1

Is It Hot in Here?

In the lab, all measurements are done using the metric system (SI System).

This module will familiarize you with the SI units of mass, volume, and

temperature.

Prepared for SSAC byCheryl Coolidge - Colby-Sawyer College

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006

Supporting Quantitative concepts and skills• Number sense: Scientific notation; ratios; order of magnitude• Algebra: Rearranging equations• Graphs: XY (scatter); trend line• Function: Linear

SSAC2006.Q199.CC1.2

Core Quantitative concept and skillNumber sense: Unit conversions

Spreadsheeting Conversions in the English and the Metric Systems

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Slide 3 presents the problem for you to solve.

Slides 4 - 6 introduce you to the use of spreadsheets to perform calculations efficiently.

Slide 7 explains the use of conversion factors.

Slides 8 and 9 provide you with the metric prefixes and review scientific notation.

Slides 10 – 12 require you to create spreadsheets to perform conversions of temperature, volume, and mass.

Slide 13 asks you to create an XY scatter graph using your mass conversions, and to add a trendline to your graph.

Slide 14 gives you the opportunity to practice using trendlines with the temperature conversions and introduces you to the TREND function.

Slides 15 – 16 contain the end of module assignments.

Overview of Module

The process of unit conversion allows you to convert a quantity from one system of measurement to another, or to convert within a system of measurement. Some cases,

such as temperature scales, require using known formulas.

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Problem

The metric system is used to record measurements in most

industrial countries of the world and in science laboratories in all countries. This module will allow you to become more familiar with metric units and to learn how to

perform conversions.

1. Suppose you are instructed to weigh out 60 grams of sodium chloride (table salt). Will that make your French fries salty?

2. Suppose your dorm room is 55 degrees Celsius. Should you get facilities to help you?

3. Suppose your next door neighbor offers you 25 milliliters of Sam Adams for $5.00. Will you have a good party?

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Skip to Slide 7 if you are comfortable with Excel

A B C D23 2 =B3*24 45 66 87 10

A spreadsheet is an easy way to perform calculations.

The numbers in Cells B3 through B7 can just be typed in. As an alternative, Excel can do this for you. Type in the first three values then highlight them (B3 through B5) and place the cursor at the bottom right of the last highlighted cell until you see a small cross. Hold down the left mouse button, drag the pattern through as many cells as you want, and release the button to fill the cells. Excel recognizes the pattern from the first three cells and copies it.

A B C D23 2 44 4 85 6 126 8 167 10 20

Getting Ready: Using a Spreadsheet – Data Input

If you want to multiply each of these numbers by 2, a formula can be created to perform this task. In Cell C3, you type the formula as shown. (All formulas begin with =.)

Click here to skip ahead

You can copy the formula by clicking on Cell C3 and placing the cursor on the bottom right-hand corner of the cell until you see a small cross.

You then drag the cursor down the column, and your results will be displayed.

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A B C D2 divide3 2 4 =c3/$c$94 4 85 6 126 8 167 10 2089 divide by 10

Getting Ready: Using a Spreadsheet – Calculation Input

A B C D2 divide3 2 4 0.44 4 8 0.85 6 12 1.26 8 16 1.67 10 20 289 divide by 10

When the formula in Cell D3 is copied, the cell referenced in

the numerator of the formula will adjust row by row, but the cell referenced in the denominator

remains constant.

0

5

10

15

20

25

0 2 4 6 8 10 12

Suppose you always want to divide the numbers in Column C by the same number – let’s use 10 for an example. You could create a formula (=C3/10) for the first cell in Column C, and drag it down Column D as described in Slide 5.

Suppose, though, that you want to divide by a value in a particular cell. So that you don’t have to change the formula for each value in Column C, you can reference the cell (here, C9) in the formula. In your formula, you refer to this cell as an “absolute” (or “fixed”) cell whose position doesn’t change when you copy the formula. To indicate that this cell is absolute, precede both the column and the row number with a dollar sign.

You can make a graph by highlighting a block of data (here, from B3 to C7) and then clicking on the chart

wizard button:

You select a graph type (in this case, an XY-scatter plot connected by smooth

lines) and follow the directions. Voila! A graph!

