Significant Figures Everyday Examples

Significant Figures – Everyday Examples

Your spouse says you have one-hundred dollars in the bank account. How big a check can you write?

Do you have exactly one-hundred dollars, expressed by 5 significant figures: $100.00?

Or was your sweetheart rounding? By how much? He or she might have meant you have somewhere between $95 and $104, rounding to the nearest $10 dollars. You can also call that rounding to two significant figures: $1.0 x 102 (though, of course, you would never write an amount of money in this way).

If you’re married to a detail-oriented person, you might actually have $100 plus or minus a bit of change. Rounding to three significant figures, or to the nearest dollar, means you have somewhere between $99.50 and $100.49. Again, if we wrote money in scientific notation, rounding $100 to three significant figures would look like $10.0 x 101.

But how big a check can you actually write? Taken literally, one-hundred dollars in the bank could legitimately mean somewhere between $50 and $149 if only one significant figure is implied. So the largest check you can write is $50.

Now don’t you wish you found a scientist to share your life? Or are you glad you did?

A gas station attendant tells you and your fellow sales team road-trippers that you only have twenty-two miles left until Davenport. Seems pretty exact, right? But just exactly how far away is Davenport?

In this case, we have two significant figures. Saying Davenport is between 15 and 24 miles away is not an appropriate interpretation of the attendant’s statement, because it rounds to the tens of miles, or one significant figure.

What we can say is that Davenport is between 21.5 and 22.4 miles away, assuming the attendant knows what he’s talking about. His measurement of 22 miles should be precise to the nearest mile.

If he’d wanted to be even more precise, he might have told you Davenport is 22.0 miles away, a number with three significant figures, rounded to the nearest tenth of a mile.

Anybody recognize the Chris Farley movie in which the original scenario is found?