# Significant Figures: Maths Question of the Week 14

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What are the major misconceptions and misunderstandings that students have when it comes to rounding to significant figures? Using real life data and actual student explanations, we can gain a deep insight into how students think.

Have a look at the question below

What percentage of students do you think get it correct?
What is the most popular incorrect answer?
What explanations do students give for the incorrect answers?

Give the question a go yourself, and try to come up with an explanation of the correct answer that would make sense to students:

At the time of writing, this question has been answered 133 times, and has been answered correctly 59% of the time. The percentage of students answering incorrectly is pretty evenly split between the 3 incorrect answers (A, B and D)

Now, looking at the alternative answers, we can probably hazard a guess as to why students have gone wrong. But why do that when we can read actual student responses? :-)

Visiting the Data Question page (which is also accessible to all who have answered the question by clinking on the small graph icon in the bottom-right corner of the question window) is very revealing.

Scrolling down, we can see that the most popular explanation given for the correct answer (at the time of writing) is:

The zeros do not count as ‘significant’ so your first significant figure is 2. You have to do it to 3 sf so you look at the third figure which is 9. The number to the right of that is 5 so you round nine up to a 0 and the 8 has to become a 9 as you are rounding up.

I also like this one:

0 is not a significant number until it is between two numbers so the three most significant figures are 2 , 8 and 9. Next number is 5 so you round it up and you get 0.0290.

Indeed, there are lots of beautiful explanations that your students can read until they find one that makes sense to them. And we as teachers can benefit by having more explanations up our sleeve to try on students that are struggling.

But what about the incorrect answers? Let’s take a look at the reasons students give for them, using the drop-down answer filter:

Answer a)

You look at the 2895 part of it and that can be rounded to 3000. But because it is a decimal you just put the 0.02895 as 0.03 And that is to 3 significant figures.

there only has to be 3 numbers and its asking for significant figures not 3 decimal points

Answer b)

You ignore the 0’s and this means it becomes 0.02895 since there is not a number in front of them.

because 289 is the first 3 significant figures

B is the only answer with three substantial figures in is.

Answer d)

0.029 0.02895 5 rounds 9 up so it becomes a 0 but 8 becomes 9 so 0.029 and you don’t need to include a 0 at the end because it doesn’t mean anything

the first three significant figures are the 239 of 0.02395 so we are trying to round 0.0239 which would be 0.0290 which is 0.029

Crystal clear explanations that give you a valuable (and fascinating!) insight into the problems your students may face when tackling the topic of significant figures.

And of course, you can include this question in a Quiz to give to your students to see how they get on. Alternatively, here is a quiz I have put together on rounding to significant figures that you might want to assign to your class:

There are lots of new and exciting features that are freely available on the Diagnostic Questions website. These include the ability to:

Import students and classes

Assign quizzes to your students which they can answer on their phones, tablets or computers

You instantly get data back from your students, including their explanations for their answers, giving you real insight into their thinking and misconceptions

The ability to compare your students’ performance with students from all over the world

Your students can benefit by being able to read 100s of high-quality explanations that other students have given to questions to help deepen their understanding of a given concept.

You can benefit from gaining a real insight into the misunderstanding and misconceptions students have with specific skills by looking at data and reading explanations from students from all over the world.