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Measurements

Measurements. What do we measure?. Fundamental properties mass (weight) k ilogram length m eter time s econd temperature Kelvin Derived quantities density, velocity, force, etc. Using the metric system.

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Measurements

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  1. Measurements

  2. What do we measure? • Fundamental properties • mass (weight) kilogram • length meter • time second • temperature Kelvin • Derived quantities • density, velocity, force, etc...

  3. Using the metric system • In the metric system, prefixes are used to identify the multiples of ten. • 103 102 101 1 10-1 10-2 10-3 • Kilo Hecto Deka BASE Deci Centi Milli Base units • mass gram(g) • length meter (m) • liquid volume liter (l) • time second (s) Each multiple is one decimal place. Move the decimal to convert

  4. Moving the decimal • For measurements that are defined by a single unit such as length, mass, or liquid volume , etc., simply move the decimal the number of places indicated by the prefix. • 400 m = 40,000 cm • 75 mg = 0.075 g • For area measurements, they are the combination of two dimensions, you move the decimal twice the number of places. • 2.5 m2 = 2,500,000 mm2

  5. Converting measurements • Metric Metric • multiples of 10 • move decimal or use conversions • English Metric • conversion factors • unit cancellation method

  6. Converting Metric English • When converting in the US (English) system or converting between US and metric units it is necessary to use proportions. • In the example below, the measurement 12 in. is converted to cm. The conversion factor 1 in = 2.54cm is written as a ratio. • 12 in. x 2.54 cm = 30.48 cm 1 in.

  7. Practice A rattlesnake is 2.44 m long. How long is the snake in cm? 1) 2440 cm 2) 244 cm 3) 24.4 cm

  8. Solution A rattlesnake is 2.44 m long. How long is the snake in cm? 2) 244 cm 2.44 m x 100 cm = 244 cm 1 m

  9. What iswrong with the following setup? 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min

  10. 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min Units = day2/hr2Not the final unit needed

  11. Steps to Problem Solving • Read problem • Identify data • Write down a unit plan from the initial unit to the desired unit • Select conversion factors • Change initial unit to desired unit • Cancel units and check • Do math on calculator • Give an answer using significant figures

  12. If the ski pole is 3.0 feet in length, how long is the ski pole in mm?

  13. 3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm

  14. Significant digits • The digits reported in a measured quantity • Indicate the precision of the measuring instrument • Calculations should not have more significant digits than the least number of significant digits in the problem.

  15. Rules – Significant Digits • 1. All nonzero numbers are significant. Ex: 456 – 3 sig. • 2. All zeros between numbers are significant. Ex: 408 – 3 sig. • 3. If decimal present, zero’s to the left are not significant. Ex: 0.0078 – 2 sig. • 4. If decimal present, zero’s to the right are significant. Ex: 0.090 – 2 sig. • 5. If no decimal, zero’s on end are not significant. Ex: 34500 – 3 sig.

  16. Adding and Subtracting • In addition and subtraction, round up your answer to the least precise measurement or least number of places behind the decimal. • For example: 24.686 + 2.343 + 3.21 = 30.239 = 30.24 • 3.21 is the least precise measurement.

  17. Multiplying and Dividing • In multiplication and division, round it up to the least number of significant digits. • For example: 3.22 * 2.1 = 6.762 = 6.8 • 2.1 contains 2 significant digits.

  18. Scientific Notation • Used for expressing very large or very small values • standard form • base x 10 exponent • base is between 1.0 and 9.999… • if exponent is positive the value is greater than 1 • if exponent is negative the value is less than 1 • convert to decimal by moving the decimal the number of places indicated by the exponent

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