Significant figures

So if it is 27 degrees, then that measurement has two digits, the first digit we know for certain, and the second digit is estimated and therefore uncertain.

But both are considered significant figures.

Now let’s look at a different thermometer, which has markings of 1 degrees Celsius.

So this time, the measurement is between the markings for 26° C and 27° C.

So you don’t have to guess on the second digit, you know that it’s 27.

But you have to guess on the third digit, which looks like it might be 27.2 degrees Celsius.

In this case, the uncertain digit is the last two.

But all three digits are considered significant figures for this measurement.

In general, when reporting measurements, the precision of your measuring device determines the number of significant digits.

If any estimation is involved in reading a number from your device --- like a thermometer or a graduated cylinder --- then you record a measurement rounded to one decimal place beyond the decimal place of the markings.

If you use a digital measurement, like a digital scale or pH probe, then there’s no estimation involved.

You can just record however many significant figures are reported by the measurement device.

So the number of significant figures is affected by the instrument used to perform a measurement.

As another example, for finding the volume of a liquid, the most common way would be to use a graduated cylinder. In order to maximize the precision of our measurement, we would pour liquid into our graduated cylinder and then locate the bottom of the meniscus.

We can draw a line there, and then read it off our measurement device.

So in this case, the meniscus is between two markings on the graduated cylinder, 4.5 milliliters and 4.6 milliliters.

The last digit we estimate, which makes it the final significant figure.

The meniscus looks evenly spaced between the markings, and so we can record 4.55 milliliters as our measurement, for a total of three significant figures.

Now that we know how to record our measurement, we want to figure out which of our recorded digits are significant figures.

There are seven rules to remember when keeping track of significant figures:

Rule 1 is that any non-zero digit is significant.

For example, if the measurement is 5.76 meters, then the three nonzero digits: five, seven, and six, are all significant, meaning that there are three significant figures.

Rule 2 is that included zeros are always significant.

So if the measurement is 1.076 meters, then we have an included zero in the middle of the measurement, and the surrounding digits are nonzero - in this case the 1 and the 7.

So there are four significant figures.

Another example, is the number 2035.

The included zero is significant because the surrounding digits are nonzero - in this case the 2 and the 3.

So there are four significant figures.

Rule 3 is that trailing zeros in a decimal number are significant.

So if we had a measurement on a balance of 6.100 grams, the two trailing zeros, since they are in a decimal number, are significant.

So there are four significant figures.

Next, rule 4 is that leading zeros are not significant.

Let’s say we had 0.000620 grams as our measurement, then we could count these first four zeroes as leading zeros.

The zero at the end is considered to be significant, going back to rule 3 which says that the trailing zeros in a decimal number are significant.

So there are three significant figures.

Rule 5 says that when scientific notation is used, all digits are significant.

So, if we put the previous measurement into scientific notation, then 0.000620 becomes 6.20 x 10-4 grams.

Here, all of the digits are considered significant, so there are three significant figures.

Rule 6 says that trailing zeros in a non decimal number are not significant.

Say we had “94000 seconds” as our measurement. The trailing zeros would be the three zeros on the right side.

But for this measurement there are only two significant figures.

According to rule 6, the nine and the four are nonzero digits which are significant.

And these three zeros to the right are not significant.

The way to make them significant would be to put a decimal point at the end.

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en inglés

Significant figures are the digits in a number that carry meaning in terms of the precision of the measurement. Significant figures are used in scientific measurements and calculations to communicate their level of precision and accuracy. They include all non-zero digits and any leading zeros that come before the first non-zero digit in a number, and exclude trailing zeros that come after the last non-zero digit unless they are explicitly indicated to be significant.

Significant figures

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