Scientific Measurement and Safety Homework Packet

Focus Learning Target

Convert between scientific notation and standard form of a number

Convert from one metric unit to another using conversion factors

Convert between English and metric units using conversion factors

Convert squared and cubed terms from one set of units to another

Convert rate expressions from one set of units to another

Convert temperature between Celsius and Kelvin

Read metric scales to the correct number of significant figures

Report values and round numbers to the correct number of significant figures

Report sums, differences, products, and quotients to the correct number of significant figures

Define density using a mathematical equation and give the appropriate units.

Perform calculations involving density, mass, and volume, giving answers with the appropriate

units and significant figures

Follow the problem-solving steps to solve word problems

Read various instruments with accuracy and precision

Scientific Notation WS#1

Scientific notation is a short way to write very large or very small numbers. It is written as the product of a number

between 1 and 10 and a power of 10.

To convert a number into scientific notation:

• Create a number between 1 and 10 by moving the decimal to the left.

• Count the number of spaces the decimal moved to determine the exponent of 1

Example: 9,846,000,000. = 9.846 x 109

To convert a number into standard form:

• Move the decimal to the right the number of spaces indicated by the exponent.

Example: 1.312 x 106 = 1,312,000

.

Convert the following into Scientific Notation:

1. 0.000073 =

2. 90,000 =

3. 0.0000078 =

4. 930,000 =

5. 7565 =

6. 438,000,000,000 =

7. 0.000000000000539 =

8. 78.95 =

Convert the following into Standard Notation:

9. 5.7 x 105 =

10. 6.21 x 10-4 =

11. 8 x 105 =

12. 4.79 x 10-3 =

13. 3.5 x 10-2 =

14. 4.3 x 107 =

15. 7.665 x 10-8 =

16. 1.64 x 10-2 =

15. Mt. Everest rises 54,768 feet in the air while Mt. Rushmore stretches a mere 8,976 feet. What is the difference in

the height of these two mountains expressed in scientific notation?

16. The Great Salt Lake covers about 45,800 mi2 Lake Tahoe covers about 7,725 mi2 What is the total area covered

expressed in scientific notation?

17. The body of an average person contains 2.502 x 10-4 lbs. of copper. Express this number in standard form.

18. The state of Colorado covers about 1.041 x 105 square miles Express this number in standard form.

19. The circumference of the Earth at the equator is about 24,900 miles. Express this number in scientific notation.

20. The speed of light is approximately 6.71×108miles per hour. Express this number in standard form.

More Practice on Significant Figures WS#3

1. Determine the number of significant figures in each of the following:

(a) 6.432 g (b) 50.319 g (c) 646 cm

(d) 5.285 cm (e) 0.889 s (f) 329.3 mm

(g) 1873.0 A (h) 890 ml (i) 0.0006246 g

(j) 4.04 x 1012 g (k) 6.59 x 10-7 m (l) 0.0009242 mg

2. Round each of the following to 3 significant figures.

(a) 707.5

(b) 2,300.2

(c) 0.0003350

(d) 2676

(e) 10.26730

(f) 18.95 x 1021

3. Complete the following addition/subtraction questions:

(a) 12 cm + 0.031 cm + 7969 cm =

(b) 0.085 cm + 0.062 cm + 0.14 cm =

(c) 3.419 g + 3.912 g + 7.0518 g + 0.00013 g =

(d) 30.5 g - 16.82 g + 41.07 g + 85.219 g =

(e) 143.0 cm + 289.25 cm + 68.45 cm - 6.00 cm =

4. Complete the following multiplication questions

(a) 2.89 cm x 4.01 cm = (b) 17.3 cm x 6.2 cm =

(c) 5.08 m x 1.2 m = (d) 5.00 mm x 7.3216 mm =

(e) 4.218 cm x 6.5 cm = (f) (4.8 x 102 m)(2.101 x 103 m) =

5. Complete the following division questions

(a) 8.071 cm2 = (b) 24789.4 km2 =

4.216 cm 43.5 km

(c) 4.819 cm2 = (d) 2.23 m2 =

9.852 cm 18.941 m

Solutions:

