Conversions Unit 2 - Math

Units: In science EVERY number comes with a unit. (If you asked for a hundred DOLLARS for your birthday and only got 100 PENNIES you would be a little disappointed. They aren’t the same thing!)

Measurements English System: RIDICULOUS!! Metric System: Based on the number ten so easy to work with. The English System of measurement (inches, feet, yards, etc) is absolutely ridiculous! Nobody uses it anymore except for America! (Not even England uses it!) The units are based on silly things and the conversion factors are random and must be memorized. For example, a “foot” is the length of the King of England’s foot. There are 12 inches in a foot. Why the magic number 12? Just because. The Metric System (also known as SI units) is a MUCH more friendly system for measuring things. It is based around the number 10 (just like our counting system) which makes unit conversions incredibly easy. You just end up moving the decimal.

Standard Units: Time = second (s) Length = meter (m) Mass = kilogram (kg) Temperature = Kelvin (K) Volume = Liter (L) Different measurements are required for different data. For example, you don’t measure length in seconds or weight in meters. Standard units have been selected to measure different types of data. Unless told otherwise, all homework solutions should be given in Standard Units. All other units in this class are obtained by combining these units in different ways.

The prefix tells you how far to shift the decimal forward or backward. Letter k M G T c m  n Name Number of Zeroes Big/Small Prefixes: kilo 3 1000x bigger mega 6 million x The prefix tells you how far to shift the decimal forward or backward. Example: 1 km = 1 (000) m 1 cm = (0.0)1 m giga 9 billion x tera 12 trillion x centi -2 100x smaller milli -3 1000 x micro -6 million x nano -9 billion x

https://m.youtube.com/watch?v=AWof6knvQwE Scientific Notation

Scientific Notation Long numbers can be written in a simplified form. We can tell the viewer how far to slide the decimal forward or backward by multiplying by powers of ten Scientific Notation

Steps: 1. First locate the decimal. 1234567.89 2. Next move the decimal until there is only ONE number in front of it. (This number can NOT be a zero.) 1.23456789 3. Count the number of spaces you moved the decimal. This is the number that goes with the 10. If the original number is BIG , the exponent will be positive. If the original number is SMALL the exponent will be negative. We moved the decimal 6 places and the original number is BIG so the exponent will be positive 6.

Steps (Cont.): 4. Keep only the first three numbers that you see. We call the number of digits that we keep “significant figures”. In this class we are going to always use three. Round the last digit as needed. These three numbers go in front of the 10. 1.23 5. Write the final number. The official form looks like 1.23 x 106 …However, the short cut used by your calculator and the homework grading system is to replace the ten with the letter E. 456789

Hiding Decimals: What if we have a number like 123,456,789? Where is the decimal? …it is hiding at the far RIGHT side. In this case, it is after the number 9. We move the decimal over 8 spaces. Note: 4 is less than 5 so we don’t round up and the number becomes: 1.23 x 108 On the homework enter it in like 1.23E8

Small Number Example: Let’s say that the answer to a homework question was 0.000002467. This number is a pain to write by hand, so let’s use scientific notation.

Steps: First: find the decimal near the beginning and move it backward until there is only one number in front of it. Remember that ZERO DOES NOT COUNT. 0.000002467 0000002.467 Count the number of spaces the decimal moved backward. It moved 6 spaces

Steps (Cont.): The original number was very, very small. This means that the six will be negative. Our final answer will have a 10 -6 at the end. We only keep the first three numbers. Again, ZERO DOES NOT COUNT. We must also look at the fourth number to decide if we need to round. 0000002.467 2.47 Because 7 is bigger than 5 we must round the 6 to a 7.

Final Step: Putting everything together we get 2.47 x 10-6 Enter this in the computer as 2.47E-6

Scientific Notation: Examples: (Write these examples in your notes) 1234567.89 = 1.23 x 106 = 1.23E6 (We keep three digits.) 5.62 x 10 5 = 562,000 Put 715 in your calculator = 4.75E12 (Don’t forget to notice the E! It matters a LOT.) 0.0000342619 = 3.43 x 10 -5 = 3.43E-5 (Negative power. Round if needed.) 6.78 x 10 -3 = 0.00678 Scientific Notation:

Do NOT round any of your answers until the very, very end of the problem. Otherwise the computer may mark you wrong. Learn how to store numbers to the memory of your calculator or else get in the habit of writing them down completely so that you don’t have problems with this. When Rounding:

Scientific Notation Challenge

The Number 0ne: To change the units on a measurement without changing the measurement itself you must multiply by the number… …One

Dimensional Analysis (Train Tracks) STRATEGY: If you have a unit you don’t want to have then. . . . … Run it over!

A few things to remember… Units can be treated as mathematical variables. They can be multiplied, added, subtracted, or divided. All the regular rules of algebra apply to them.

Basic Conversion: How many seconds are in a week? 1 Week 7 Days 24 Hours 60 Min 60 Seconds 604,800 Seconds 1 Week 1 Days 1 Hours 1 Min

Two Layer Conversion: My corn grows 5 in / week. How many feet / year is that? 5 in 1 ft 1 wk 365 days 21.7 ft wk 12 in 7 days 1 yrs yr

Units with exponents: My fish tank holds 3 cubic feet of water. How many in3 is that? 3 ft ft ft 12 in 12 in 12 in 5.18 E3 in in in 1 ft 1 ft 1 ft

Metric Conversions: The PREFIX is the first letter (it adjusts the size). The BASE unit is the second letter (it names the unit).

Always Remember Prefix gets a 1. Base unit gets 10 to an exponent from the card. Always convert to base unit first.

Basic Conversion: How many millimeters are in 3.75 meters? 3.75 m 1 mm 3750 mm 10-3 m

Multiple step Conversion: How many kilobytes are in 4.5 gigabytes? 4.50 x 106 4.5 Gb 109 b 1 Kb 4,500,000 Kb 1 Gb 103 b

Combined Conversion: If I am 1.77 meters tall, how many feet is that? cm 1 in 1 ft 5.81 ft 10-2 m 2.54 cm 12 in

Advanced Conversion: A glacier is moving 5 mm/s How many yards per year is that? 172,477.8123 5 mm 10-3 m 1 mi 5280 ft 1 yrd 60 s 60 min 24 hrs 365 days 1.72 x 105 yrds s 1 mm 1609 m 1 mi 3 ft 1 min 1 hr 1 day 1 yr yr