Chapter 3 - Scientific measurement. Using and expressing measurements

Transcription

1 Chapter 3 - Scientific measurement Using and expressing measurements

2 How far off was Usain Bolt from winning gold in the 100m last weekend?

3 What is a measurement? How do scientists make reporting measurement easier? Scientific notation! For example - every gram of Hydrogen contains 602,000,000,000,000,000,000,000 atoms 6.02 x is much easier to understand Positive exponent = very large number Negative exponent = very small number

4 Using Scientific notation (Division and multiplication)

5 Using Scientific notation (Division and multiplication)

6 What is the difference between accuracy and precision? Accuracy: The closeness of the measurement to the true value Precision: The closeness of a set of measurement taken under the same conditions

7 How do you determine whether a measurement take in a lab is a suitable value? You asses the error of your measurement, by comparing the experimental value with the accepted value Experimental value = value measured in the lab Accepted value = correct value for the measurement based on reliable references Error = the difference between these two values Percent error = the relative error of a measurement

8 How do you calculate percent error?

9 What is a significant figure? The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Instruments differ in the number of significant figures that can be obtained from their use and thus in the precision of measurements.

10 What are the rules in how significant figures are used?

11 Example problem Suppose that the winner of a 100-meter dash finishes the race in 9.98 seconds. The runner in second place has a time of seconds. How many significant figures are in each measurement? Is one measurement more accurate than the other? Explain your answer. There are three significant figures in 9.98 and four in Both measurements are equally accurate because both measure the actual time of the runner to the hundredth of a second.

12 How do you use significant figures in calculations? In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. The calculated value must be rounded to make it consistent with themeasurements from which it was calculated. When rounding you must first decide how many significant figures the answer should have. This decision depends on the given measurements and on the mathematical process used to arrive at the answer. Once you know the number of significant figures your answer should have, round to that many digits, counting from the left If less than 5, number os dropped, Greater than 5 round to 1

13 Additional rules for significant figures Addition/Subtraction problems The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places Multiplication/Division Like addition/subtraction probems you need to round the answer to the same number of significant figures as the measurement with the least number of significant figures. The position of the decimal point has nothing to do with the rounding process when multiplying and dividing measurements.

14 Section 3.2: Units of Measurement

15 Why does science use the metric system? The international system of units was first used in France in 1795 In 1960, the SI was accepted internationally There are seven base SI units SI Base Units Quantity SI base unit Length Mass Temperature Time Amount of substance Luminous intensity Electric current meter kilogram kelvin second mole candela ampere Symbol m kg K s mol cd A

16 Why do we not always use base units? How is the metric system made more user friendly? Prefixes are commonly used to express measurements in suitable units Commonly Used Metric Prefixes Prefix mega kilo deci centi milli micro nano pico Symbol M k d c m μ n p Meaning 1 million times larger than the unit it precedes 1000 times larger than the unit it precedes 10 times smaller than the unit it precedes 100 times smaller than the unit it precedes 1000 times smaller than the unit it precedes 1 million times smaller than the unit it precedes 1 billion times smaller than the unit it precedes 1 trillion times smaller than the unit it precedes Factor

17 What is the difference between mass and weight? Weight is a force that measures that pill on a given object by gravity Your weight is different on Earth and the Moon Mass is the measure of quantity of matter An object can become weightless but never massless

18 What is the difference between the celsius scale and the kelvin scale? The difference is C That is because the Kelvin system starts at absolute zero A one degree increase on the Kelvin scale is equal to one degree increase on the Celsius scale

19 How do you calculate density? Density is the ratio of the mass of an object to it s volume

20 Do gases have density? Yes! Density difference is what allows helium balloons to rise

21 How is density related to temperature? In general, as temperature of a substance increases, so to does its volume As such, the density will increase with temperature Water is an important exception Volume increases as temperature decreases You will learn about this in chapter 15!

22 Section 3.3: Solving conversion problems

23 What is a conversion factor? A conversion factor is a ratio of equivalent measurements For example

24 What is dimensional analysis? Dimensional analysis is a method of problem solving that uses the units that are part of a measurement to solve a problem It allows you to solve conversion problems in which a measurement with one unit is changed into an equivalent measure with another unit