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A B C D2 divide3 2 4 0.44 4 8 0.85 6 12 1.26 8 16 1.67 10 20 289 divide by 10

A B C D2 divide3 2 4 0.400004 4 8 0.800005 6 12 1.200006 8 16 1.600007 10 20 2.0000089 divide by 10

Getting Ready: Using a Spreadsheet – Number Formatting

When working with percentages in Excel, it is best to treat them as decimals rather than values greater than 1 (e.g., 0.51 instead of 51%). Multiplying your decimals by 100 to obtain percents can, at times, needlessly complicate your equations and hinder Excel’s ability to understand what you’re trying to calculate.

To tell Excel to display the result as a percent, simply highlight the cells with your decimals, and follow the formatting directions previously discussed. However, instead of choosing “Number” from the “Category” list, choose “Percentage”, and select the number of additional decimal places you wish to use.

Depending on the default settings of the version of Excel you are using, the values generated by your equations may display an unnecessary number of decimal places.

To fix this, right-click on the cell or group of cells you wish to change and choose “Format Cells” from the pop-up menu. Select the “Number” tab, and choose “Number” from the “Category” list, if not already selected. In the “Decimal places” scroll box that appears on the right, type in the number of decimal places you would like to use.

A B C D2 divide3 2 4 0.44 4 8 0.85 6 12 1.26 8 16 1.67 10 20 289 divide by 10

A B C D2 divide3 2 4 40%4 4 8 80%5 6 12 120%6 8 16 160%7 10 20 200%89 divide by 10

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Getting ready: conversion factors

A conversion factor is a ratio that expresses an equality between two units. For example, there are 12 inches per foot. This fact can be stated as an equation: 12 inches = 1 foot. The equation can be rearranged to produce two conversion factors, each equal to one:

12 inches1 foot

and 1 foot 12 inches

Multiplying a number by a conversion factor is essentially multiplying the number by one, which does not change the amount that the number represents.

3 × 2 = 3 2

and

3 × ft = 3 ft

You choose the form of your conversion factor based on what units you need to eliminate and what units you want in your final answer. If you were converting 100 inches to feet, the correct form of the conversion factor should have the desired unit

(feet) and its associated number (1) in the numerator, and the unwanted unit (inches) and its number (12) in the denominator. When you multiply your starting value of 100 inches by the conversion factor, you end up with inches in the numerator and inches in

the denominator, which is a quantity equal to one that can be eliminated:

100 inches × 1 foot = 100 inches × 1 foot = 100 × 1 foot = 8.33 feet 12 inches 12 inches 12

The form of a ratio is always NumeratorDenominator

Note – You can “chain” conversion factors as needed. If you wanted to convert inches to miles, you could use one factor to convert inches to feet, followed by a second factor

converting feet to miles.

=1 =1

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Getting ready: The metric prefixes

An advantage of the using these prefixes is you can modify a multitude of units with the same prefix. For example: a kilogram is equal to 1000 grams (mass),

a kilosecond is equal to 1000 seconds (time), a kilometer is equal to 1000 meters (length).

The use of the prefixes enables you to avoid excessively large or excessively small numbers. For example, 0.00000000345 grams is easier to read as

3.45 nanograms.

The metric system is based on powers of 10. Each change of one decimal place (one exponent) represents a ten-fold difference – 103 is ten times as large as 102, or one order of magnitude larger. The difference

between a Megabyte and a Gigabyte is three orders of magnitude, or a 1000-fold difference.

Very large or small numbers are often represented using scientific notation. To convert a very large positive number to scientific notation, move the decimal point to the left from its original position and place

it after the first digit, then count how many places that the decimal was moved. This counted number becomes the positive exponent: 345678 is 3.34567×105. To convert a very small number to scientific

notation, move the decimal point to the right from its original location, place it after the first nonzero digit, and count how many places you moved the decimal point. The counted number is your negative

exponent: 0.000678 is 6.78×10-4. In Excel, numbers in scientific notation are input as follows. In a number like 3.2×105, the “×10” is represented as “E”, thus 3.2E+5. A number with a negative exponent, such as

7.44×10-3, becomes 7.44E-3 in Excel.

Common Metric Prefixes

Prefix Symbol Value Power

giga G 1,000,000,000 10+9

mega M 1,000,000 10+6

kilo k 1,000 10+3

no prefix - 1 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

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Getting ready: metric conversions

Once you have a feel for the units of the metric system, you do not need to use conversion ratios. