Unit 1 Into to Measurement. Uncertainty in Data Precision: A reliable measurement will give about the same results time and time again under the same.

Unit 1 Into to MeasurementUnit 1 Into to Measurement

Uncertainty in DataUncertainty in DataPrecision: A reliable measurement will give

about the same results time and time again under the same conditions. Precision refers to the reproducibility of a measurement.

Accuracy: A measurement that is accurate is the correct answer or the accepted value for the measurement. High accuracy = close to accepted value.

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Examples:More Examples:True Value = 34.0 mLMeasurements = 34.2 mL, 34.1 mL, 34.2 mLAccurate and/or Precise?True Value = 29.3 cmMeasurements = 32.3 cm, 32.5 cm, 32.4 cmAccurate and/or Precise?True Value = 27.3 sMeasurements = 27.9s, 30.2s, 26.9sAccurate and/or Precise?

Significant FiguresSignificant FiguresYou are often asked to combine measurements

mathematically. When measurements are combined mathematically, the uncertainty of the separate measurements must be correctly be reflected in the final answer.

A set of rules exists to keep track of the significant figures in each measurement.

The significant figures (SIG FIGS) in a measurement include the certain digits and the estimated digit of a measurement.

SIG FIG RULES !!SIG FIG RULES !!Nonzero numbers are always significant.

◦ 14 =◦ 523=

Zeros between nonzero numbers are always significant. Sandwich Zeros◦ 101 =◦ 2005 =

Zeros after significant figures are significant only if they are followed by a decimal point. (All final zeros to the right of the decimal are significant).◦ 100.0 =◦ 2030.0=

Place holder zeros are NOT significant. To remove placeholder zeros, rewrite the number in scientific notation.◦ 0.001 =◦ 0.0000034 =

How many sig figs in these How many sig figs in these measurements?measurements?

3.4567 = _____3.00047 = _____0.00003409 = _____2.05 X 105 = _____0.100 = _____3000 = _____

Sig Figs in CalculationsSig Figs in Calculations

For multiplication and division: The least number of sig figs in the measurements determines how many sig figs in the final answer.

Ex: 6.15 m x 4.026 m = 24.7599 m2 What is the fewest # of sig figs? (3) so the answer is rounded to 24.8 m2

If a calculation involves several steps, ONLY ROUND FINAL ANSWER, carry extra sig figs in intermediate steps. If the digit to be rounded is less than 5, round down; if 5 or more, round up.

Ex. 24 cm X 32.8 cm = 763.2 cm2

 ◦Round 763.2 cm2 to ____________

 Ex. 8.40 g 4.2 g/mL = 2 g/mL 

◦2 g/mL must be rounded to ____________

For addition and subtraction: The sum or difference has the same number of decimal places as the measurement with the least number of decimal places.

EX: 951.0g + 1407 g + 23.911 g + 158.18 g = 2540.091 g But the measurement with the fewest places past decimal is 1407 g ( It has no digits past decimal) SO the final answer must be rounded to 2540. g

Ex. 49.1 g + 8.001 g = 57.101 g 

◦Round the answer to ___________ Ex. 81.350 m – 7.35 m = 74 m 

◦Round the answer to ____________

Percent ErrorPercent ErrorPercent error compares a measurement with its

accepted value. A percent error can be either positive or negative.

% ERROR = measured - accepted x 100 accepted

% ERROR = what you got – what is correct x 100 what is correct

Scientific NotationScientific NotationSome measurements that you will encounter in

physics can be very large or small. Using these numbers in calculations is cumbersome. You can work with these numbers more easily by writing them in scientific notation. A number written in scientific notation is written in the form 

M X 10n

Where M is a number between 1 and 10 (known as the coefficient) and 10 is raised to the power of n (known as the exponent). Circle the numbers that are in correct scientific notation:

  1 X 104 12 X 1012 0.9 X 103 2.54 X 10-3 9.99 X 102

Step 1: Determine M by moving the decimal point in the original number to the left or right so that only one nonzero digit is to the left of the decimal….do it!!!

27508. Step 2: Determine “n” , the exponent of 10, by

counting the number of decimal places the decimal point has moved. If moved to the left, n is positive. If moved to the right, n is negative.

2.75084 places to the left, n = 4Answer = 2.7508 X 104

Write the following quantities in scientific notation…do it!!!

0.0050 = 235.4 = 18,903 =0.0000101 =Write the following quantities in arithmetic

notation…do it!!!1.45 X 104 =2.34 X 10-3

6.02 X 1023 =

Units and MeasurementsUnits and MeasurementsThe International System of measurement or

“metric” system is the preferred system.Make sure you are familiar with the basic units that

we will be using many times throughout the year.

Quantity Unit Abbreviations

Time Second s

Length Meter m

Mass Gram g

Temperature Kelvin K

Make sure to be familiar with the common prefixes that make the base unit larger (kilo- for example) and prefixes that make the unit smaller ( examples milli - and centi-)

You should know how to quickly change between the units, for example, from liter to milliliter or kilograms to grams. Prefix Symbol

Kilo k.

Hecta h.

Deca da

Base Unit

Deci d

Centi c

Milli m

Factor Label/ Dimensional AnalysisFactor Label/ Dimensional Analysis

Dimensional Analysis: A technique of converting between units.

Dimensional analysis use conversion factors. A conversion factor is always equal to 1. For example: 1000m or 60 minute

1 km 1 hourConversion factors can be flipped to allow for

cancellation of units.Choosing the correct conversion factors requires

looking carefully at the problem.

Step 1: Show what you are given on the left, and what units you want on the right.

 Step 2: Insert the required conversion factor(s) to

change between units. In this case we need only one conversion factor, and we show it as a fraction, 1 hr/60 min. We put units of minutes on the bottom so they will cancel out with the minutes on the top of the given.

 Step 3: Cancel units where you can, and solve the

math.

For example let’s look at the following question:Example 1: Given that there are

5280feet in a mile, How many feet are in 2.78 miles?

Example 2: Convert 89 km into inches

Example 3: How many gallons are in 146 Liters? 1 Gal= 4 quarts 1 L = 1.057 quarts 1 L=1000ml

Example 4: How many seconds in 5.00 days?