1. Scientific Measurement

2. Are you ready for today? Yes No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1617 18 19 20 21 22 23 24

3. Accuracy - How close a measurement is to the true value
Precision - How close a set of measurements are to one another.

4. How accurate or precise was this person?
Both
Neither 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

5. Precise or Accurate? Accurate Precise Both Neither 1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 19 20 21 22 23 24

6. Precise or Accurate? Accurate Precise Both Neither 1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 19 20 21 22 23 24

7. Scientific Notation
all numbers are expressed as whole numbers between 1 and 9 multiplied by a whole number power of 10.
Ex = 1.25 x 102
= x 10-5

8. You try some...
Write the following numbers in scientific notation: A) 5,000 E) B) 34,000 F) C) 1,230,000 G) D) 5,050,000,000 H)

9. Significant Figures or Digits
Significant Figures are used to show the accuracy and precision of the instruments used to take the measurement.

10. What is the measurement?1 .5 1 1

11. What is the measurement?1
0.55
0.7
0.6
0.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

12. What is the measurement?1
0.55
0.70
0.67
0.65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

13. Measurements To show how precise the instrument is:
Read the measurement to one decimal place what the instrument is marked

14. Read the water level
4.85
7.2
4.3
4.35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

15. Read the water level
17.0
16.8
15.18
15.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

16. Counting Significant Digits
Non-zero digits are always significant
1,2,3,4,5,6,7,8,9 are always significant
Rules for Zeros:
Leading Zeros never count as significant
Captive zeros (zeros between non-zero digits) are always significant
10,
Trailing Zeros are significant ONLY IF there is a decimal in the number.
234, ,

17. If we want to write the number 700 with 3 significant digits we can do so using the following two methods:
OR ×102

18. You try some...
How many significant digits do the following numbers have? A) 20 F) 7.00 K) 65,060 B) 22.0 G) 87,001 L) C) 20.1 H) M) D) 56,000 I) N) 4.30×104 E) 75,000. J) 570 O)

19. How many significant digits does the following number have? 201 2 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

20. How many significant digits does the following number have? 22.01 2 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

21. How many significant digits does the following number have? 0.0003541 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

22. How many significant digits does the following number have? 56,0001 2 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

23. How many significant digits does the following number have? 75,000.2 5 1 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

24. How many significant digits does the following number have? 7.001 2 3 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

25. How many significant digits does the following number have? 4.30 x 1082 3 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

26. How many significant digits does the following number have? 0.000400508 2 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

27. How many significant digits does the following number have? 0.000435 8 2 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

28. How many significant digits does the following number have? 10,023,0008 4 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

29. Pair-up Exercise
You and a partner will practice your significant digits. Your job is to come up with a number containing both zeroes and non-zero digits. You will trade boards back and forth – on my mark. The partner that gets the correct number of significant digits will get the point. The partner with the most points will win the round. We will do best of 9.

30. Rounding Numbers to the Correct Significant Figures
Count (from left to right) how many significant figures you need.
Look at the next number to see if you need to round your last sig. fig. up or down.
Round the following to 3 sig. figs
1,344
24,500
12,345
x 10-3

32. Significant Digit Calculations
We have two ways of categorizing sig. fig. calculations:
Addition and Subtraction
B) Multiplication, Division, other math

33. Addition and Subtraction Rules
When we add and subtract we are only worried about the number of decimal places involved in the numbers present. We do not care about the number of actual significant digits. We will always pick the number that has the least decimal places.

34. You try some...
A) B) C) D) 100 – 5.8 E) 2.5 – 1.25 F) – 32.11

35. Tens Ones Tenths Hundreths
To what decimal place/place value should the following answer be rounded to
Tens
Ones
Tenths
Hundreths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

36. Tens Ones Tenths hundreths
To what decimal place/place value should the following answer be rounded to
Tens
Ones
Tenths
hundreths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

37. Ones Tenths Hundreths Thousandths Ten thousandths
To what decimal place/place value should the following answer be rounded to
Ones
Tenths
Hundreths
Thousandths
Ten thousandths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

38. Hundreds Tens Ones tenths
To what decimal place/place value should the following answer be rounded to
Hundreds
Tens
Ones
tenths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

39. Multiplication, Division, other math
If we are multiplying, dividing, using exponents, trigonometry, calculus, etc we must use the least number of significant digits of the numbers in the set. For example...

40. You try some...
A) 12 × 5.00 F) 119 / 32 B) 8.45 × 4.3 G) / 29.8 C) × H) / D) 5.6 × 11.7 I ) 981 / E) 34.1 × 0.55 J) 43.2 / 12.45

41. How many sig. figs. Should your answer be reported in for the following: 12 × 5.00
One
Two
Three
Four 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

42. Density
Density – the amount of matter present in a given volume of a substance, the ratio of the mass of an object to its volume.
D = mass
Volume

43. Percent Error

44. Temperature
Celsius Scale – based on the freezing point (0oC) and boiling point (100oC) of water.
Kelvin Scale – based on absolute zero (the temperature at which all motion ceases). 1 degree Kelvin is equal to 1 degree Celsius.
Fahrenheit Scale – used in US and Great Britain. Degrees are smaller than a Celsius or Kelvin degree.

46. Conversions between temperature scales
Kelvin/Celsius
K = oC + 273
Fahrenheit/Celsius
oF = 1.80(oC)

47. Exact Numbers are counting numbers or defined numbers (such as 2
Exact Numbers are counting numbers or defined numbers (such as 2.45 cm = 1 in) - never limit the number of significant figures in a calculation.