Scientific Notation

Taking note... scientifically?

Scientific notation is a shorthand that makes really big or really small numbers easier to work with. For example an electron is roughly 0.0000000000000282 m in diameter. Scientists use scientific notation to save time from writing all of those zeros. How do we do this?

A number written in scientific notation has two parts.

A coefficient (number) between 1-10
An exponential power of 10

Both parts of a number written in scientific notation should always be kept together.

Multiplying by powers of 10 has the effect of moving the decimal point, but not changing any of the other values in the number.

Multiplying by a positive power of 10 makes the number larger, and multiplying by a negative power of 10 decreases the number.

So, the diameter of an electron 0.0000000000000282 m can be rewritten as 2.82 x 10^-15 m

Calculations with scientific notation

Addition and Subtraction

Adding or subtracting two numbers in scientific notation requires that the exponent on the 10 is the same. If it is not we need to change one of the numbers to match the other. We can do this by moving the decimal point. Then we can add or subtract as normally, keeping sig figs in mind.

Multiplication and Division

multiplication and division is much easier. We can split up the calculation into two parts, the coeficient and the power of 10. First, multiply or divide the coefficients. Then if we are multiplying we add together the exponents on our base 10. If we are dividing then we subtract the exponents on the base 10.

Using Scientific Notation on a Calculator

Practice

Do the following worksheets without the answer key. Then check your answers on your own.

sig-fig-and-SN-practice-with-rules.pdf

scientific notation wkst Key.pdf

sig figs wkst 1.pdf

sig figs wkst 1 Key.pdf

Review Quiz

Complete this review quiz and submit it.

Significant Figures Quiz

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