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The Metric System

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The Metric System

Why do I need to learn and be able to use the metric system?

Everyday Metric

- http://www.nisenet.org/viz_lab_image_scaler

Metric Conversions

Metric Prefix Table

PrefixSymbolMultiplierExponential

giga G 1,000,000,000 109

mega M 1,000,000 106

kilo k 1,000 103

Base Unit 1 100

deci d 0.1 10¯1

centi c 0.01 10¯2

milli m 0.001 10¯3

micro µ 0.000001 10¯6

nano n 0.000000001 10¯9

pico p 0.000000000001 10¯12

Nanoscience

- 1 human hair is ~50,000 nanometers across; or 50 nanometers is one-thousandth the width of a human hair.
- 1 bacterial cell measures a few hundred nanometers across.
- The smallest things the naked eye can see are 10,000 nanometers.
- 1 nanometer = 10 hydrogen atoms in a line.

Why should I care about nanoparticles?

Because it is being used now!

Untrathin glass treatment

Nanocrystals are used in photovoltaic cells as well as drug research

Using nanotechnology, Cornell scientists created a fabric that can detect biohazards like E. coli and other pathogens.

Stain repellent clothing

sunscreen

Antibacterial paint in hospitals

How to Convert

- Memorize the conversion factors.
- When moving from a large prefix to a smaller prefix your answer will always be a larger number. EX: 1 megameter = 107 decimeter
- When converting a small prefix to a larger prefix your answer will always be a smaller number. EX: 1 nanometer = 10-7 centimeter

Dimensional Analysis

Follow these steps to set up a dimensional analysis problem

1. List all given information with the correct units.

2. Write down what you are trying to determine along with the correct unit.

3. List the conversion factors needed to solve the problem.

4. Write your given information as a fraction with the correct units.

5. Set up a chain of “fractions” (conversion factors) to convert from the given units to the desired units. To cancel out the original unit, place that same unit in the denominator where it will cancel out later.

6. Verify that all units cancel out except the units of the desired answer.

7. Do the math and record the final answer to the correct number of significant digits and in proper scientific notation. Include the correct units.

8. Circle your final answer.

Dimensional Analysis Problem

- What is the size in cm of a 15 nm gold particle?
- 15 nm2. ?cm
- 1m = 109 nm and 1m = 100 cm
- 15 nm
1

- 15 nm l 1m l100cm = 15 x 10-7 cm
1 l 109 nm l 1m

= 1.5 x 10-6 cm

NASA: Human error caused loss of Mars orbiter

November 10, 1999

WASHINGTON (AP) -- Failure to convert English measures to metric values caused the loss of the Mars Climate Orbiter, a spacecraft that smashed into the planet instead of reaching a safe orbit, a NASA investigation concluded Wednesday.

The Mars Climate Orbiter, a key craft in the space agency's exploration of the red planet, vanished after a rocket firing September 23 that was supposed to put the spacecraft on orbit around Mars.

How To Measure

- Lab equipment is calibrated to a certain accuracy that is unique to each piece of equipment, so your recorded measurement can not always contain 1 or 2 decimal places.
- You determine how to record your measurement based on the calibration of the tool.

First Let’s Define

- Accuracy: How close a measurement is to the true value. Your measurement tool has an effect on the accuracy of a measurement
- Precision: How repeatable are your measurements. This is more reflective of your lab technique.

So How Do We Measure With Accuracy?

- Look at the calibration lines on your tool.
- You know the measurement at these lines, but you do not know how far it is between the lines.
- You record what you know and guess between the lines.
- The last digit given for any measurement is the uncertain or estimated digit
- Lets take a look

Read the Bottom of the Meniscus

Which is correct? 66 ml, 66.0 ml, 66.1 ml, 67 ml, 67.0 ml, 67.5 ml

Practice

- 1cc = 1 cubic centimeter= 1 ml
- Calibration lines every 0.5 cc
- Guess between the lines
- Which is correct? 8 cc, 8.0 cc, 8.5 cc

Another Example

- How is this tool calibrated?
- What is the correct volume? 80 ml, 85 ml, 87ml, 90 ml

Significant Digits

- AKA significant figures or sig digs or sig figs
- Determined by the measuring tool so they relate the accuracy of the tool.
- Used to determine the number of significant digits in a calculated answer.
- You can not calculate an answer that is more accurate than the least accurate measurement.

Rules to Determine # Sig Digs

There are three rules on determining how many significant figures are in a number:

- Non-zero digits are always significant.
- Any zeros between two significant digits are significant.
- A final zero or trailing zeros in the decimal portion ONLY are significant.

Practice

Identify the number of significant figures:

1) 3.08002) 0.00418

3) 7.09 x 10¯54) 91,600

5) 0.0030056) 3.200 x 109

7) 2508) 780,000,000

9) 0.010110) 0.00800

Calculations With Sig Digs

RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement with the least number of significant digits.

Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3

- Check the number of significant digits in each of the original measurements:
22.37 shows 4 significant digits.

3.10 shows 3 significant digits.

85.75 shows 4 significant digits.

- Our answer can only show 3 significant digits because that is the least number of significant digits in the original data.
- 5946.50525 shows 9 significant digits. We must round in order to show only 3 significant digits. Our final answer becomes 5950 cm3.

Calculations With Sig Digs

RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g

- Look to the original problem to see the number of decimal places shown in each of the original measurements.
3.76 shows 2 decimal places

14.83 shows 2 decimal places

2.1 shows 1 decimal place

- We must round our answer to one decimal place (the tenth place). Our final answer is 20.7 g

Practice Problems

Solve the following problems and report answers with appropriate number of significant digits.

1) 6.201 cm + 7.4 cm + 0.68 cm + 12.0 cm = ?

2) 1.6 km + 1.62 m + 1200 cm = ?

3) 8.264 g - 7.8 g = ?

4) 10.4168 m - 6.0 m = ?

5) 12.00 m + 15.001 kg = ?

6) 131 cm x 2.3 cm = ?

7) 5.7621 m x 6.201 m = ?

8) 20.2 cm divided by 7.41 s = ?

9) 40.002 g divided by 13.000005 ml = ?