# Significant figure

Hi, I have a question regarding significant figure.

One rule when multiplying measured quantity is that the final answer needs to use the least number of significant digits provided in the question.

Now.. if v = 17 m /s and t= 0.8 s. What is d?

d = v * t
d = 17 m / s * 0.8 s
d = 13.6 m

Now, v has two significant digits. But what about t? Can we consider t to have two significant digits instead of one?

So, should I leave the answer the way it is (3 significant digits), round it up to 14 m (2 significant digits), or round it down to 10 m (could be considered as 1 or 2 significant digits)?

My dillema is if t is considered as having 1 significant digit and I do need to round the answer down to 10 m, wouldn't it be much less precise than 13.6? Why should I make it less precise, wouldn't a more precise answer better than the unprecise one?

Also, if I do need to round it down to 10 m, how should I write down my final answer? Just plain 10 m or 1*10^1 m ?

Thanks very much,

James

First of all, 10 has 2 significant digits. In fact, any zeroes on the right of the number is significant. e.g. 1.2000 has 6 significant digits. (This is used to show how accurate the number is)

I see a problem there, the final answer uses the most number of significant digits. This makes a lot more sense and helps solve dilemmas like this.

The answer you want is 14m in this case. (although in real life, 13.6m is the appropriate answer)

Side note: the scientific notation for powers of ten, such as the number 10, is indeed 1*10^1. And similarly 100 is 1*10^2.

P.S. This 'significant figures' thing is only taught in Regents science classes. Many people would give their answers in the least power of ten used (by this I mean hundreds, tens, ones, tenths, and so forth) like in your equation, the lowest power is the tenths power, so your answer would be in the tenths as well, 13.6m. But do what feels right. You would say that .2 * .2 is .04, right? you wouldn't round it to the nearest tenth.

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Thanks for the reply, livingod! I agree that zeroes at the end of a measurement are significant if it's in scientific notation. My textbook describes:

"Scientific notation is used to indicate if zeroes at the end of a measurement are significant: 4.50 x 10^7 has three significant digits and 4.500 x 10^7 has four significant digits. The same number written as 45 000 000 km has AT LEAST two significant digits, but the total number is unknown unless the measurement is written in scientific notation."

According to that passage, the number 10 has at least 1 significant digit. And it could have two significant digits. Also, what about the 0.8? Does it only have one significant digit?

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Livingod said:
First of all, 10 has 2 significant digits. In fact, any zeroes on the right of the number is significant. e.g. 1.2000 has 6 significant digits. (This is used to show how accurate the number is)

I see a problem there, the final answer uses the most number of significant digits. This makes a lot more sense and helps solve dilemmas like this.

The answer you want is 14m in this case. (although in real life, 13.6m is the appropriate answer)

Side note: the scientific notation for powers of ten, such as the number 10, is indeed 1*10^1. And similarly 100 is 1*10^2.

P.S. This 'significant figures' thing is only taught in Regents science classes. Many people would give their answers in the least power of ten used (by this I mean hundreds, tens, ones, tenths, and so forth) like in your equation, the lowest power is the tenths power, so your answer would be in the tenths as well, 13.6m. But do what feels right. You would say that .2 * .2 is .04, right? you wouldn't round it to the nearest tenth.
10 does NOT have two significant figures.

it would have to be "10." with a decimal point.

andrew: do you think i should have "10." as the answer? Also, generally in physics, is it a good practise to always round the answer to the appropriate number of digits (although less precise)? Or is it better to have a more precise answer?

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17 * 0.8 = 10