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Mastering Measurement: Significant Figures & Metric System Guide

Learn about significant figures, counting rules, scientific notation, metric system basics, unit conversions, and dimensional analysis for accurate measurements. Practice problems included.

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Mastering Measurement: Significant Figures & Metric System Guide

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  1. Measurement

  2. 1 2 3 4 5 Significant figures (sig figs) • How many numbers mean something • When we measure something, we can (and do) always estimate between the smallest marks.

  3. Significant figures (sig figs) • The better marks the better we can estimate. • Scientist always understand that the last number recorded is actually an estimate 1 2 3 4 5

  4. Which numbers count? • All nonzero numbers in a recorded measurement are significant • Zeros between nonzeros are significant • 12004 • Zeros in front of nonzeros are NOT significant • 0.045

  5. Which numbers count? • zeros at the end of a number after the decimal point are significant • 45.8300 • Zeros after the number but no decimal are NOT significant • 458300

  6. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • A dozen is exactly 12 • There are 2405 students in this school • Being able to locate, and count significant figures is an important skill.

  7. Sig Figs • How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0.0485 g • 0.004085 g • 40.004085 g

  8. Sig Figs • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g

  9. Problems • 50 is only 1 significant figure • if it really has two numbers, then how can I write it? • Scientific notation • 5.0 x 101 • now the zero counts.

  10. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least in the question • 3.6 x 653 = 2350.8 • With sf: 2400

  11. Multiplication and Division • Same rules for division Practice • 4.5 / 6.245 • 4.5 x 6.245 • 9.8764 x .043 • 3.876 / 1983 • 16547 / 714

  12. The Metric System An easy way to measure

  13. Measuring • The numbers are only HALF of a measurement “It is 10 long” • 10 what? • Numbers without units are meaningless!

  14. The Metric System • Easier to use because it is a decimal system • Every conversion is by some power of 10. • A metric unit has two parts: A prefix and a base unit. • prefix tells you how many times to divide or multiply by 10.

  15. Base Units • Length - meter more than a yard - m • Mass - grams - about a raisin - g • Time - second - s • Temperature - Kelvin or ºCelsius K or C • Energy – Joules - J • Volume - Liter - half a two liter bottle- L • Amount of substance - mole - mol

  16. Prefixes • kilo k 1000 • deci d 1/10 • centi c 1/100 • milli m 1/1000 • kilometer - about 0.6 miles • centimeter - less than half an inch • millimeter - a paperclip wire

  17. k h D d c m Converting in Metric • how far you have to move on this chart tells you how far and which direction to move the decimal place. • The box is the base unit: meters, Liters, grams, etc.

  18. k h D d c m Conversions • convert 25 mg to grams • convert 0.45 km to mm • convert 35 mL to liters • It works because the math works, we are dividing or multiplying by 10 the correct number of times

  19. Converting from metric to standard • Requires conversion factors • Use dimensional analysis • Units must work out in the final answer

  20. Dimensional Analysis • A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm) • in meters? • A race is 10.0 km long. How far is this in miles? • 1 mile = 5280ft • 1 meter = 3.281 ft • Pikes peak is 14,110 ft above sea level. What is this in meters?

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