Scientific Measurement

Scientific MeasurementAre you ready for today?

YesNo123456789101112131415161718192021222324Accuracy - How close a measurement is to the true value

Precision - How close a set of measurements are to one another.How accurate or precise was this person?

AccuratePreciseBothNeither123456789101112131415161718192021222324Precise or Accurate?

AccuratePreciseBothNeither123456789101112131415161718192021222324Precise or Accurate?

AccuratePreciseBothNeither123456789101112131415161718192021222324Scientific Notationall numbers are expressed as whole numbers between 1 and 9 multiplied by a whole number power of 10.Ex. 125 = 1.25 x 1020.00004567 = 4.567 x 10-5You try some...Write the following numbers in scientific notation:A) 5,000E) 0.0145B) 34,000F) 0.000238C) 1,230,000G) 0.0000651D) 5,050,000,000H) 0.000000673

Significant Figures or DigitsSignificant Figures are used to show the accuracy and precision of the instruments used to take the measurement.What is the measurement?010011.5What is the measurement?01

0.550.70.60.8123456789101112131415161718192021222324What is the measurement?01

0.550.700.670.65123456789101112131415161718192021222324MeasurementsTo show how precise the instrument is:Read the measurement to one decimal place what the instrument is markedRead the water level

4.857.24.34.35123456789101112131415161718192021222324Read the water level

17.016.815.1815.2123456789101112131415161718192021222324Counting Significant DigitsNon-zero digits are always significant1,2,3,4,5,6,7,8,9 are always significantRules for Zeros:Leading Zeros never count as significant0.00004560.0032

Captive zeros (zeros between non-zero digits) are always significant10,0340.005008

Trailing Zeros are significant ONLY IF there is a decimal in the number.234,000234,000.00.045600If we want to write the number 700 with 3 significant digits we can do so using the following two methods:700. OR 7.00102

You try some...How many significant digits do the following numbers have?A) 20F) 7.00K) 65,060B) 22.0G) 87,001L) 0.9090C) 20.1H) 0.00018M) 18.01D) 56,000I) 0.0109N) 4.30104E) 75,000.J) 570O) 0.0001How many significant digits does the following number have?20

1230123456789101112131415161718192021222324How many significant digits does the following number have?22.0

0123123456789101112131415161718192021222324How many significant digits does the following number have?0.000354

3167123456789101112131415161718192021222324How many significant digits does the following number have?56,000

0123123456789101112131415161718192021222324How many significant digits does the following number have?75,000.

2513123456789101112131415161718192021222324How many significant digits does the following number have?7.00

1234123456789101112131415161718192021222324How many significant digits does the following number have?4.30 x 108

1234123456789101112131415161718192021222324How many significant digits does the following number have?0.00040050

5824123456789101112131415161718192021222324How many significant digits does the following number have?0.00043

5824123456789101112131415161718192021222324How many significant digits does the following number have?10,023,000

3845123456789101112131415161718192021222324Pair-up ExerciseYou 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.Rounding Numbers to the Correct Significant FiguresCount (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. figs1,3440.0005678424,50012,3452.45678 x 10-3

Significant Digit CalculationsWe have two ways of categorizing sig. fig. calculations:

Addition and Subtraction

B) Multiplication, Division, other mathAddition and Subtraction RulesWhen 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.You try some... A) 14.0 + 2.45 B) 12 + 7.2 C) 0.00123 + 1.005 D) 100 5.8 E) 2.5 1.25 F) 43.786 32.11

To what decimal place/place value should the following answer be rounded to 14.0 + 2.45

123456789101112131415161718192021222324TensOnesTenthsHundrethsTo what decimal place/place value should the following answer be rounded to 12 + 7.2

TensOnesTenthshundreths123456789101112131415161718192021222324To what decimal place/place value should the following answer be rounded to 0.00123 + 1.005

OnesTenthsHundrethsThousandthsTen thousandths123456789101112131415161718192021222324To what decimal place/place value should the following answer be rounded to 100 + 5.8

HundredsTensOnestenths123456789101112131415161718192021222324Multiplication, 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...

You try some... A) 12 5.00F) 119 / 32 B) 8.45 4.3G) 756.2 / 29.8 C) 0.0125 7.532H) 0.976 / 0.0044 D) 5.6 11.7I ) 981 / 756.23 E) 34.1 0.55J) 43.2 / 12.45

How many sig. figs. Should your answer be reported in for the following: 12 5.00

OneTwoThreeFour123456789101112131415161718192021222324DensityDensity the amount of matter present in a given volume of a substance, the ratio of the mass of an object to its volume.D = massVolume

Percent Error

TemperatureCelsius 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.

Conversions between temperature scalesKelvin/Celsius K = oC + 273Fahrenheit/Celsius oF = 1.80(oC) + 32Exact Numbers are counting numbers or defined numbers (such as 2.45 cm = 1 in) - never limit the number of significant figures in a calculation.