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Measurement & conversions

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Measurement & conversions

1. 1. Measurement & Conversions
2. 2. Measurement in SI <ul><li>SI (System International) </li></ul><ul><ul><li>Used by scientists throughout the world to communicate results. </li></ul></ul><ul><ul><li>Metric system </li></ul></ul><ul><ul><li>Uses multiples of 10 </li></ul></ul>SI Base Units Quantity Unit Used in SI (symbol) Length or distance meter (m) Volume or capacity liter (L) Mass gram (g) Density gram per cubic centimeter (g/cm 3 ) Time second (s) Temperature degrees Celsius (°C)
3. 3. Common SI Prefixes Prefix Meaning Symbol Example kilo- 1,000 k km hecto- 100 h hm deka- 10 da dam (none) 1 m deci- 0.1 d dm centi- 0.01 c cm milli- 0.001 m mm
4. 4. Length <ul><li>Meter (m) </li></ul><ul><li>Practice </li></ul><ul><ul><li>Larger lines on the metric ruler in the picture show centimeter divisions </li></ul></ul><ul><ul><li>Smaller, unnumbered lines show millimeter divisions. </li></ul></ul><ul><ul><ul><li>How many centimeters long is the shell? </li></ul></ul></ul><ul><ul><ul><li>How many millimeters long is it? </li></ul></ul></ul>Common Conversions 1 km = 1,000 m 1 m = 100 cm 1 m = 1,000 mm 1 cm = 10 mm
5. 5. Liquid Volume <ul><li>Volume </li></ul><ul><ul><li>Amount of space that a liquid takes up. </li></ul></ul><ul><li>Liter (L) </li></ul><ul><li>Practice </li></ul><ul><ul><li>Graduated cylinders (see picture) measure in milliliters (mL). </li></ul></ul><ul><ul><li>Notice that the water in the cylinder has a curved surface (meniscus). </li></ul></ul><ul><ul><li>To measure the volume, you must read the level at the bottom of the meniscus. </li></ul></ul><ul><ul><li>What is the volume of water in this graduated cylinder? </li></ul></ul>Common Conversions 1 L = 1,000 mL
6. 6. Mass <ul><li>Amount of matter in an object </li></ul><ul><li>Gram (g) </li></ul><ul><ul><li>Approx. 1 paperclip </li></ul></ul><ul><li>Practice </li></ul><ul><ul><li>What is the mass of the apple? </li></ul></ul><ul><ul><li>Suppose a recipe for applesauce called for one kilogram of apples. About how many apples would you need? </li></ul></ul>Common Conversions 1 kg = 1,000 g
7. 7. Temperature <ul><li>Celsius scale used </li></ul><ul><li>T Celsius = (5/9) X (T Fahr - 32) </li></ul><ul><li>Water freezes at 0°C </li></ul><ul><li>Water boils at 100°C </li></ul>
8. 8. Converting Between Units in SI <ul><li>Simply move the decimal point </li></ul><ul><li>2 Questions to Ask </li></ul><ul><ul><li>In which direction did I move the decimal point? </li></ul></ul><ul><ul><li>How many places did I move the decimal point? </li></ul></ul>
9. 9. Steps to Convert <ul><li>K i ngs (kilo) kill humans, H umans(hecto) kill D ragons (deka), BASE (meters, liters, grams ), D ogs(deci) eat cats, C ats(centi) eat M ice(milli )&quot; OR </li></ul><ul><li>King Henry Died By Drinking Chocolate Milk </li></ul><ul><li>(kilo) (hecto) (deka) (base) (deci) (centi) (milli) </li></ul><ul><li>Example: 12.9 cm = _____ m </li></ul><ul><li>Place finger on what is given (Ex. cm). </li></ul><ul><li>Count # of places you move to get to the unit that is wanted while moving finger. (Ex. 2 left to get to m) </li></ul><ul><li>Move decimal over that many places in the same direction that you moved your finger. (Ex. Move decimal over to the left 2 spaces) </li></ul><ul><li>Example: 12.9 cm = 0.129 _ m </li></ul>
10. 10. Converting SI Units Further Practice <ul><li>4.8 kg = ______ mg </li></ul><ul><li>6.3 cm = _____ mm </li></ul><ul><li>12 L = _______KL </li></ul>
