How is significant figures different to rounding?

Significant figures and rounding are similar ideas with a few key differences between them. Significant figures usually represent the accuracy or precision of a number based on the measurements taken whereas rounding is done to simplify a number to make it easier to work with. For example, when you’re trying to split the cost of something so you round to 2 decimal places because the smallest form of money you can use is pennies.

Significant figures is a stated principle for the expression of numbers to required digits while rounding off of numbers is a Mathematical work to put numbers to required significant figures.

significant figures does not count zeros that are after the decimal point directly, rounding does

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!).

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.

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

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!

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.

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

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

The difference comes from

deciding the cut off point. For example rounding 0.00523 to 2 Decimal Points : The cut off point would be 2 digits after the decimal point. So we round at 0.00|5 and the 5 rounds up to a hundredth giving 0.01.

Rounding to 2 significant figures : the cut

off would be after the first 2 digits not including zeros. So we round at 0.0052|3 and 3 rounds down to 0 leaving 0.0052.

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.

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.