Measurements in Physics

Fundamental Units The SI system (AKA the System International or the metric system There are 7 fundamental units: Meter (m)- measures distance Kilogram (kg) – measures mass Second (s) – measures time Ampere (amp) –measures electric current Kelvin (K) – measures temperature Mole (mol) – measures chemical quantities Candela (cd) – measures light intensity

Derived Units Derived units are combinations of two or more fundamental units. Examples of derived units: Newton- Measures force Hertz –Measures frequency Joule – measures energy Coulomb – measures charges Volt – measures potential difference Watt – measures power Ohm – measures resistance

Why Use the SI Units? Unlike our common measurements, the metric system is based on multiples (or powers of) 10.

Scientific Notation The conversions and expression of measurement sin the metric system are made easy by Scientific Notation The format is always: #.### x 10# Note: The number before the decimal cannot be a zero, it must be a 1-9 digit! Example 3.0x108 The power of the ten is referred to the magnitude of the number Positive exponents are large numbers Negative exponents are small numbers

Converting to and from Simply count decimals! Q. Write in decimal notation: 3.6x1012 Since the power is positive, I know that the number has to get larger. The magnitude is 12, so I have to move the decimal 12 places to the right.

Con’t Write in decimal notation 4.36x10-11 Since the power is negative, I know that the number has to get smaller. The magnitude is 11, so I have to move the decimal 11 places to the left.

Con’t Write in scientific notation 300000000 Since this is a large number I know the power of ten will be positive. So I count the number of times I move the decimal over so that just one nonzero number is in front of it and make this number the positive power of ten.

Con’t Write in scientific notation: 0.00000000578 Since this is a small number, the magnitude of ten must be negative. So I count the number of places I move the decimal until one number is in front of it, and make this the negative power of ten.

Let’s Practice… Try- Your turn to practice Tough- This is hard, but you can do it!

Significant figures One benefit of scientific notation, is it allows numbers to represent only the significant figures. To determine the number of significant figures: Is the decimal point absent or present?

Let’s Practice… Teacher- Let me model to help you out. Together- Volunteers? Try- Your turn to practice. Tough- This is hard, but you can do it!

Pre-Fixes Instead of writing out the power of ten (like we just did), scientists often use prefixes on the base unit to establish the magnitude of the measurement. The prefixes you need to know are listed on page 1 of your reference table. These prefixes also signify the order of magnitude of a measurement (by looking at the notation on our chart)

Another word for “order of magnitude”

Converting Formats To convert between scientific notation and prefixes: Put the number in scientific notation Find the power of ten from the notation on the chart Rewrite the original number replacing the power of 10 (so the x10#) with the prefix. Don’t forget to use the correct base units! To convert between prefixes and scientific notation (or powers of 10) Make sure your units have a prefix. Find the prefix on the chart. Rewrite the original number replacing the prefix with the power of 10 notation from the chart. Don’t forget to use the base units (that no longer have the prefix)

Let’s Practice Q. Write in standard units: 19 KJ The prefix we have is a K. Looking on the chart, the notation of K is x103, so I rewrite the 19, replace the K with x103 and put on my base unit of J. My answer is 19x103 J

Let’s Practice Q. Write with a prefix : 6.9 x 10-9 m The notation we have is x 10-9 , and looking at the chart that is the “nano” prefix. So I rewrite the number 6.9 and preplace the power of ten with the symbol for nano so my answer is 6.9 nm.

Let’s Practice… Teacher- Let me do another one Together- Let’s try one together Try- Your turn to practice Tough- This is hard, but you can do it!

Converting Between Prefixes We can use the following chart: Easy trick: The number of zeros correspond to the power of ten for the prefix! Another hint: when your going from big to small prefixes multiply. When you go from small to big prefixes divide.

Convert Between Units Complete the following conversions Teacher: 350 µg = _______ mg Together: 20 km = _______ m Try: 850 l = _______ ml Try: 8 cm = _______ m Try: 3 mg = _______ g Tough: 3x108m = _____________km

Approximating Size Now that you practiced measuring the metric system, you will often be asked to approximate the size of something. Based on what you learned fill in the following chart to help you remember: The measurement of… Is approximately…. one shoulder to the opposite finger tip 100 m (remember this equals 1 m) 10-1 m 10 -2 m 100 m 1 kg 1 g 100 kg

Performing Operations It is easy to perform mathematic operations as long as we can use our calculators! Go over for each kind how to… take the sin, cos, or tan; take the inverse functions; to put into and out of sci notation; enter in numbers in notation

Math Review Can you successfully…? Solve for a specific variable Perform exponent operations Solving for the missing side of a right triangle Find an angle in a right triangle Find out by doing each section of the worksheet at the corresponding station. Once you are done, get your answers checked. Based on what you did incorrectly and your conversation with Miss Shea, fill out page 8 of your notes. Notice: If you don’t have quality notes written for EACH section, you will receive a zero for today’s work!