1. a) 4 b) 5 c) 3 d) 4 e) 3 f) 4 g) 5 h) 2 i) 3 j) 3 k) 3 i) 3

2.a) 708 b) 2.30 x 103 (c) )0.000335 (d) 2680 (e) 10.3 (e ) 19.0 x 1021

3. a) 7981 cm b)0.28 cm c) 7.052 g d)140.0 g e) 494.7cm

4. a) 11.6 cm2 b)110 cm2 c) 6.1 m2 d) 36.6 mm2 e) 27 cm2 f) 1.0x106 m2

5. a) 1.914 cm b) 570 km c) 0.4891 km d) 0.118 m

Metric Conversions Practice WS#4

Write the correct abbreviation for each metric unit.

1) Kilogram _____

2) milliliter _____

3) nanosecond _____

4) Kilometer _____

5) meter _____

6) picometer _____

7) decimeter _____

8) centimeter _____

9) gram _____

10) microgram _____

11) Liter _____

12) Mega Liter _____

Try these conversions, using the method of dimensional analysis.

13) 7000 mg = _______ g

14) 8.6 m = _____ cm

15) 704 km = _______ m

16) 68 g = _______ Kg

17) 8500 m = _______ Km

18) 680 µm = _____ m

19) 95 mL = _____ L

20) 45 g = _____ mg

21) 90 cm = _____ m

22) 6.3 cm = _____ mm

23) 16 dm = ______mm

24) 8 Km = _____ cm

25) 5 ml = _______ µL

26) 120 mg = _____ Kg

27) 45 g = ________ mg

28) 9.8kg= _________g

29) Circle the greatest metric measurement in each problem

a. 500 cm 6000 mm 4 m

b. 0.2 L 240 mL 50 cL

c. 3000 mg 250 cg 3 kg

Dimensional Analysis:

Dimensional Analysis – the method of converting units.

Conversion Factor – factional quantity used to convert units.

When we are given a quantity in some units, we can convert these to another unit according to:

given unit desired unit

given unit desired unit

Some Common Units and Their Equivalents 2.54 cm = 1 in 1 kg = 2.2 lbs 1 gal = 3.79 L 1 lb = 16 oz

0.621 mi = 1.00 km 1 mi = 5,280 ft 1 gal = 3.785 L 1 mL = 1 cm3

1lb= 453. 59 g 1 acre= 43,560 ft2 1L= 1.057 qt 1L= 1000cm3

Single Step Unit Conversions

a. Convert 46.0 cm to inches

b. Convert 58.9 mg to g

c. Convert 593.4 nm to m

Multistep Unit Conversions

a. 68.5 mi = in

b. Convert 1789 ft to km.

Conversion Factors: 1 ft = 12 in, 1 m = 39.37 in, 1 km = 1000 m

c. Isopropyl alcohol has a density of 0.786 g/cm3. What is the volume in liters of 5.9 kg of this liquid?

Conversion Factors: 0.786 g = 1 cm3, 1 mL = 1 cm3, 1 L= 1000 mL, 1 kg = 1000 g

Conversion Involving Units Raised to a Power

a. A circle has an area of 2659 cm2. What is the area in square meters?

b. 5.2 m3 = ft3

c. 165 g/cm2 = lb/in2

Dimensional Analysis Practice Problems WS#5

For all problems, please show your dimensional analysis setup and give your answer to the correct

significant figures. Remember you can use any of the conversions shown above.

Perform the following single step unit conversions:

1. Convert 0.568 mg to g.

2. Convert 357 km to m.

3. The density of iron is 7.87 g/cm3 . How much volume does 24.5 g of iron occupy?

Perform the following multistep unit conversions:

4. Convert 75 mL to gallons.

5. Convert 4.59 mi2 to m2

6. 5. 57 x 10 4 nm to m

7. How many square meters (m2 )does a 90. 0 ft2 rug occupy? (1 ft = 12 in.)

8. How many liters of air are in a room that is 1250 m3?

9. What is the volume of a 49.5 g gold spoon? (Density of gold is = 19.32 g/cm3 ).

10. What is the density of mercury (13.6 g/cm3) in units of kg/m3?

11. The volume of a wooden block is 6.30 in3. This is equivalent to how many cubic centimeters?

12. Most Starbucks drinks contain caffeine. One Grande Iced coffee with milk contains 125 mg of

caffeine. How many Grande Iced coffee’s will contain 8.00g of caffeine?

