MEASUREMENT

• Numbers are very important in science and the way in which scientists interpret them must be uniform. In other words, all scientists must be speaking the same language so they can understand one another.

• In science a procedure called peer review is utilized. In this process an individual does an experiment and wants to give the information to the science community. She/he publishes it in a scientific journal so other scientists can look at their work. Some scientists then try to repeat the experiment and see if they can produce the same results. This insures that people have not made mistakes or lied about their research.

DATA

• Therefore when numbers are used as data (quantitative data) we must understand what we mean by them.

• The numbers we use are from experiments in which we measure things.

• Some things can be measured exactly while others cannot. • People can be measured exactly because it is

done one by one. However, other things like the length of a piece of paper cannot be measured exactly.

• Your measurement depends on how precise your instrument is.

• One of the rulers above (when measuring in inches) is more precise. Which one and why?

• Why is this important?

SIG FIG RULESThere are a few rules we will learn to determine

the number of significant figures in a number:• Numbers for data that are counted one by one have

INFINITE significant figures. • All numbers 1-9 are significant• Zero’s are significant EXCEPT when:

• Trailing zeros: The number is greater than 1, there is no decimal and they are at the end of a number. • EX: 3,000 (The last 3 zero’s are NOT significant)• EX: 3,000. (These zeros ARE significant)

• Leading Zeros: The number is less than 1 and they appear at the front of a number.• EX: 0.0002 (The first 4 zeros are NOT significant)• EX: 0.000200 (The first 4 zeros are NOT significant but

the last two ARE.)• Middle zeros: Zeros in between to significant digits are always

significant.• EX: 2020 (the middle zero is significant but the last one

is not)• EX: 0.000040010 (the leading zeros are not significant

but the middle and trailing zeros are)

PRACTICE TIME

State the number of significant numbers in each set:

1. 0.020003 = ____ 2. 0.0002300 = ____ 3. 0.000103 = ____

4. 0.0009 = ____ 5. 0.0000033 = ____ 6. 0.000900 = ____

7. 2,000,000= ____ 8. 500. = ____ 9. 500.000 = ____

10. 8020 = ____ 11. 90,000 = ____ 12. 208,030 = ____

13. 8,000. = ____ 14. 80,200 = ____ 15. 23.00 = ____

16. 3340.0 = ____ 17. 90 = ____ 18. 0.000 = ____

19. 2000 = ____ 20. 200,000 = ____ 21. 2000. = ____

22. .8070 = ____ 23. 0.02020 = ____ 24. 0.03003 = ____

SCIENTIFIC NOTATION

Instead of using standard notation scientists write numbers in scientific notation. This system uses the base 10 as a multiplying factor to move the decimal place around.

X 100 = times 1

X 101 = times 10 X 10-1 = times .1

X 102 = times 100 X 10-2 = times .01 And so on……. The base 10 moves the decimal around.

So why do we use this? The answer is simple. In science we commonly have to use numbers that are very large or very small and scientific notation is easier to use than standard notation. For example the number of atoms in 12.01 grams (1mole) of carbon is:

602,000,000,000,000,000,000,000 This would be a pain to write so instead we use: 6.02 X

1023

SCI. NOT. RULES So how do we do this? Here are some general

rules: The decimal place should be moved to the

right of the first non-zero number. The number in front of the base 10 needs to

be a number 1 – 10. The number of times you move the decimal

becomes the superscript of the base 10. Positive if the number is greater than zero and negative if less than zero.

NOTE: Only significant numbers are included in scientific notation.

CONVERT THE STANDARD NOTATION INTO SCIENTIFIC(WATCH YOUR SIG FIGS)

1. 660,000 = ___________2. 8,000. = ____________

3. 9050 = ___________4. 5,001 = ____________

5. 2.000 = ____________6. 4403.0 = ____________

7. 0.0120 = ___________8. 0.0500 = ____________

9. .00202 = ____________10. 0.0020 = ____________

CONVERT THE SCIENTIFIC NOTATION TO STANDARD(WATCH YOUR SIG FIGS)

1. 6.02 X 10-4 = ____________________2. 2.02 X 10-8 = ____________________3. 2.00 X 10-5 = ____________________4. 9. X 10-2 = ______________________5. 9 X 100 = _______________________6. 5.0089 X 106 = ___________________7. 3.0 X 105 = _____________________8. 3 X 106 = _______________________9. 5.000 X 101 = ___________________10. 4.00 X 102 = _____________________

ROUNDING

What is rounding? It comes from the

idea that some numbers are irrelevant or not significant and therefore not reliable.

In science, we do not round like math. We must round to the appropriate number of sig figs.

1) 15.6 (2)

2) 15.6 (1)

3) 690 (1)

4) 5,555 (2)

5) 8.12 X 104 (2)

6) 9.5 X 102(1) 7) 4.5 X 104(1)

ROUND THE VALUE TO THE NUMBER OF SIG. FIGS. INDICATED BY THE PARENTHESIS.

1. 555.5 (1)______ 2. 7.586500 (4)______ 3. 650 (1)_______

4. 0.0055 (2)______ 5. 1.500 (1)________ 6. 0.3400 (1)______

7. 428.09 (3)______ 8. 666,500. (4)______ 9. 0.7500 (1)_____

10. 0.0630 (1)______ 11. 0.4355 (1)________12. 9.50 (1)_____

13. 995. (2)________ 14. 199,500 (3)______

15. 2.9995 (4)_______

SIG FIG CALCULATIONS

As has been discussed, numbers are very important and their reliability is crucial when using them for practical applications.

When doing science we often take the data that we have measured and manipulate it to find a multitude of other information. In other words, we take the numbers from our

experiment and we will add, multiply, subtract, and divide them in order to calculate other derived quantities.

However, the problem arises in that all numbers are NOT created equally.

ADDITION & SUBTRACTION

Look at all the numbers that are in your calculation and determine which has the least number of decimal places. Your answer should have the same number of decimal places as this one. (Units must be the same)

EX: 1.230g +12.5g + 25.36521g = 39.0 9521 Final answer rounded = 39.1g

MULTIPLICATION & DIVISION

Look at all the numbers that are in your calculation and determine which has the least amount of significant figures. Your answer should have the same number of significant figures as this one. Treat units like variables in algebra

EX: 3,000. m3 = 300 m = 3.0 X 102 m 10. m2

EX:(12.220 ft) X (11ft) = 13 4.42 ft2 = 130 ft2

CALCULATION PRACTICE

1. 654.0g5/6g = ___________________2. (5500m-9)(56.m) = _________________

 

3. 8.632 nm+ 8.3 nm – 30.0 nm = _____ 4. 18 g +6.80 L+0.050 L– 226 =_____

 

5. (60.0g)/(230 cm3) - .0520g/cm3 = ______6. (0.020ml)(300.560ml) + 1 ml2 =___

 

7. 6.9 X 107 nm3 / 4.00 X 107 nm = _______ 8. (1 X 107 kg3)(2.45 X 10-4 ft-3) = ___

 

9. 2.55 X 102 ml4 + 6.6 X 103 ml4 = _______10. 4 X 10-2 ft2 - 2.00 X 10-3 ft-3 = ____

 

11. (6.9 X 107 Kg3 / 4.00 X 106 Kg3) - 8 X 101 kg- 2.3 X 101 kg3________________