Algebra Period 4

Scientific Notation 5-4



You've had this since 6th grade!
It is just a bit more complicated
You restate very big or very small numbers using powers of 10 in exponential form

Move the decimal so the number fits in this range:
less than 10 and greater than or equal to 1
That is 1 ≤ n < 10
Scientific notation is the product of two factors
one of the factors is a number that is 1 ≤ n < 10 and the other factor is a power of ten

Count the number of places you moved the decimal and make that your exponent

Very big numbers - exponent is positive

Very small numbers (decimals) - exponent is negative (just like a fraction!)


Remember that STANDARD notation is what you expect (the normal number)



When you multiply or divide scientific notations, use the power rules!

Just be careful that if your answer does not fit the scientific notation range, that you restate it.

(2.5 x 10 ^-3)(4.0 X 10 ^-8)
multiply the first factors or (2.5)(4.) and multiply the powers of ten
(10 ^-3)(10 ^-8)

(2.5)(4)= 10
so initially you have 10 X 10 ^-11
but 10 does not fall into the required 1 ≤ n < 10
so changed 10 into scientific notation or 1.0 X 10¹
so you have 1.0 X 10¹ X 10 ^-11
or 1 X 10 ^-10

What about
6.0 x 10 ⁷
3.0 X 10²
First divide 6.0/3.0 = 2.0
and use the exponent rules of 10 ^{7 -2} or 10⁵
so 2.0 X 10⁵

4.2 X 10⁵
2.1 X 10³

= 2 X 10²

2.5 X 10 ^-7
5.0 X 10 ⁶
first 2.5/5 = 0.5 and 10^-7/10⁶ = 10^-7-6 = 10^-13
so initially you have
0.5 x 10^-13 but 0.5 is not within 1 ≤ n < 10
so change 0.5 to scientific notation
5.0 X 10 ^-1 and mult that by 10^-13
5 X 10 ^-14