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**Observations Qualitative Quantitative (measurements) Two parts needed**

Observed directly Color, texture, magnetic, state of matter, etc Quantitative (measurements) Two parts needed Number AND unit (Naked numbers are meaningless)

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Examples of Units

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**Why do we need standard units?**

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**Units English system “unrelated” units 1 ft = 12 in Metric system**

Units related by powers of 10 Units can be made larger or smaller with prefixes

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**English System Mass: 1 pound = 16 ounces Length: 1 foot = 12 inches**

1 yard = 3 feet Volume: 1 gallon = 4 quarts 1 quart = 2 pints = 32 ounces 1 pint = 2 cups

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Metric System Mass: gram (g) Length: meter (m) Volume: liter (L)

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**Need to know: Metric Prefixes English system relationships**

Useful relationships for converting between systems

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**Converting between units Dimensional Analysis Factor-Label Method**

1. Within same system 2. Between systems BOTH require a conversion factor

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**Metric System Can change size of the unit by applying a prefix**

1 kilometer (km) = 1000 meters (m) kilo = 1000

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**Conversion factor Convert from millimeters (mm) to meters (m)**

Start with equivalence statement 1 m = mm Can divide to get conversion factor

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1 m = mm mm 1000 mm OR 1 m = mm 1m 1 m 1m = 1 = mm 1000mm m Can always multiply something by “1” safely

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**Converting from one unit to another**

How many km are there in 200 m? Have m Want km Know 1 km = 1000 m 200m x 1 km = km m Use conversion factor that will let units cancel to give wanted unit

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**Does your answer make sense?**

How many km are there in 200 m? Going from m (a small unit) to km (larger unit), so we should have fewer km than m Answer: km (fewer km than m)

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200m x 1 km = km m Which conversion factor do we want? Units to be cancelled on bottom Units wanted on top

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**Converting between systems**

Set up same way, except that you need a conversion (bridging) unit between the two systems 1 lb = 454 g How many pounds are there in 114 grams?

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114 g x 1 lb = 0.25 lb 454g

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**Uncertainty in Measurements**

Measurement is only as good as the “measuring” instrument Must choose an appropriate device To weigh your cat, should you use a truck weigh station or a baby scale? Why?

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The number of digits that you can actually “count” for a real measurement depends upon the measuring device. Includes all measured number plus one “uncertain” last digit, which is estimated Can only estimate one place beyond the lines or marks

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Significant figures - all digits in a number representing data or results that are known with certainty plus one uncertain digit.

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**Suppose that two people read the bottom ruler and get measurements of 5.36 cm and 5.37 cm.**

Which one is the correct reading?

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5.4 cm +/ cm (5.3 – 5.5 cm) 5.36 cm +/ cm ( cm) Which has less uncertainty? 5.4 (ca 2%) (ca 0.2%)

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**Uncertainty in Measurements**

Measuring device determines uncertainty and number of significant digits (numbers that have meaning)

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**Accuracy and Precision**

Accuracy: How close measurements are to actual value Precision: How close measurements are to each other

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Figure: 01-25

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