DERIVED UNITS

Combining measurements to describe physical properties

DERIVED UNIT Derived units are created from

combining other base units Examples:

Volume: the amount of space an object takes up

Density: how much mass is in a certain volume

VOLUME Volume is derived by taking the following

formula: Volume = l x w x h

To solve, you do the same things to the units as you do to the numbers If you have a box 10cm x 10cm x 10cm: Volume = 10cm x 10cm x 10cm Volume = 1000 cm3

The derived unit is cm3

NOTE

1 cm3 = 1 mL

This is an important conversion. Make sure it is easily found in your notes

For example: 25cm3 = 25mL

DENSITY Density is the ratio of mass to volume Mathematically this is expressed as

follows: Density = mass

volume Each variable is abbreviated

D = density m = mass V = volume

DENSITY The density formula is summarized as:

D = m V

Again, the units are also divided by each other

Below are some examples of density units: g/cm3

g/mL kg/m3

EXAMPLE An object has a mass of 15.0g and a

volume of 5.0mL. What is the density?

NOTE: I am much more interested in the unit than the number answer

SOLUTION D = M/V

D = (15.0g)/(5.0mL)

D = 3g/mL

NOTE: In addition to dividing the number, you also divide the units

TRY THESE A car travels 200km in 4 hours,

calculate the speed. A student at college buys 8 books. His

total price is $160. What is the price per book?

A bullet covers 5000m in 2 seconds, calculate the speed.

USING DENSITY TO SOLVE FOR MASS AND VOLUME

You can also solve for mass and volume.

Normally, you would use algebraWe are going to use a

technique called dimensional analysis

TITLE: FLAME TEST LAB Purpose: To determine an unknown

substance using a flame test. Procedure:1. Insert flame loop into a chemical sample.2. Make all of your observations about the

flame.3. Repeat for each of your known

chemicals.4. Insert flame loop into unknown sample.5. Determine the unknown.

DIMENSIONAL ANALYSIS Another way to solve problems is using

a process called dimensional analysis You will be solving density problems

using dimensional analysis Dimensional analysis: method of

solving problems where the units cancel out

EXAMPLE If a block has a density of 25kg/L and a

volume of 10L, what is the mass? For dimensional analysis, you need to be

able to cancel out units until the one you are solving for is left

Step 1: You always begin with the known value that has 1 UNIT after the number.

NOTE: 10L only has liters (L) after the number

Therefore, you start the problem with 10L

EXAMPLEStep 2: Find the conversion in the problem. The conversion is the number that has 2 units after the number.NOTE: 25 kg/L has two units after the number, both kilograms (kg) and liters (L)Step 3: Put the two values together in a “T chart” so that 2 of the units cancel and you are left with 1 unit.

DIMENSIONAL ANALYSIS Step 1: Write your known starting

value 10L

Step 2: Set up a T chart to cancel out units using the conversion (density) 10L | 25kg_

| 1L Step 3: Cancel out the units to solve

(for mass) 10L | 25kg_ = 250kg

| 1L

TRY THIS OUTA block has a density of 15g/mL. If the block has a mass of 5g, what is the volume?

NOTE: When you set it up, you will want to cancel grams (g)

TRY ONE OUTA block has a density of 10g/mL. If the block has a mass of 0.025 kg, what is the volume?

HINT: To cancel out units, they must be the SAME unit.

ANSWERD = 10g/mLM = 0.025kg = 25g (convert unit)

V= ?25 g | 1mL = 2.5 mL| 10 g

USING DIMENSIONAL ANALYSIS IN METRIC

Before, we looked at using ratios to solve for metric conversions. Now we will use dimensional analysis.

The steps are the same, the only difference is we use the 2 units from the chart to convert.

REMINDER: Step 1: Convert to the base unit first Step 2: Convert to the second unit next

EXAMPLE Convert: 250mm = ??? hm

First, find the metric conversions on your sheet 1m = 1000mm 1hm = 100m

Second, take your starting value (250mm) and convert it to the base unit

CONVERT TO BASE UNIT250mm | 1m_____ = 0.25m

| 1000mm

NOTE: You put the mm on the bottom to cancel out the 250 mm on topSince the 1000mm is on the bottom, you divide

CONVERT TO SECOND UNIT0.25m | 1hm_____ = 0.0025hm

| 100m

NOTE: You use the answer from the first step in the second stepSince the 100m is on the bottom, you divide

TRY THESEConvert the following metric

units

225mg = ______g33.4cm = ______hm4.56x1010nL = ______ cL

HOW DO YOU DETERMINE SIG. FIGS. IN DERIVED

UNITSWhen multiplying or dividing, you find

the number with the fewest number of sig. figs.

This is the number of sig. figs. in your answerExample: 3.024 x 2.11 = 6.38064

(4 sig. figs.) (3 sig. figs.)

Change to correct sig. fig.= 6.38(Fewest sig. figs. is 3)

TRY THE FOLLOWING1. 2.2500 x 2500 =

2. 2.04 x 10-3 x 8.808 x 102 =

3. 4.05 x 105 =3.625 x 102

ANSWER 2.2500 x 2500 = 5.6 X 103 (2 sig. figs.)

2.04 x 10-3 x 8.808 x 102 = 1.80 (3 sig. figs.)

4.05 x 105 = 1.12 x 103 (3 sig. figs.)

3.625 x 102

NOTE: You must round correctly, when doing significant figures

PROBLEM #1 Solve using significant figures:

______(367.21)*(24.783)_____

(19.5623)*(5.987218)*(521.931)

PROBLEM #2An object has a mass of

2.25x103 mg and a density of 5.0g/mL. What is the volume?