Chapter 2: Units of Measurement

What is an SI unit?

A unit from the international system of units

What is the metric and SI unit for volume?

**Metric:** Liter (L)

**SI:** Cubic meter (cm³)

What is the metric and SI unit for length?

**Metric:** Meter (m)

**SI:** Meter (m)

What is the metric and SI unit for mass?

**Metric:** Gram (g)

**SI:** Kilogram (kg)

What is the metric and SI unit for temperature?

**Metric:** Degree celcius (°c)

**SI:** Kelvin (K)

What is the metric and SI unit for time?

**Metric:** second (s)

**SI:** second (s)

What is the metric system?

The units of measurement used by scientists

* Uses metric prefixes
* Based on factors of 10

What devices can you use to measure

* Volume
* Mass
* Length
* Temperature
* Time

**Volume:** Graduated cylinder

**Mass:** Electronic balance

**Length:** Ruler, yardstick, anything like that

**Temperature:** Thermometer

**Time:** Stopwatch

At what temperature does water freeze?

32°F or 0°C

At what value does Kelvin start and what does it mean?

0K → absolute zero

* No particle motion

Measurement

A quantity that has a number and a unit (5.2 m)

Error

The difference between the true value and estimation

What are the two types of error?

Random and Systematic

Random Error

Equal probability of the estimation to be higher or lower than the true value

Systematic Error

All estimates are either ALL lower or ALL higher than the true value

* Occurs in the same direction

Accuracy

The degree of agreement between the true value and the measured value

How do you determine accuracy?

Average the data, compare it to the true value

Precision

A measure of the agreement of replicate measurements; exactness of measurement

How do you determine precision?

Find the range of all measured values

* The lower the range, the better the precision

The instrument's precision is represented in…

the uncertain value of the measurement

Precise vs Approximate Quantities

2\.00 g = exactly measured

About 2 g = rounded, not exact

Measured Numbers

A quantity obtained when you measure a quantity such as your height, weight, or temperature

Significant Figures

All digits in a number representing data that are known w/ certainty plus one uncertain digit

What is the purpose of significant figures?

Used to represent the amount of error associated w/ a measurement

What counts as a significant figure?

* Non-zero digits (**7**)
* Zeros between non-zero digits (7**0**6)
* Zeros at the end of a decimal value (8.65**00**)
* In the co-efficient of scientific notation (5.40 x 10²)

What DOES NOT count as a significant figure?

* Zeroes used as placeholders in large numbers w/o decimals (435**0000**)
* At the beginning of a decimal number (**0.00**65)

How many sig figs?

* 0.0030
* 507
* 54900
* 6.00 x 10²

0\.0030 = **2 sig figs**

507 = **3 sig figs**

54900 = **3 sig figs**

6\.50 x 10² = **3 sig figs**

What are counted numbers and defined equalities considered?

Exact numbers

What are counted numbers?

Numbers that are counted: 8 baseballs

* You cannot have half a baseball

What are defined equalities?

Values given in a system of measurement: 1L = 1000 mL

How would you round these numbers? (2 and 3 sig figs)

* 3246
* 2131

3246 → 2 sig figs: 3200 | 3 sig figs: 3250

2131 → 2 sig figs: 2100 | 3 sig figs: 2130

How do you determine the number of sig figs in the answer of a multiplication or division problem (measured numbers)?

Each number that is being multiplied or divided has some number of sig figs. Round to the lower number of sig figs.

What would 1 cm x 1 cm be?

1 cm²

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like 4 x 4 = 4²

What is the rule when adding or subtracting measured numbers?

The result of the calculation cannot have greater significance than any of the quantities that produced the result.

* The answer will have the same number of decimal places as the value with the least decimal places

Solve

* 21.5 cm x 0.30 cm / 1.88 cm
* 2000 mg + 397 mg
* 2100 L + 890 L
* (5.1 cm + 0.66 cm) / 1.33 cm

1) 21.5 cm x 0.30 cm / 1.88 cm

2 sig figs x 2 sig figs / 3 sig figs = 2 sig figs

\*Math\* = 3.430…to two sig figs ***3.4 cm***

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2) 2000 mg + 397

2000 ← last sig figs is in the thousands place

\+ 397 ← last sig fig is in the ones place

\-------- The answer should be to the thousands

2397 = ***2000 mg***

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3) 2100 + 890

2100 ← last sig figs is in the hundreds place

\+ 890 ← last sig fig is in the tens place

\-------- The answer should be to the hundreds

2990 = The 9 after the first 9 makes the # 3000

BUT now the number doesn’t have sig figs to the hundreds place. So, we have to convert to scientific notation

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30|00 ***3.0 x 10³ L*** = sig figs to the hundreds place

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4) (5.1 cm + 0.66 cm) / 1.33 cm

First, solve inside the parenthesis

5.1 ← last sig figs is in the tenths place

\+ 0.66 ← last sig fig is in the hundredths place

\-------- The answer should be to the tenths

5.76 = don’t round yet, just know that this value should be thought of in terms of 2 sig figs

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Then do the division 5.76/1.33 2 sig figs/3 sig figs

4\.3308….2 sig figs bc its smaller ***4.3 cm***

Calibration

Smallest divisions of a ruler (lines closest together in measurements)

What is the difference between calibrations with and without a 1

With a 1: 0.1 for example, ends in the tenths place, so you round to one place more such as 2.83 (hundredths place)

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Without a 1: 0.5 for example, ends in the tenths places, therefore the estimated measurement will also end in the tenths place such as 36.8

Meniscus

Curvature of water in a tube

How do u measure values with a meniscus?

