Scientific Notation

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Scientific notation is a way of expressing really big or really small numbers in a more convenient manner.

Scientific notation takes the form of N x 10$^n$. N is a number between 1 and 10 and $n$ is an integer value. The exponent, $n$, will be negative if the number we are expressing is less than 1 and positive if it is greater than 1.

For example, one might write the number $0.00000516$ as $5.16\times10^{-6}$.

How do we do this?

When we look at whole numbers, the decimal point is implied at the end of a number.

i.e. $3,400,000,000,000.$

We need to move that decimal point to the left until we get a number between 1 and 10. We need to move the decimal point 12 times, so we would write the number like this:

$3.4\times10^{12}$

For numbers less than 1, we will move the decimal place to the right until we have a number between 1 and 10.

$0.00000000890$ becomes $8.90\times10^{-9}$ because we moved the decimal point 9 times.

We should also be able to go from scientific notation back to the "full" number. The number $2.45\times10^{-5}$ can be written as $0.0000245$ by moving the decimal point in 5 spaces to the left (we know the negative exponent indicates a number less than 1).

Significant Figures

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Significant figures, otherwise known as sig figs, are the meaningful digits in a measurement or calculation. The number of significant figures in a number is determined by how the number was measured or calculated. Ultimately, the number of sig figs in your measurement or calculated result is indicative of the precision.

Significant Figure Rules

1) All nonzero digits are significant. 2) Interior zeroes (zeroes between two nonzero digits) are always significant. 3) Leading/trailing zeroes: Imagine placing the number of interest inside a map of the United States as shown below.

(a) If a decimal point is present in the number (e.g. 0.00320), begin drawing an arrow from the side of the US with the Pacific Ocean, striking through all zeroes until you reach a nonzero number. The remaining numbers (no matter if they are zero or nonzero) are always significant.

(b) If a decimal point is absent in the number (e.g. 3200), begin drawing an arrow from the side of the US with the Atlantic Ocean, striking through all zeroes until you reach a nonzero number. The remaining numbers are significant.

Math With Significant Figures

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Check out the video for all the rules on how to report an answer from a calculation with the appropriate number of significant figures!

Click here to try out the Part A quiz for this section.

When you're confident in the skill, take the Part B quiz!