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Lecture 1.3 Conversion of Units

Lecture 1.3 Conversion of Units. We have all measured things before, but how would you define it? Measurement: comparing an unknown quantity to a standard unit (known quantity) What are some standard unit we use now?. How can we convert from one unit to another?.

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Lecture 1.3 Conversion of Units

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  1. Lecture 1.3 Conversion of Units

  2. We have all measured things before, but how would you define it? • Measurement: comparing an unknown quantity to a standard unit (known quantity) • What are some standard unit we use now?

  3. How can we convert from one unit to another? • In chemistry, you will have to calculate numbers and convert it into different units • A ‘conversion factor’ is used to convert it between units • The quantity does not change, but the unit does • Ex: 60 minutes vs 1 hour… same quantity but different unit

  4. How many minutes are there in 2.5 hours? • In order to solve this, we need to find the ‘conversion factor’ • The relationship between hours (the number given) and minutes (the number wanted) is 1 hour=60 minutes

  5. So the conversion factor will be written as 1 hour or 60 minutes 60 minutes 1 hour • So which one do I use? • The unit that was Given will always be on the bottom (denominator) • The unit that we Want will always be on the top (numerator)

  6. How many minutes are there in 2.5 hours? • Step 1: What is Given? • What number is given to you in the problem? • Step 2: What do we Want? • What are we trying to solve? • Step 3: What do we know that connects the two? • What is the relationship between the two? • Step 4: Write it out • Step 5: Calculate

  7. 2.5 hours 60 minutes = 150 minutes 1 hour

  8. How many seconds are there in 24 hours? • Sometimes, we need to use two conversion factors • We know that 60 sec.=1 min, and 60 min= 1 hour

  9. 24 hours 60 minutes 60 seconds 1 hour 1 minute 86400 sec 86000 sec 90000 sec

  10. How many seconds are there in 7 hours? • How many hours is 567,000 seconds? 30,000 sec (25200) 158 hrs(157.5)

  11. Practice • How many cm is 22.5 inches? (1 in.= 2.54 cm) • How many cm is 9 feet? (1 feet=12 inches) • How many feet is 987 cm? • How many cm are there in 4.87 yards? (3ft=1yrd) • How many yards are in 343,000 cm?

  12. 57.15 cm • 274.32 cm • 32.38 feet • 445 cm • 3751 yrds

  13. How to convert between metric units • Many countries came together in 1960 to form an international unit of measurements, called Systeme International (SI), or metric system • Examples: • Mass: Kilogram • Length: Meter • Time: Second • Electric current: Ampere

  14. SI units can also be used to measure extremely large or small numbers using prefixes • Instead of saying an atom is 0.00000000001 meters thick, can say its 10 nanometers • 1 “nano” represents 10-9 of a number

  15. How to convert between metric units • 4.5 meters will be how many millimeters? • Step 1: What is Given? • What number is given to you in the problem? • Step 2: What do we Want? • What are we trying to solve? • Step 3: What do we know that connects the two? • What is the relationship between the two? • Step 4: Write it out • Step 5: Calculate

  16. The relationship between meters and millimeters is : 1 meter = 103 millimeter • How did we come up with it? • Ans: Count the number of steps! • The “3” is positive because you are going down three steps

  17. 1 2 3

  18. 4.5 meters 103 millimeters = 4500 mm 1 meter 1256 centimeters will be how many kilometers?

  19. 5 4 3 2 1

  20. 1256 centimeters will be how many kilometers? • The relationship between cm and km is: • 1 cm = 10-5 km • The “-5” is negative because you are going up five steps • Quick reasoning test: 105 km does not equal to 1 cm.

  21. Practice • Convert 253 meters into kilometers • Convert 0.0345 hm into cm • Convert 1.02 cm into mm

  22. .253 km (1 m= 10-3 km) • 345 cm (1 hm = 104 cm) • 10.2 mm (1 cm = 101 mm)

  23. Scientific Notations • Scientific notation can be used to write a small number like 0.00000233, or a large number like 8700000000 • We can write the first number as 2.33 x 10-6 and second number as 8.7 x109 • Notice that significant figures are consistent • You move the decimal point to the left if the exponent is negative, to the right if it is positive

  24. Scientific notation always follows this rule : N x 10n • N is always a single digit, followed by a decimal point if it needs more significant figures • n is any whole number

  25. Practice: write the following in scientific notations • 3980000 • Ans: 3.98 x 106 • 5100.1 • Ans: 5.1001 x 103 • 23.040 • Ans: 2.3040 x 101 or just 2.3040 x 10

  26. 0.0000000000910 • Ans: 9.10 x 10-11 • 0.0000000501 • Ans: 5.01 x 10-8 • 0.00003 • Ans: 3 x 10-5 • 579,000,000,000,000 • 5.79 x 1014

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