* ∪
* ∩

∪ = at the bottom of the curve

∩ = at the top of the curve

Prefixes

A special feature of the metric system that can be placed in front of any unit to increase of decrease its size by some factor of 10

State the value, abbreviation, and scientific notation

* Kilo
* Deci
* Centi
* Milli
* Micro

Kilo

* **Value:** 1000
* **Abbreviation:** k
* **Scientific Notation:** 10³

Deci

* **Value:** 0.1 or 1/10
* **Abbreviation:** d
* **Scientific Notation:** 10⁻¹

Centi

* **Value:** 0.01 or 1/100
* **Abbreviation:** c
* **Scientific Notation:** 10⁻²

Milli

* **Value:** 0.001 or 1/1000
* **Abbreviation:** m
* **Scientific Notation:** 10⁻³

Micro

* **Value:** 0.000001 or 1/1000000
* **Abbreviation:** µ or mc (science vs. health)
* **Scientific Notation:** 10⁻⁶

What are the representing values for this:

_cm³ = _cc = _mL

1 cm³ = 1 cc = 1 mL

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*cc = means cubic centimeter = cm³*

Equalities

Use two units to describe the same measured amount

What types of relationships are equalities written for?

1. Metric → Metric
2. U.S → U.S
3. Metric → U.S/ U.S → Metric

What is unique about the structure of conversion factors?

They can be written in two ways

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1 hr/60 min OR 60 min/1 hr

What is different about converting Metric → Metric or U.S → U.S compared to Metric → U.S or U.S → Metric?

*Metric → Metric or U.S → U.S* are EXACT meaning significant figures DO NOT need to be accounted for

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*Metric → U.S or U.S → Metric* are NOT EXACT meaning significant figures must be accounted for

* 1 kg = 2.20 lb (measured value)

Why do significant figures matter in Metric → U.S or U.S → Metric conversions + what is the exception?

They contain 1 measured number that counts towards the sig figs

* ONE EXCEPTION: 1 in = 2.54 cm

What would this percentage conversion factor mean?

* 18% body fat by mass
* Jewlery with 18% gold

1) mass of fat (part) / mass of body (whole)

Percentages are out of 100 = 18% = 18/100

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We assume this is the human body, so we will measure in kg.

18 kg/100 kg lastly, the 18 is measured, while the 100 is exact, meaning we look at the sig figs of 18 = 2 sig figs

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2) mass of gold (part) / mass of jewelry (whole)

same process as above, 18 is measured EXCEPT since it’s jewelry, we will use grams (smaller unit)

What is the formula for unit conversions?

Given x Ratio = Need

Solve (unit conversions)

* How many kilograms is equal to 164 pounds?
* How many minutes are in 1.4 days? (Hint: Two Steps)

1. How many kilograms is equal to 164 pounds?

First, make a flowchart, to represent the math you will do. We are given pounds and we need to find a way to transfer the value into kilograms

lb → Kg search for conversion: 1 lb = 2.20 kg

1 lb/2.20 kg OR 2.20 kg/ 1 lb

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Given x Ratio = Need 164 lb; for the math to work, the pounds must be on the bottom so we will use 2.20 kg/ 1 lb, not 1 lb/2.20 kg

Multiply the top numbers and then divide by the bottom value, which in this case is 1, so nothing changes. 360.8

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Lastly, we figure out the amount of sig figs needed. The 164 has 3, and the 2.20 has 3 as well, so the answer will also need 3 sig figs ***361 kg***

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2) How many minutes are in 1.4 days?

Like before, we will make a flow chart to assist us in our calculations

days → _____ → minutes Now we think, what’s intermediate between days and minutes that can help us here? Right! The hours.

24 hours in a day and 60 minutes in each hour.

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1\.4 days x (24 hours/1 day) x (60 minutes/1 hour)

If we do the math, we get 2016. Now we need sig figs

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1\.4 = 2 sig figs The other two conversions are exact, and do not count towards the sig fig count.

2016 would be 2000 but now we only have 1 sig fig! So, we have to write it in scientific notation ***2.0 x 10³ minutes***

Density Formula

D = m/v (mass/volume)

What type of property is density?

Physical

What is the density of water at 4°C?

1\.00 g/mL

What are the units used for the densities of solids and liquids?

g/cm³ OR g/mL

* 1 cm³ is equal to 1 mL

What are the units used for the densities of gasses?

g/L

What does ∆ mean?

Change in/subtract

How do you find the volume of a solid using the water displacement method?

∆V = V₂ - V₁ (2 should be an f and 1 should be an i)

2/f = Final volume (before solid)

1/i = Initial volume (after solid)

How can you use density as a conversion factor?

Since density is g/mL OR g/cm³ you can simple put it into fraction form with a 1 at the bottom

* 45 g/mL 45g/1mL

What is specific gravity?

A relationship between the density of a substance and a preferred substance (usually water)

* Relative density

What is the formula for specific gravity?

sp gr = density of substance/density of water

What is special about specific gravity?

It is a unitless quantity

* The units cancel out

What is specific gravity used for?

It can be used to determine how a substance will react to water (the preferred substance)