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Significant Figures
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You've probably done a calculation where the calculator spit out a number with a decimal that goes on and on. You probably also used a gut feeling for where to round it. Well, scientists don't like gut feelings. They have come up with rules for where to round calculations. These rules tell them which digits, or "figures," in a calculated answer are significant.

Significant figures (or "sig figs") are the digits in a number that actually mean something.

Example: How Many Miles is 34,000 Feet?
Say you want to know how many miles up you are when the pilot of a plane says you are cruising at 34,000 feet.
You have to convert feet to miles.
Original measurement
over 1.
conversion factor
down-arrow   down-arrow
34,000 feet x conversion factor 1 mile/5280 feet = (34,000*1 mile)/(1*5280) =
up-arrow up-arrow                          up-arrow
"feet" cancel but miles remain.
Multiply across the top and bottom.
34,000 miles/5280= 34,000 divide 5,280 miles = 6.4393939393 miles
Answer given by my calculator.

Do you conclude you're flying exactly 6.4393939393 miles up? No. When the pilot said you were flying at 34,000 feet, he meant about 34,000 feet. So your answer can only mean about 6.4393939393 miles.

A scientist would say that a lot of the digits in 6.4393939393 are not significant. That's because the original measurement of 34,000 feet wasn't all that accurate to begin with.
People who saw this lesson also found the following lessons useful:
Place Holder Zeroes
Significant Figures and Measurements
Determining Number of Significant Figures in Answer
Scientific Notation and Significant Figures
Significant Figures and Conversion Factors
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