13. A person’s sodium intake be limited to 2,400 mg. The mass percent of sodium in table salt is 39.33.

How many grams of table salt can Lily consume?

Temperature Conversions WS#6

The two most common temperature scales are the Fahrenheit scale and the Celsius scale.

Kelvin is a temperature scale designed so that 0 (zero) K is defined as absolute zero and

the size of one unit is the same as the size of one degree Celsius. Absolute zero is a

hypothetical temperature at which all molecular movement stops. All actual temperatures

are above absolute zero. Absolute zero would occur at -273 C, 459.69 F or 0K. Many

scientists use this scale (because all the temperatures are positive, making calculations

simpler) to the Celsius scale.

Temperature Conversion Formulas

°F =9/5 °C + 32

°C = 5/9 (°F - 32)

K= °C + 273

Questions

1. Convert the following numbers from degrees Fahrenheit to degrees Celsius.

a. 0 F ________C

b. 32 F (freezing point) ________C

c. 70 F (room temperature) ________C

d. 98.6 F (body temperature) ________ C

e. 100 F ________C

f. 212 F (boiling point) ________C

2. Complete the chart using the correct conversion formula.

Fahrenheit Celsius Kelvin

339

17

-25

100

89.5

-27

3. When Nicky was packing for the trip she went on weather.com and found that the average temperature

in Los Angeles is 32.0 Celsius . Why did she not pack any coats and sweaters?

4. Your friend from London is using a recipe for pizza from an Italian cookbook. You notice that that he set

the oven temperature at 175F. What would you advise him to do?

5. What is the one characteristic of the Kelvin scale that is not a characteristic of either the Celsius or

Fahrenheit temperature scales?

Reading Metric Scales WS#7

There are two kinds of numbers in the world, Exact and Inexact numbers.

Exact Numbers: example: There are exactly 12 eggs in a dozen.

example: Most people have exactly 10 fingers and 2 eyes.

Inexact numbers: example: any measurement.

If I quickly measure the width of a piece of paper, I might get 220 mm. If I am more

precise, I might get 216 mm. An even more precise measurement would be 215.6

mm.

Example:

1. Determine the volume (in mL) of the liquids in the following graduated cylinders.

a)__________ b)___________ c)__________ d)_______

2. Draw in the meniscus for the following readings:

a) 49.31 mL b) 19.2 mL c) 28.65 mL d) 64.8 mL

3.

a._________ b.______ c.______ d.______

Density: WS#8 Density is the relationship of the mass of an object to its volume. Density is usually reported in units of

grams per cubic centimeter (g/cm3 ). For example, water has a density of 1.00 g/cm3. Since a cubic

centimeter contains the same volume as a milliliter, in some cases you may see density expressed as

g/mL.

Density = Mass/Volume

Let’s say we have 19 grams of gold and 19g of Helium. 19g of gold would fit in 1 cube with the

dimensions 1cm x 1cm x 1cm. 19g of Helium would fill approximately 106 cubes with the dimensions

1cm x 1cm x1cm.

Example: Silver has a density of 10.5g/ml. What does this mean?

For silver you are able to put 10.5 grams of silver in a cube that is 1cm x 1cm x 1cm (as shown above)

Ethanol has a density of 0.789 g/cm3.

a. What is the mass of 325 cm3 of ethanol?

b. What is the volume of 65.0 g of ethanol?

1. A block of aluminum occupies a volume of 30.5 mL and weighs 82.35 g. What is its density?

Known:

Unknown:

2. What volume of silver metal will weigh exactly 1500.0 g? The density of silver is 10.5 g/cm3.

Known:

Unknown:

3. Find the mass of the 350.0 mL of benzene. The density of benzene is 0.8765g/mL.

4. A block of lead has dimensions of 5.50 cm by 6.20 cm by 7.00 cm. The block weighs 35.87 g.

Calculate the density of lead.

