Using Scientific
Notation
What exactly IS scientific notation?
Scientific notation is simply a method to make a very large or small number easier to work with.
It has three parts to it: the coefficient, base, and exponent. The coefficient must be greater than or
equal to 1 and less than 10. The base is always 10, and the exponent is the number that shows
how many places the decimal point must move to change the number back to its original state.
Formula
a × 10^b
Now that may have been a little confusing right? Well that’s okay, let’s see an example.
Let’s try writing 567,000 in scientific notation.
5.67 x 10^5 = 567,000
First of all there is always a decimal at the end of whole numbers, we don’t write it, but its still
there. Now we take that decimal and move it backwards until we get a number that is greater
than or equal to one and less than 10. That number was 5.67. Afterwards count how many places
you moved and that is going to be the exponent number. The 10 will always be the same. So
therefore 567,000 written in scientific notation is 5.67 x 10^5.
Now that we have the basics down, lets simplify an equation then write it in
scientific notation.
1. 7.8 x 10^8 ÷ 2.6 x 10^-3
We would solve this like any other equation. Divide 7.8 and 2.6. You get 3. Now for the 10^8
and 10^-3. You actually have to subtract the exponents. So 8- -3 is 11 since it’s a double
negative it turns into a plus. The answer is 3 x 10^11.
2. (2.2 x 10^5)(4.5 x 10^11)
So 2.2 times 4.5 is 9.9 then we have to deal with the exponents. We have to add them together,
so 5 plus 11 is 16. The answer is 9.9 x 10^16.
Practice
1. 16 x 10^-3 ÷ 4 x 10^4
2. (6.8 x 10^3)(9.5 x 10^5)
3. (3.2 x 10^6)(1.7 x 10^4)
Answers at the bottom
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1. 4 x 10^-7
2. 6.46 x 10^9
3. 5.44 x 10^10
Good luck on the midterm guys