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 414,113,120 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: | 4 | . | 1 | 4 | 1 | 1 | 3 | 1 | 2 | 0 |
Decimal Count: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
There are 8 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 = 4.1411312 (Please notice any zeroes on the end have been removed)
b = 8
Now the whole thing:
4.1411312 x 108
Check your work:
108 = 100,000,000 x 4.1411312 = 414,113,120
414,113,118 | 414,113,119 | 414,113,121 | 414,113,122 |
4.14113118 x 108 | 4.14113119 x 108 | 4.14113121 x 108 | 4.14113122 x 108 |