Significant Figures

What are “Sigi Figi’s”? Significant: is important or accurate. Significant Figures (“Sigi Figi’s”) are necessary for scientist to communicate the accuracy of the quantitative information we share. In science we have two responsibilities, measure accurately and record responsibly.

Recognizing Sigi Figi’s There are 4 rules for recognizing if a number is significant or not. #1 All non zero numbers are Significant: Ex. 1247 has 4 sigi figi’s 3 598 499 has 7 S.F. This leaves only 0’s that we need to define.

Sigi Figi’s Continued #2 Any trapped zeros ARE significant. Ex. 1209 4 S.F 103.08 5 S. F #3 Any “Why Bother Zeros” Are significant. Ex. 1.00 Why bother putting the zeros? Because it was measured that accurately. The 1 and the 0’s are significant. 3 S.F. 456.90 5 S.F.

Sigi Figi’s Still Continued #4 Any leading zeros and place holders are ?????? 0.0056 What is the purpose of the first 0? It is there to help find the decimal . It is not significant. We can write .0056 as the same #. The other 0’s are a little tricky. We can fix this by using scientific notation.*

Scientific Notation Scientific Notation has two purposes: 1. To make writing very large and very small numbers easier. 2. To show significant figures. Scientific notation is simple: There can only be one number in front of the decimal and it cannot be a zero. All significant digits are written behind the decimal with a power of 10 to show the actual location of the decimal.

Let’s Try Scientific Notation 123 000 Find the Decimal 123 000. Move the Decimal so there is only 1 number in front. 1.23 The trailing zero’s were not trapped or why bother so we must assume they were not significant. Now multiply by the power of 10 equal to the number of spaces you moved the decimal. If it was a big number then the exponent is positive. 1.23 x 105 This number is easy to recognize there are 3 S. F.

Let’s Try Another One Remember this: 0.0056 The decimal is shown. 0.0056 Move the Decimal so there is only 1 number in front. 5.6 All of the leading zero’s were not significant. Now multiply by the power of 10 equal to the number of spaces you moved the decimal. The number was a small number so the exponent is negative. 5.6 x 10-3 This number is easy to recognize there are 2 S. F.

You Try 147902 6 S. F. 0.9600500 7 S. F. 14790 4 S. F. 1 902 000 1.902 x 106 4 S. F. 0.000 0560 5.60 x 10-5 3 S. F.

Now that you know Sigi Figi’s, what do we use them for? Sigi Figi’s are necessary when we do calculations in science. Let’s see. All values in science are measured. Since they are all measured all values have error. This means that none of the quantitative values we work with are perfect. When we do calculations we must take into account the error we are using. Let’s see why.

Error and its effect on Calculations. I measure the side of a room to be 5.0 m my partner measures the other side of the room to be 7 m. What is the area of the room? First we must see the error. In science the last number recorded is the number the measurer is uncertain about. It has an error of + or – 1.

Calculating with Error Mathematically: Scientifically: 5.0 x 7 is 35 is 40? Scientifically there is a whole different Story. With error 5.0 could be 5.1 or 4.9 5.1 x 7 = 35.7 or 4.9 x 7 = 34.3 With error 7 could be 8 or 6 5 x 8 = 40 or 6 x 5 = 30 As you can see the error of one digit can dramatically effect the calculated result.

How Sigi Figi’s Help When we do multiplication or division in science we use sigi figi’s to help us determine what the most reasonable answer is. The rule is the least number of sigi figi’s given is the number we can keep in the answer.

Let’s try this again 5.0 has 2 S. F. 7 has 1 S. F. Do the math: 5.0 x 7 = 35 35 has 2 S. F. We are only allowed to keep 1 Keep the 3 and round according to the next number… the 5. So the 3 becomes a 4 or 40. 40 does not clearly show 1 sigi figi so convert to Sci Not. 4 x 101 Wow, try telling your math teacher that 5 x 7 is 40!

How do we fix this? The answer is in the hands of the scientist. The scientist is to measure accurately and record responsibly. If my partner had measured 7.0 m in the first place there would have been 2 sigi figis’. 5.0 x 7.0 is 35 and stays 35.

You Try What is 13/ 7? 1.857… = 2 What is 25 x 4? 100…= 1 x 102 0.75…= 0.750 or 7.50 x 10-1

Other Calculations Other calculations that are not done as often in physics are addition and subtraction. The rule for addition and subtraction is the least level of accuracy figure is used to determine the accuracy of the result.

Let’s Try 23.0 + 15.6 = 38.6 23.00 + 15.6 = 38.6 23 +15.6 = 39 19.5- 14.63 = 4.9 19.53 – 14.63 = 4.90 19 – 14.63 = 4

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