The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
Calculating scientific notation for a positive integer is simple, as it always follows this notation:
a x 10b
Follow the steps below to see how 80,314,460 is written in scientific notation.
To find a, take the number and move a decimal place to the right one position.
Now, to find b, count how many places to the right of the decimal.
New Number: | 8 | . | 0 | 3 | 1 | 4 | 4 | 6 | 0 |
Decimal Count: | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
There are 7 places to the right of the decimal place.
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 8.031446 (Please notice any zeroes on the end have been removed)
b = 7
Now the whole thing:
8.031446 x 107
Check your work:
107 = 10,000,000 x 8.031446 = 80,314,460
80,314,458 | 80,314,459 | 80,314,461 | 80,314,462 |
8.0314458 x 107 | 8.0314459 x 107 | 8.0314461 x 107 | 8.0314462 x 107 |