5. 38.5 g of iron shot is added to a graduated cylinder containing 55.50 mL of water. The water level

rises to the 59.10 mL mark. Calculate the density of iron.

6. A student filled a graduated cylinder with water and read the miniscus at 35.8 ml. The student then

dropped a solid material into the graduated cylinder and the water level rose to 45.9 ml. If the solid

material had a density of 2.99 g/mL, determine the mass of the solid object.

7. Refer to the table of densities at the right to answer the following questions.

a. Sketch a graph of mass vs volume for Iron, copper and mercury b. Find the mass of these metal cubes: (Show your work below)

Silver cube ______________

Zinc cube ______________

Aluminum cube ______________

8. Ethanol has a density of 0.789 g/cm3.

a. What is the mass of 325 cm3 of ethanol?

b. What is the volume of 65.0 g of ethanol?

9. Coconut oil is the oil extracted from the kernel or meat of the coconut. It serves many uses from

culinary and nutrition to hair and beauty. . One cup is equivalent to 216.21 cm3. If 1 cup of

coconut oil has a mass of 200.0 g, what is the density of olive oil in g/cm3?

10. What would you expect to happen if the cup of coconut oil in question 9 is poured into a container

of ethanol? Why?

11. Ships float on water, even though the density of steel is much greater than water. Explain

Substance Density

(g/mL)

Aluminum 2.70

Titanium 4.54

Zinc 7.13

Tin 7.31

Iron 7.87

Nickel 8.90

Copper 8.96

Silver 10.50

Lead 11.35

Mercury 13.55

Gold 19.30

Measurements:Review Sheet WS#9

1. Determine the number of significant digits in each of the following:

a. 63.30 cm b. 9,843.02 L c. 2.00012 km d. 0.0001010450 sec

e. 9.65 kg f. 9.701oC g. 0.5 mL h. 365 kg .

i. 8000.12 mm j. 904,000 h k. 3.4 x 103 g l. 7 x 10-5mm

2. Convert between scientific notation and regular notation, without changing the number of sig fig's:

a. 5800 g = 5.8 x 103 g b. 3.6 x 105 m = 360000 m

c. 23,000,000 m = ____________ m d. 3.6 x 10-5 m = _____________ m

e. 6,000 cm = ____________ cm f. 3.60 x 105 m = _____________ m

g. 6,000. cm = ____________ cm h. 6.00 x 101 kg = _____________ kg

3. Round each of the following off to the specified number of sig fig's:

a. Round 68.241 g to... 4 sf: __________ 3 sf: __________ 2 sf:__________

b. Round 9.2983 g to... 4 sf: __________ 3 sf: _________ 2 sf: __________

c. Round 773.99 g to... 4 sf: __________ 3 sf: __________ 2 sf: ___________

d. Round 90,001 g to... 4 sf: __________ 3 sf: __________ 2 sf: __________

4. Perform all calculations and express your answer with the appropriate sig figs & units:

a) 67 cm x 55 cm = 3700 cm2 b) 4.29 m x 9.83 m = _____ c) 870 mm x 430 mm = _____

d) 0.034 g/L x 8.8 L = _____ e) 5.79 m/hr x 2.34 hr = _____ f) 1.405 m x 6.39 m = _____

g) 5.00 cm x 6.00 cm = _____ h) 5.6 m2 x 6.23 m = ______ i) 5.471 g/mL x 24.0 mL = ___

j) 45.9 mi ÷ 1.50 hr = _______ k) 320 m ÷ 160 sec = _______ l) 234.6 g ÷ 67.4 mL = _____

5. An experiment calls for 19.96156 g of substance A, 25.2 g of substance B, 0.0088 g of substance C, and 9.44

g of substance D.

a) How many significant digits are there in each measurement?

b) What is the total mass of substances in this experiment?

c) How many significant digits are there in the answer to part b?

