How is significant figures different to rounding?

When writing a number to a significant figure you have two options, either to remove and ignore all the least significant digits when writing the new number, or to round them to it's closest number depending upon if it's below or above 5.

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My answer:

Significant figures and rounding are related concepts. Often you hear something like:

give the answer to 3 significant figures

when you're doing a calculation.

For example if you get an answer like 4.127 cm and you're asked to give it to 3 significant figures, that just means you're only allowed to include 3 digits.

4.127 has 4 digits, so you have to get rid of one of them. You get rid of the one with the least meaning, the least contribution to the total. This is obviously the smallest one.

So the 7 has to go.

But if you write 4.12 your answer would be misleading.

Why?

Because 4.127 is closer to 4.13 than 4.12

So the idea of rounding is a way of making sure that when you get rid of the 7, you pay attention to the fact that 7 is closer to 10 than it is to 0.

In fact 6, 7, 8, 9 are all closer to 10 than 0, which means they all round UP

0, 1, 2, 3 and 4 are all closer to to 0, which means they round DOWN.

The tricky one is 5, which is bang in the middle. By convention, we choose to round 5 UP because it means we have the same number of digits rounding up as rounding down. (5 digits each, which is symmetrical and maths people love symmetry)

This means that 5, 6, 7, 8 and 9 all round UP

and 0, 1, 2, 3 and 4 round DOWN.

All this means that if you are asked to give your answer of 4.127 to 3 significant figures, then 4.13 is a more accurate answer than 4.12.

Hope this helps!

Rounding as a general concept is making a number simpler but keeping its value close to what is was originally. Significant figures help round to the most important number, however it depends how many significant figures you want to round to. For example rounding to 1 significant figure you would look at the first non-zero value (anything that’s not zero), whereas 3 you’d look at the third non-zero value. With keeping in mind that the number you are rounding off, if the number after it is equal to or greater than 5 you round to the next number, if it is less than 5 you keep it the same. E.g. 3487 rounded to 3 significant figures would be 3490, as 1. The 8 in 3485 is the third significant number therefore we are rounding it off, and 7 > 5 therefore 8 becomes 9 as that’s the next number up.

When you have a number, such as 1234.56, you can round to any place. For example, to the neareast hundred would be 1200, or to 1 decimal place would be 1234.6.

With significant figures, it is rounded to a certain number of non-zero numbers. For example, to 3 significant figures would be 1230 because their are three non-zero numbers.

At GCSE, you usually round to decimal places. So when rounding to a decimal place you round to the number of decimal places specified and this will be the number of digits after the decimal point. So let's take for example 2.1578 and round it to three decimal places:

I would end up with 2.158.

A significant figure is different as you need to end up with the total amount of digits specified. The way of getting significant figures is the same as rounding but you just end up with a different result. So let's take the same number: 2.1578 and round it to three significant figures. This means we need to end up with the three largest digits which are 2.15. However, as it is similar to rounding we will end up with 2.16 as the digit before the 5 was a 7, so you need to round up.

So in conclusion the number 2.1578

three decimal places - 2.158

three significant figures - 2.16

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