than 0.0000000013
It can also make calculations easier, as in this example:
Example: A tiny space inside a computer chip has been measured to be 0.00000256m wide, 0.00000014m long and 0.000275m high.
What is its volume?
Let’s first convert the three lengths into scientific notation:
Then multiply the digits together (ignoring the ×10s):
2.56 × 1.4 × 2.75 = 9.856
Last, multiply the ×10s:
10-6 × 10-7 × 10-4 = 10-17 (easier than it looks, just add -6, -4 and -7 together)
The result is 9.856 × 10-17 m3
It is used a lot in science.
Examples: Suns, Moons, and Planets
The Sun has a mass of 1.988 × 1030kg
It is easier than writing 1,988,000,000,000,000, 000,000,000,000, 000 kg (and that number gives a false sense of many digits of accuracy).