6. Using two different instruments, Rachel measured the length of my foot to be 77 centimeters and 77.00

centimeters. Explain the difference between these two measurements

7. Temperature conversions:

Formulas: Ko= Co + 273 Fo = 9/5 Co +32 Co = 5/9(Fo-32)

a. The weather forecaster predicts that today’s high will be 90. Which temperature scale is being

used? What would be the corresponding temperature on the other two scales?

b. “It was so cold yesterday that the temperature only reached 265.” Which temperature scale is

being used? What would be the corresponding temperature on the other two scales?

c. “Today’s temperature of 41 in Chicago set a record high for the month of August.” Which

temperature scale is being used? What would be the corresponding temperature on the other two

scales

Some Common Units and Their Equivalents 2.54 cm = 1 in 1 kg = 2.2 lbs 1 gal = 3.79 L 1 lb = 16 oz

0.621 mi = 1.00 km 1 mi = 5,280 ft 1 gal = 3.785 L 1 mL = 1 cm3

1lb= 453. 59 g 1 acre= 43,560 ft2 1L= 1.057 qt 1L= 1000cm3

8. For all problems, please show your dimensional analysis setup and give your answer to the

correct significant figures.

a. 1.2 kg = ________dg

b. 2.00 x 10-5m = ________in

c. 25.4 mm = ________cm

d. 1.2 miles = ________km

e. 15.47 m3 = ________km3

f. 17.0 ft/s = ________m/min

g. 342 miles/hr = ________km/s

h. 1.45 L = ________gallons

i. 4.100 g = ________mg

j. 1.2 kg/yard = ________lbs/m

k. 2.00ft3/min = ________L/hour

l. 7.5 mi2 = ________ in2

m. Change a speed of 72.4 miles per hour to its equvalent in meters per second.

n. Convert a density of 13.6 g/mL to its equivalent in lb/ft3.

o. Alex was pulled over on her way from Los Angles to Las Vegas by an officer claiming she was

speeding. The speed limit is 65 mi/hr and Alex had traveled 97 km in 102 minutes. How fast

was Alex’s’s average speed? Does she deserve a ticket?

9. The density of helium gas is 0.178 g/L. What would be the mass of 375.0 mL of this gas?

10. The density of iron is 7.86 g/ml. What volume of iron will have a mass of 50.00 g?

11. A piece of wood that measures 3.0 cm by 6.0 cm by 4.0 cm has a mass of 80.0 grams. What is the

density of the wood? Would the piece of wood float in water? (volume = L x W x H)

12. A cup of gold colored metal beads was measured to have a mass 425 grams. By water

displacement, the volume of the beads was calculated to be 48.0 cm3. Given the following

densities, identify the metal.

Gold: 19.3 g/mL

Copper: 8.86 g/mL

Bronze: 9.87 g/mL

13. A piece of carbon, density is 3.514 g/cm3 is placed in a graduated cylinder and the water level rises

from 4.11 mL to 9.20 ml. Find the mass of the piece of carbon.

14. Calcium chloride is used as a deicer on roads in the winter. It has a density of 2.50g/cm3. What is

the volume of 8.58 kg of this substance?( Hint: Make sure to convert kg to g)

15.

a. By looking at the graph, which sample has the highest density?

b. Find the density of each substance. Make sure to show work and include the units.

c. What mass of salt water has a volume of 52mL?

d. What volume of alcohol has a mass of 30.0g?

e. If a solid with a density of 0.85g/ml was placed in a graduated cylinder containing all three

substances, where would it be located?

Percent Error: A way to compare a measurement with a commonly accepted value for that measurement.

Percent Error is sometimes used to test the accuracy of the instrument or device that you are using.

% Error = measured value – accepted value x 100

accepted value

16. An experiment performed to determine the density of silver yields a value of 0.58 g/cm3. The

theoretical value for the density of silver is 10.50 g/cm3. Find the percent error.

17. The density of water at 4ºC is known to be 1.00 g/cm3. Kim experimentally found the density of

water to be 1.085 g/cm3. What is her percent error?

18. For each of the volume devices below record the scale reading

a._______ b._______ c._______ d._______