Scientific notation
We can use scientific notation to write very large or very small numbers in a concise
way. It is also called standard notation.
For example:
The population of the Earth in May 2010 was approximately 6 820 000 000.
This can be written in scientific notation as:
6.82 x 109
The mass of an electron is approximately 0·00000000000000000000000000000091 kg.
This can be written in scientific notation as:
9.1 x 10 -31 kg
Numbers written in scientific notation:
have a number between 1 and 10 – the decimal point is after the first significant digit
that are multiplied by a power of 10 – the power is equal to the number of places the decimal point
has changed.
If the original decimal number is bigger than 10, the power is a positive number.
If the original decimal number is between 1 and 10, the power will be zero.
If the original decimal is smaller than 1, the power is a negative number.
The decimal point
goes after the 6.
The original number
was bigger than 1
so the power is +14.
657 000 000 000 000 is written as:
6.57 x 1014
There are 14 digits between
where the decimal point was
and where it has been put.
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The decimal point
goes after the 5.
The original number
was less than 1 so
the power is -15.
0·000000000000005 is written as:
5 x 10 -15
There are 15 digits between
where the decimal point was
and where it has been put.
When changing from scientific notation to an ordinary decimal:
if the power is positive, the decimal number will be bigger than 10
if the power is 0, the decimal number remains the same
if the power is negative, the decimal number will be less than 1
the power tells us how many digits there has to be between where the decimal point is and
where it goes in the decimal number
we use zeros to fill in the missing numbers.
Power is +5 so the
decimal number is
bigger than 1.
Need to add three zeros so
there are 5 digits between
the positions of the decimal
points.
2.61 x 105 = 261 000
Power is -3 so the
decimal number is
smaller than 1.
Need to add two zeros
so there are three digits
between the positions of
the decimal points.
5.3 x 10 -3 = 0.0053
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© Owned by State of NSW through the Department of Education and Training 2010. This work may be freely reproduced and distributed
for non-commercial educational purposes only. Permission must be received from NSW DET for all other uses.
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