can you explain significant numbers to me?

Question

i just cant understand it. i would appreciate it if you would give me a simple explaination on how they work

Answer 1

Here's another way to put it....

Let's say you measure 1 cup of flower for a cake. You do this as carefully as possible with a measuring cup. You end up with what you believe is "exactly" one cup of flower. (e.g. "1 cup" not "1.30230 cups". Now it's clear that with a more specific measuring device you'd find that it was actually "1.01201202343240920384" cups of flower (or something like that) however the accuracy of your measurement is limited to your measuring device.

So...let's say you add your cup of flower (measured with a measuring cup) to a cup of flower that was measured precisely (e.g. 1.00000056 cups). Woudl you have 2.00000056 cups???

The answer is no. Because you were only sure of your answer to one significant figure, when you add the two, you can only be accurate to one significant figure. Therefore you'd have 2 cups (afterall...how do you know if it's 1.9, 2.0, or 2.1???). The 00000056 are all "insignificant numbers"

Your "poorly measured sample" effectivly reduces the accuracy of the measurement.

The more accurate the measuring devices (collectivly) the more "significant figures" you'll have.

Answer 2

okay, here's a start

you probably won't understand them completely until you practice some and see the affect in calculations

first, the basic theory

if I get out a ruler and measure something and it is 3.2 inches long and 4.7 inches wide, these measurements have to be based on the ruler I was using, which was only marked in tenth (.1) inches

4.7 is not the exact width, it may be 4.712432343 or whatever but since my ruler only goes to .1, I can't measure any closer

if I multiplied the two dimensions to get an area, I get 15.04 in^2

if I were to write it like that, it would mean that I knew it was really 15.04, but since my 4.7 could have been 4.71 and my 3.2 could have been 3.23 then that multiplication would have given me 15.16..a different number

so I don't really know if the area is 15.04 or 15.16 because I didn't have an accurate enough number to start with

since I only knew the first dimensions to 2 significant figures, I can only know the answer that much, further figures are not meaningful based on my starting knowledge

I do know that the answer is 15 (not 15.6 which would round to 16 and not 14.4 which would round to 14, but if I express more than 2 significant figures in my answer, i am just fooling myself, i don't really know those numbers

another example, what if you ask somebody to count the people at the football game and report it to you to the nearest hundred

he came back and said 9200

again, you don't know if that is 9205, or 9176, you just know to the nearest hundred

if somebody said, if we make all of them into football teams, how many teams can we make, well 9200/11=836.36

but you don't know if you could make 836 teams or only 835, because you only knew the first number to the nearest 100

if it was actually9238 people, then 9238/11=839.8 teams,

you do know that it will be 84x teams because you have that much significance, so you report the number as 840, but that last zero is not signifcant, it doesn't mean that you know it will be a 0, just that you know it will be 84 and then some digit, that zero, is not significant

all the signifcant digit writing conventions are based on the same theory but they are just ways of writing so that you can tell someone the level of your significance with just the number

for instance, if you know that you really do have exactly 840 of something, instead of writing 840, you write 840. and that decimal tells you that that zero is a significant 0, not a placeholder

840.0 means that you really know the tenths too

this was pretty long but I thought it might be helpful
normally when teaching significant digits we talk about the conventions of writing and the rules for keeping your significant figures to the correct number of digits, but we don't explain the theory or purpose very well

good luck

Answer 3

Significant numbers are the numbers that you are sure about. For example: 1000 has one significant didgit cuz u r not sure whether it was an exact number or 999.99 has been rounded to 1000. Thus it has only one significant digit. Like 1000.0 will have 5 sig digs cuz after decimal ther's a zero which means its an exact number not a rounded one. Another main thing is that if u write in scientific notation like 2.45x10^4 or 1.00x10^8 will only have 3 sig digs not 5 cuz you don't count the 10 or its power.

Answer 4

A) All non-zero numbers are significant.
B) All zeros between significant numbers are significant, for example the number1002 has 4 significant figures.
C) A zero after the decimal point is significant when bounded by significant figures to the left, for example the number 1002.0 has 5 significant figures.
D) Zeros to the left of a significant figure and not bounded to the left by another significant figure are not significant. For example the number 0.01 only has one significant figure.
E) Numbers ending with zero(s) written without a decimal place posses an inherent ambiguity. To remove the ambiguity write the number in scientific notation. For example the number 1600000 is ambiguous as to the number of significant figures it contains, the same number written 1.600 X 106 obviously has four significant figures.
Several Notes:

Answer 5

24,000 has 2 sig figs. Only the 2 and 4 are significant because the three zeros afterwards are just place holders. 0.025 has 2 sig figs as well. Zeros are once again place holders. 25.0400 has 6 sig figs. Trailing zeros after a decimal point are significant. In summary: EDIT: Lozza is wrong about the rules about zeros. The rules I stated here are correct. Numbers Non-Zero numbers are always significant. Trailing Zeros after a decimal are significant. Sandwiched Zeros are significant. Leading Zeros and trailing zeros without a decimal are insignificant.

Answer 6

Analogy to Significant Numbers.

Your friend asked you how much you have in your pocket.

You said $10.

Now you may have an extra 10 cents but thought it is too small to be of significance so you never mention it to your friend.

Now, your friend asked you again, "Are you sure that's all you have?"

Then you said, "Actually, I have $10.10".

Now, in your first reply, the significant number you reported is 2. In your second reply, the significant number you reported is 4.

Answer 7

Be careful what kind of "flower" you use for your cake. If it's the flower of the cannibis plant you can end doing 5 to 15. Using flour is safer.

Amazingly, a 1-cup measurement, with only 1 significant digit, says only that there is more than 1/2 cup of flour and less than 1-1/2 cups. Either way, it rounds to 1.

Answer 8

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RE:
can you explain significant numbers to me?
i just cant understand it. i would appreciate it if you would give me a simple explaination on how they work

Answer 9

when adding and subtracting, you round BEFORE you calculate and you round to the least amount of digits after the decimal place=
5.6 + 2.394 + 456.33 becomes 5.6 + 2.4 + 456.3

when multiplying and dividing you round after calculating and to the least number of significant digits.... significant digits are all non-zero numbers except when a decimal number includes 0's... so 345.3 has 4 significant digits while 300 has only 1, and 0.0003 has 4.

Answer 10

guessing youre in Chemistry,

Sig figs are used in Multiplication, Division, addition, and subtraction

best way to teach is by explaination

2.0 * 3.5 = 7.0

2.0 * 3.55 = 7.1

you show the zero in three instances
it is between decimal and number
one of the factors has more than one decimal place and you need to fill that place
and when it is an exact number 0.33333

pretty much the same for the other signs
if you dont get it (wing it)