Move the decimal to the right of the first nonzero digit. This results in a real number a.
Note the number of places n and the direction that you moved the decimal point.
If the decimal point is moved left, write the number as a * 10^n. If the decimal point is moved right, write the number as a * 10^(- n).
Remove any unnecessary zeros.
To write one hundredth and one micron in scientific notation, let's reference the standard form written in Part A.
0.01 & 0.000001
Now we can follow the steps. Let's begin with one hundredth.
Step
Work
Result
1
a=001
2
The decimal point moved 2 places to the right.
n= 2
3
Since the decimal moved to the right, we will write it as a * 10^(- n).
001 * 10^(- 2)
4
Remove the unnecessary zeros.
1 * 10^(- 2)
Let's continue with one micron. 0.000001
Step
Work
Result
1
a=000001
2
The decimal point moved 6 places to the right.
n=6
3
Since the decimal moved to the right, we will write it as a * 10^(- n).
00000001 * 10^(- 6)
4
Remove the unnecessary zeros.
1 * 10^(- 6)
So one hundredth written in scientific notation is 1 * 10^(- 2) and one micron is 1 * 10^(- 6).
c
The smallest size particle that the filter will stop is one hundredth of a micron. We can get the standard form by multiplying their standard form equivalent. Then we will do the same for the scientific version.
We can also multiply both of the standard forms to obtain the same answer in standard form. The smallest size particle that the filter will stop is 1 * 10^(- 8), or 0.00000001.