11. 11. Conversion Practice <ul><li>Convert between the following units: </li></ul><ul><li>600 millimeters = _?_ meters </li></ul><ul><li>0.35 liters = _?_ milliliters </li></ul><ul><li>1,050 grams = _?_ kilograms </li></ul><ul><li>250 millimeters = _?_ meters </li></ul><ul><li>1.5 liters = _?_ milliliters </li></ul><ul><li>750 grams = _?_ kilograms </li></ul><ul><li>Note: See Edhelper wkshts for further practice </li></ul>
12. 12. Metric System Summary <ul><li>Metric (SI) units are used almost entirely throughout science and will be used in this course! </li></ul><ul><li>Length—units are meters </li></ul><ul><li>Volume—units are liters </li></ul><ul><li>Mass—grams </li></ul><ul><li>Prefixes in order of largest to smallest </li></ul>(k) (h) (da) (d) (c) (m) kilo hecto deca Base deci centi milli 1000 100 10 [meter] 0.1 0.01 0.001 [liter] [gram]
13. 13. Scientific Notation <ul><li>Purpose </li></ul><ul><ul><li>To make it easier to work with very large or very small numbers </li></ul></ul><ul><li>Rules </li></ul><ul><ul><li>Form: # x 10 exponent </li></ul></ul><ul><ul><li># must be 1 or greater and less than 10 </li></ul></ul><ul><ul><li>Exponents show how many places the decimal would have to be moved to get the decimal point directly behind the number. </li></ul></ul>
14. 14. Steps to Scientific Notation <ul><li>Examples (Larger than 1) </li></ul><ul><ul><li>4,000 = 4.0 x 10 3 (this means 4 times 10 3 , or 4 X 1000) </li></ul></ul><ul><li>Example (Small than 1) </li></ul><ul><ul><li>0.0001 = 1 x 10 -4 </li></ul></ul><ul><li>Steps </li></ul><ul><li>Identify where the decimal is currently located. Put your pen on it. </li></ul><ul><li>Move the decimal so that it is directly behind the number (between 1 and 10). Count how many spaces over you moved while moving. </li></ul><ul><li>Put the number in correct scientific notation. # x 10 exponent </li></ul><ul><ul><ul><li>If you moved the decimal to the left 3 spaces, then the exponent will be a + 3. </li></ul></ul></ul><ul><ul><ul><li>If you moved the decimal to the right 3 spaces, then the exponent will be a - 3. </li></ul></ul></ul><ul><li>General Rule: Decimal moved left : exponent up </li></ul><ul><li> Decimal moved right : exponent down </li></ul>
15. 15. Scientific Notation <ul><li>Examples (Larger than 1) </li></ul><ul><ul><li>4,000 = 4.0 x 10 3 (this means 4 times 10 3 , or 4 X 1000) </li></ul></ul><ul><ul><li>36,000 = 3.6 x 10 4 </li></ul></ul><ul><ul><li>2,390,000,000 = </li></ul></ul><ul><ul><li>1 = 1 x 10 0 10 = 1 x 10 1 100 = 1 x 10 2 </li></ul></ul><ul><li>Examples (Smaller than 1) </li></ul><ul><ul><li>0.0001 = 1 x 10 -4 </li></ul></ul><ul><ul><li>0.00000036 = </li></ul></ul><ul><ul><li>0.000000000000287 = </li></ul></ul>
16. 16. Scientific Notation <ul><li>Converting numbers to scientific notation which already have a form similar to scientific notation. </li></ul><ul><ul><li>12.6 x 10 2 = 1.26 x 10 3 </li></ul></ul><ul><ul><li>1333.8 x 10 4 = 1.3338 x 10 7 </li></ul></ul><ul><ul><li>0.00023 x 10 8 = </li></ul></ul><ul><ul><li>0.0006 x 10 13 = </li></ul></ul><ul><ul><li>122.8 x 10 -8 = </li></ul></ul><ul><ul><li>0.003 x 10 -5 = </li></ul></ul><ul><li>Decimal left, exponent up. </li></ul><ul><li>Decimal right, exponent down. </li></ul><ul><li>Remember if a negative number gets smaller, it goes from -5 to -8 and vise versa. </li></ul>
17. 17. Scientific Notation <ul><li>Examples (Backward conversion) </li></ul><ul><li>If exponent is -, move that many places to the left to make it smaller. </li></ul><ul><li>If exponent is + , move that many places to the right to make it bigger. </li></ul><ul><ul><li>3.6 x 10 -4 = 0.00036 </li></ul></ul><ul><ul><li>4.22 x 10 6 = 4,220,000 </li></ul></ul><ul><ul><li>8.6 x 10 8 = </li></ul></ul><ul><ul><li>7.876 x 10 -8 = </li></ul></ul>