Supporting Students with Decimal Places vs. Significant Figures

sAInaptic knows how confusing mathematical exam questions can be to students, especially those who struggle to transfer skills learned in Maths to Science. As a teacher, one issue you may encounter is “How do I best support my students with understanding precision in calculations?”  This could be in standard calculation questions, or when handling measurements and experimental data. Do not fear though, help is at hand! This quick 2-minute read will help you to understand the difference between two common ways to show precision: decimal places and significant figures. Both are crucial for making sure your students’ answers are spot on!

Understanding Decimal Places:

Decimal places refer to the number of digits to the right of the decimal point in a numerical value. When you’re dealing with measurements or calculations that need exact answers, using decimal places becomes essential. For example, in the measurement of length, weight, or volume, using decimal places allows for a more exact representation of the actual value.

Let's say you measure something and find it's 3.456 meters long. That number has three decimal places, showing it's very precise.

Understanding Significant Figures:

On the other hand, significant figures are a touch trickier. They're a general way to show precision in a number. A significant figure is any number that helps make a number precise, like all the non-zero digits and even some zeros. For example, if you weigh something and it's 450.20 grams, there are five significant figures. It includes the non-zero digits (4, 5, 2), the zeros after the dot, and the zero between 5 and 2 – they all help make the number more exact.

Rounding to Different Decimal Places:

This is the easy part! If you’re asked to give your answer to a certain number of decimal places, you’re looking at rounding up your answer to that number of values after the decimal place.

Let’s look at an example, rounded to different numbers of decimal places. You’ve done your calculation, and the calculator gives you the following number “48.390712”. The value is currently to 6 d.p., which is too precise! Most questions require your answer to be 2 or 3 d.p. The table below shows this number rounded up to different numbers of decimal places. Remember the general rule of ‘5’ - if the number to the right is 5 or more then you round up, if it’s 4 or less you round down.

As you can see, the precision of the answer (how close it is to the actual value calculated) decreases as the number of decimal places reduces.

Rounding to Different Significant Figures:

When dealing with significant figures, it can be a bit trickier as we’re now dealing with ALL the numbers, both before and after the decimal point. If we look at the previous example (48.390712) this is currently standing at 8 significant figures!  

Let’s look at a different answer, this time we’re going to round to different numbers of significant figures! After completing a calculation you have the following answer displayed on your calculator “56,307.201”. In terms of rounding, the same rule of 5 applies. The table below shows what this would look like to different numbers of significant figures:

Choosing the Right Method:

So, when should your students use decimal places or significant figures? Well, it depends on what they’re doing. In a science experiment where exact measurements matter a lot, go for decimal places, as they help to show accuracy. For regular calculation problems, like rounding numbers, significant figures work just fine.  

Of course, students may be specifically asked to provide their answer to a certain number of decimal places or significant figures, so make sure to emphasise how important it is for them to read the question carefully, and underline key points/requirements.

Conclusion:

As with all exam craft, practice makes perfect, and ensuring you embed these differences into your daily teaching practice will help students became more confident in their use. Modelling and example answers are also crucial to support students with their understanding. Below you will find a couple of example questions utilising both decimal places and significant figures.  

Example 1:

Calculate the charge flow in a toaster if the energy transferred is 4,000J, and the mains potential difference is 230V. Use the equation given below:

energy transferred = charge flow × potential difference

Show your working out, and give your answer in coulombs (C)  to 2 decimal places.

charge flow = energy transferred ÷ potential difference

charge flow = 4,000 ÷ 230

charge flow = 17.3913043… C

Answer to 2 d.p.: 17.39 C

Example 2:

A bungee cord has an unstretched length of 15.0 m. The mass of a student on the bungee is 62.0 kg. The gravitational field strength is 9.80 N/kg.

Calculate the change in gravitational potential energy (g.p.e.) from the position where the student jumps to the point 15.0 m below.

Use the following equation:

gravitational potential energy  = mass x gravitational field strength x height

Show your working out and give your answer joules (J). Give your answer to 3 significant figures.

g.p.e. = 62.0 x 9.80 x 15.0

g.p.e. = 9,114 J

Answer to 3 significant figures: 9,110 J

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