[JonathanEyoon]

Hi all I'm having trouble understanding Significant figures.  Can someone explain it to me where I could easily understand  Thanks and I appreciate it

[ARGOS++]

Dear JonathanEyoon;

Have you already study:   "Significant Figures”

At what moment your troubles arise?

Good Luck!
                    ARGOS⁺⁺

[JonathanEyoon]

thanks for the wikipedia link~ I'm taking a look at it right now. I may have questions about addition/subtraction and multiplication/division later.



When it comes to significant figures, what is the difference between 4.0g and 4.00g?

We were asked by the teacher and couldn't figure it out 

[constant thinker]

3. All zeros appearing to the right of an understood decimal point or nonzeros appearing to the right of a decimal after the decimal point are significant. Example: '12.2300' has six significant figures: 1,2,2,3,0 and 0. The number '0.00122300' still only has six significant figures (the zeros before the '1' are not significant). In addition, '12.00' has four significant figures.

That's from wiki. The difference is that 4.0 has 2 sig figs and 4.00 has 3 sig figs. All zeros to the right of the decimal point are significant.

This can be a tough concept to understand though because you have numbers like .0025 which only has 2 sig figs, but there are 4 numbers, two of which are 0's, after the decimal point. You have to convert to scientific notation. That's what the sig fig rules are relative to. So to figure out how many sig figs are in a number like .0025 convert to scientific notation. This will make your life easier.

.0025 --> 2.5 X 10^-3

As you can see you only keep two numbers so only two of them are significant.

As a reference though 4.0, 4.00, and 400.0 in scientific notation are:
4.0 --> 4.0 X 10¹
4.00 --> 4.00 X 10¹
4000 --> 4.000 X 10 ²
As you can see in scientific notation you have 2 and 3 sig figs respectively. Those at the end are always kept for reasons I can't explain.

[Arkcon]

4.0 has two sig figs., 4.00 has three sig figs.  Yes, it's just that simple!

But wait, there's more...! (I'm going to stop doing that now, it's silly)

When you say, 4.0, you make a statement about your accuracy.  You're saying, "It is between (about*) 3.6 to 4.4"  When you say -- 4.00, you're saying it is between (again, about*) 3.96 to 4.04.  As you can see, the second time around the numbers are "better" i.e. more accurate.

You can only say I measured it to 4.00, if you have an instrument that works to that many decimal places.  Sometimes you have one, sometimes you don't, sometimes it's a good quality balance scale, on a shaky table, and you can't use the last decimal place, even if you want to.

Your final answer can only have as many significant figures as your worst measured value.  So, for example, if you've taken ten readings, nine of them at 3 sig figs and one at 2 sig figs(lab bench was used for can-can practice that day), you report the average to two sig figs.

These are some of  the early concepts on sig figs that everyone has to learn.

*Some people use different rules for rounding, just so you know

[Borek]

*Some people use different rules for rounding, just so you know

Some people will reject whole idea of significant figures as a fautly approach to reporting accuracy. After reading their arguments I would not dare to say they are wrong.

[Arkcon]

*Some people use different rules for rounding, just so you know

Some people will reject whole idea of significant figures as a fautly approach to reporting accuracy. After reading their arguments I would not dare to say they are wrong.

I can relate, but the wikipedia entry, even with the citations, is a little heavy handed in their arguments.  The NIST may feel that it's a dumb crutch to prevent false reports of precision, but if you can't support why your answers have x degree of precision in the production of a pharmaceutical, the FDA will shut you down.

[Alpha-Omega]

Constant Thinker-EXCELLENT EXPLANATION THERE...I love the way you laid that out...very logically conceived...I actually printed that out...have it pinned on the wall....beautifully said...