There are two types of numbers in science: exact (counting) numbers and inexact (measurements and calculated quantities). Exact or counting numbers represent objects. For instance, a dozen eggs has exactly 12 eggs. You can’t have 12.01 eggs. Measurements and numbers based on calculations will always have some uncertainty. Significant digits are used to represent that uncertainty or the amount of confidence you have in a measurement.
Uncertainty occurs because we use equipment to make measurements. You can only measure a length as exact as the increments on the ruler you are using. Significant digits are the numbers we know with certainty plus one more that is estimated.Basic Rules:
- All non-zero digits are significant
- All zeros between non-zero digits are significant
- Zeros to the right of the decimal and to the right of a non-zero digit are significant
- Zeros to the right of the decimal, but to the left of all non-zero digits are not significant
- If there is no decimal, zeros to the right of the last non-zero digit are not significant
Rules for Calculations:
- In addition and subtraction, use the LEAST number of DECIMALS.
- In multiplication and division, use the LEAST number of SIGNIFICANT DIGITS.
- Apply each rule using the order of operations.
I have a question about the problems in number 42. All of them are multiple step equations that combine multiplication/division with addition/subtraction, and I'm not sure when to round. Question a) reads:
ReplyDelete320.55 - (6104.5/2.3)
Do you round the answer of 6104.5/2.3 and then subtract that rounded answer from 320.55, or do you just subtract the answer of 6104.55/2.3 from 320.55 without rounding first?
You use the order of operations, so you would divide (2654.13043...), then round to the least # of sig dig (2). So you would then have 2.7 x 10^3.
ReplyDeleteTHEN you subtract and use the least # of decimals, or in this case, digits to the right. The final answer would then be -2.4 x 10^3.
Why did you round it to 2400 and then change that to 2.4 to 10^3?
ReplyDeleteAny # over 1000 must be in sci not
ReplyDeletewhat are the conversion rates we are supposed to use for pounds to grams and for in^3 to gal.?
ReplyDeleteThe conversion are on the back cover of your text
ReplyDeleteIn excel, is there a function that will round number to sig digs, or do we have to manually enter each rounded number into the cell?
ReplyDeleteQuestion #2 on the post lab asks us to compare our range and standard deviation of the density to all the class' values. Do you want us to compare the density using the calculated volume, or the density using the displacement method, or both?
ReplyDeleteIn excel, you have to tell it how many digits to show and use. Use the sig dig rules to decide.
ReplyDeleteYou need to evaluate your results to the class results for both methods.
But how do you tell excel how many sig digs to show and use?
ReplyDeleteFormat/cells/number/choose how many decimals
ReplyDeleteIf we get 0 as an answer in the excel chart do we have to use sig digs, like 0.00, 0.0, etc., or can we just put 0 regardless of how many sig digs were in the calculation?
ReplyDeletefor percent deviation, should we round using one significant figure because we are multiplying by 100?
ReplyDelete100 is a scalar. It doesn't have sig dig.
ReplyDeleteso then what rules do we use? the subtraction/addition rules, or the multiplication/division rules?
ReplyDeleteshould we use addition/subtraction sig dig rules for standard deviation
ReplyDeleteFor % and stdev use the mult/div rules.
ReplyDeleteso would i have to work out all the standard deviations separately on a piece of paper to see the number of sig digs?
ReplyDeleteNo, use the measurements.
ReplyDeleteso we use the least number of sig digs out of all our recorded measurements?
ReplyDeleteFor the stdev for each type of measurement/calc, use the least sig dig. You will have a different # of sig digs for vol, than height, than mass, ...
ReplyDelete