Scientific Notation
Scientific notation is a number written as the product of a number greater
than or equal to l but less than 10 and a power of 10.
To convert a number from standard form to scientific notation, write the
number as a product of two factors.
- The first factor is a number greater than 1 but less than 10.
- The second factor is a power of 10 in exponent form.
Standard Notation
26,000
4,700,000
*3 billion = 3,000,000,000
129,300,000
219,000,000,000
Scientific Notation
2.6 x 104
4.7 x 106
3 x 109
1.293 x 108
2.19 x 1011
Remember with any whole number – the understood decimal is at the end of
the numbers!
When you are converting a number in standard notation to scientific
notation. Do the following:
1. Pin a decimal behind the digit counting from left to write.
2. Count the number of digits remaining to the right of the digit
that you have just inserted. This will be your exponent.
*When ever a number is written in word form or number word form
ALWAYS change that number to standard form before changing to
scientific notation.
To convert (change) a number from scientific notation to standard form,
move the decimal point to the right the same number of places as the
exponent.
Example: Scientific Notation
3.5 x 108
Standard Notation
350,000,000
You ask yourself how many digits do I have to the right of the decimal?
Then subtract that number of digits from the exponent and add that many
zeros to your original number. 3.5 – one digit to the right of the decimal.
One subtracted from eight is seven. Add seven zeros to 3.5. Then insert
commas working from right to left.
More Examples:
Scientific Notation
7.15 x 106
6.24 x 108
9.14 x 107
6.1482 x 105
8.89 x 107
Standard Notation
7,150,000
624,000,000
91,400,000
614,820
88,900,000