The high-schooler typically first learns of significant figures when learning chemistry, since it is an essential part of recording and manipulating data. This resource covers the significance of significant figures (haha) and how to perform basic operations with them.
https://chemquiz.net/sig/ is a good site to practice with sig figs after understanding the content in this resource!
This resource is associated with Maggie Z’s Schoolhouse session “Significant Figures in Chemistry.“
Imagine that you have a 100.0 liter fish tank. Then, you use a micropipette to remove one microliter (0.000001 liters). How much water is left? If you treat both measurements as exact, you would say 99.999999 liters. However, the problem is that most measurements we have aren’t exact, and it is simply not appropriate to assume that level of precision in our measuring tools.
That is why we have the concept of significant figures. It allows us to can record measurements with the appropriate level of precision, and perform operations on those numbers accordingly.
It is perhaps easier to first guess than read about how sig figs work. Here is a chart of some numbers and how many significant figures they have:
As you can see, sig figs are quite intuitive. Start counting with the first nonzero digit in the number. If there are trailing zeros, they only count if there are decimals involved.
Use scientific notation! That would be 7.0 * 10³. The exponent is considered to be exact, which means that it has infinite precision and doesn’t need to bother with sig figs.
Multiplying and dividing with sig figs is quite straightforward. The number that has the least significant figures limits the precision of the entire expression, and the answer must have that number of sig figs. For example, 56 * 3 = 200. Since 3 has only one sig fig, the answer must have one as well. However, if 3 were considered to be an exact number, then the expression would equate to 170.
🧮 Try these yourself! Click the dropdown for the answer.
1600
The answer just so happens to work out as the same as what we would’ve gotten if we didn’t account for sig figs.
(In math, we almost never care about sig figs, because all numbers are exact.)
0.04
The answer must have one sig fig.
0.72
1 is exact, so it does not limit the precision of the result.
60000 or 6 * 10⁻⁴
There should be one sig fig, due to the 8.
2.4
There should be two sig figs, due to the 91.
If we were to account for sig figs when considering the fish tank problem at the beginning of this resource, we would say that 100.0 liters – 0.000001 liters = 100.0 liters.
Instead of simply keeping track of the lowest number of sig figs, we keep track of the least precise decimal place. The least precise decimal place in the above equation is the tenths place, and the answer must reflect that. We round in order to ensure we have precision to the appropriate decimal place.
🧮 Try these yourself! Click the dropdown for the answer.
480
We can only afford to be precise to the tens place.
50000
This is quite similar to the fish tank example!
2.72
2 is exact and does not limit the precision of the result.
53
This one works out perfectly, since the last significant figure is in the same place in both numbers.
1100
With exponents and radicals, we typically simply go by the number of sig figs in the base or radicand. (The base is the bottom number in an exponent, and the index is the number inside the radical.)
This is because we assume that powers and indices are exact if they are whole numbers. Following this reasoning, sqrt45 = 6.7.
🧮 Try these yourself! Click the dropdown for the answer.
7.7
1.8 * 10⁹
2.2
45
End of resource content. Check introductory blurb for practice resources.
✸ Thank you for reading!
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This resource was published on The Sparchive on September 5, 2026.