Metric System And Significant Digits (Page 2 of 2) in pdf

Significant Digits. The number of digits reported in a measurement give scientists a sense of the accuracy

of the equipment that was used. Typically when making measurements, you should estimate the last digit

as best you can. For example, along the metric ruler below, one could assume the arrow is pointing to 1.7

cm. The .7 is an estimate. However, reporting to 1.7435 would be improper due to the fact that the tool for

measuring is not that precise. In other words you should only ever have one digit that is estimated.

Estimate the volumes of the material below:

a._____

b._____

c._____

How many significant digits does something have? In most cases it is simply the total number of digits

present. It is assumed that the last digit you report is estimated (on an electric balance, the balance

estimates the final digit. On a thermometer or graduated cylinder or other technology, YOU will estimate

that final digit). The problem with just counting the total number of digits is when you have zeros in the

number. 12cm is the same as 120mm but they have different numbers of digits. This means that whole

numbers that end in zeros or decimals that start with zeros have an ambiguous number of significant digits

because they could be digits that were measured or they could simply be place holders. Therefore 300

might have 3 significant digits or it might only really have 1. This is the reason scientists created scientific

notation. Example: if something was found to be 130 grams and the zero digit was estimated it would be

reported like this: 1.30 x 10 2 (this shows that it has three significant digits). But if something was found

to be 130 grams and they estimated the hundredths place so that the zero was really just a placeholder it

would be reported like this: 1.3 x 102 this would show it has two significant digits.

4. Follow the rules to determine the number of significant digits in each measurement

a. 478cm:_______

b.6.01g: _______

c. .043kg x 10

m______

–2

d. 4.3 x10

e. 7.0 x 10

kg________

Calculations to the proper amount of significant digits

When calculating things such as volume, density etc., it is important that your end result represent the

original precision of the instruments that you measured with. A basic guideline—When adding/subtracting

your final result should not contain more decimal places than your original number that had the fewest

places. example—31.132cm + 3.1468 cm + 1.1cm = 35.3788cm but because I didn’t measure all things

to that many decimals I need to report it as 35.4cm

When multiplying/dividing measurements, your answer should not normally reflect any more significant

digits than that measurement that has the fewest number of significant digits.

Example—3.46g / 32ml = 0.108125g/ml but would be reported as 0.11g/ml

5. Perform the operation indicated and then round off the answer to the proper number of significant digits

a. 11,254.1mm + 0.1983mm = _______________________________

b. 66.59g – 3.113g = ______________________________________

c. 8.16cm x 5.1355cm = ___________________________________

d. 0.0154g / 883 ml= _______________________________________

Metric System And Significant Digits Page 2