Day 7 – Scientific Notation

TEXT: Intermediate Algebra by Miller, O’Neill & Hyde

Videos from Khan Academy.

What is scientific notation?

Sometimes numbers are too large or small (close to zero) to be comfortably expressed in our usual or standard notation. Scientific notation expresses a number as the product of two factors. The first factor captures the most significant digits. The second part, the magnitude, is a power of ten, showing us how large or small the number is.

Conversion

To convert a number in standard notation, count the number of times it takes to move the decimal point so that it is just to the right of the first nonzero digit (reading left to right). If the number was large, then the exponent is positive. If the number was small (close to zero), then the exponent is negative.

Examples:

1. The main span of the Brooklyn Bridge 19,146 inches. We move the decimal 4 places to the left and since the number is positive, we get 1.9146 x 10^4 inches.
2. A student collects a water sample from the foot of the Brooklyn Bridge as part of her project. She looks at the water under a microscope and sees cells of algae that are 0.000026 m by  0.000078 m wide. We move each of the decimal points over 5 places to the right to get. 2.6 x 10^-5 m by 7.8 x 10^-5 m.

Complete the chart on facts regarding the Brooklyn Bridge (from Life and Wikipedia):

Quantity	Standard Notation	Scientific Notation
car crossings/day (2008)	123,781
pedestrians opening day		1.503 x 10^5
total weight of bridge	29360000 lbs
weight of suspended portion		1.324 x 10^7 lbs
length of wires on bridge		1.406 x 10^4 miles

Note that the above examples from the bridge all involved large numbers. To get small numbers, let’s go to the world of micro-organisms:

Quantity	Standard Notation	Scientific Notation
ebola virus	.00000014 m long
rhino virus		2.3 x 10^-8 m diameter

Performing operations using scientific notation.

You must be able to in particular multiply and divide. See the videos below: