How is significant figures different to rounding?

Significant Figures describe the precision of a number. The more significant figures, the more precise the value.

Rounding is a process that you perform in order to truncate a number, making it easier to write down, but losing some precision in the process.

Significant figures does not include 0s coming before whereas rounding does. For example if you had the number 0.0234563 and you were asked to round it to 2 decimal places the answer would be 0.02 as you include that 0 in your counting. Whereas fi you were asked to find it to 2 significant figures the answer would be 0.023 as you would not include that 0 in your counting of 2 significant figures. Hope this helps :)

It isn't particularly different- it is used in exactly the same way. It's often used because its more scientific and there are conventions across orders of magnitude (e.g. if one answer is in the 10's of thousands and another is in the hundreds, it can be better to ask to significant figures). This is especially true when working out something such as energy where the same amount of energy can be expressed in J or KJ

Significant numbers is a way to round numbers, it is based on rounding to the nearest unit/ten/hundred and so on. Rounding significant after the decimal is the same as rounding to decimal places

Significant figures are how many digits (single numbers are required. Rounding to a decimal place is how many digits are after the decimal place. Rounding is when you work out if the last digit stays the same or goes up one point or down one point. You do this by looking at the number digit after this if it is 5+ then you round the number up. If 4 and below it stays the same.

Hey!

Technically, the idea of significant figures is part of rounding, i.e. rounding is a bigger idea that includes significant figures within it, so the two are not actually that different.

Perhaps what you are referring to is "rounding to x significant figures" vs "rounding to x decimal places".

In this case, significant figures is the number of non-zero digits of accuracy you shorten a number to, including numbers before the decimal point.

Meanwhile, decimal places is the number of non-zero digits of accuracy you shorten a number to, only considering numbers after the decimal point.

Let's use an example:

Say we have the number 7283.1234

If we round this number to 3 significant figures, we round it until we only have three digits of accuracy, so 7280 is our answer.

Meanwhile, if we round this number to 3 decimal places, we round it until we have three digits of accuracy after the decimal point, so 7283.123 is our answer.

I hope this clears things up!

Hi Ellis!

Significant figures is the number of digits in a number which appear after the first non zero number. Here are a couple examples :

12345.9 - This has 6 significant figures (1,2,3,4,5,9)

1.236 - This has four significant figures (1,2,3,6)

2.83004 - This has six significant figures (2,8,3,0,0,4)

0.0034 - This has two significant figures (3,4). Remember you only start counting numbers after the first non-zero.

Another example of this would be 0.00000246 - 3 significant figures (2,4,6).

When rounding you round to decimal places, units tens, hundreds etc. With the numbers above you have outcomes like this:

12345.9 rounded to the nearest 100 is 12,300. You look at the hundreds column (345) and see than 345 is closer to 300 than 400, so you round down. The number of significant figures does not have an effect on rounding.

1.236 rounded to two decimal places is 1.24 (You round three up because 6 is higher than 5)

1.236 rounded to one decimal place is 1.2 (You keep two the same because 3 is less than 5)

In short- Significant figures are the number of digits after the first non-zero. Rounding is done by decimals, units, hundreds, ett as seen in the above examples

Rounding would be what you are doing, significant figures, decimal places, or place value would be where you would round it to. These can be the same, for instance if we took the number 5.467, we could round it to 2dp which would be 5.47, which is the same as rounding to 3sf in this case.

-The number of Significant Figures is the number of digits in a value.

3.437 has 4 significant figures.

3.44 has 3 significant figures.

-Rounding means making a number "simpler",.

Rounding 3.437 to 2 significant figures, --> 3.4

Significant figures is basically rounding to the least accurate part of the calculation. For instance, 4.33x2.5433 is equal to 11.012489 but the least accurate part was 4.33 having only two decimal places. Therefore, we round up the final answer to two decimal places and achieve 11.01

Significant figures reflect the precision of a measuring device - in simple terms how many numbers it can measure down to. So an ordinary ruler for example can measure down to 1mm, and so numbers like 13.6 cm are possible to be recorded with it but 13.67 is not and neither is 13.60.

Rounding is often done for convenience. Take the value for pi for example which goes on forever. Using it with its infinite digits beyond the decimal is not very practical so we often round it 3.14. (Unless… see meme below ?)

When calculating answers you will often get a number with many decimals on your calculator. So the question becomes to how many significant figures should we round this? If you used practical data (the following is true in physics especially) then you always round to the lowest number of significant figures that was provided as this reflects the least precise measurement you could take. We do this because we recognise that the precision of our final answer is limited by the precision of our least precise measurement.

Hope that helps!

Now for the meme… a long standing jokes that engineers will just round irrational numbers to whatever is most practical!