How is significant figures different to rounding?

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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!

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.

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

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.

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.

With rounding you are looking at place value, but with significant figures you have to remember that significant figures do not include 0s in the higher place value spots. For example in 0.0092, the first significant figure would be 0.009 (since you do not count the 0s before the first significant figure).

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.

Significant figures is not different to rounding, it is a way to round numbers. You can choose to round it to (including but not limited to) the nearest hundreds, tens, integers, specified decimal places, and at last significant figures.

Rounding is when a number is rounded to the nearest specific whole number. If the last digit is a 5 or more it will be rounded up, if lower than a 5 it will be rounded down.

For example, 4.45 rounded to the closest whole number would be 4. 4.55 would be rounded to 5.

Significant figures relate to the detail required. 4.45 displayed as 2 significant figures would be 4.4

13,945,700 to 3 significant figures would be 13,900,000 or in standard form, 1.39 x 10^7

When you round a number you always start from the first digit. With significant figures, the zeros at the front of the number are ignored, and you start counting from the first non-zero digit (a significant figure!).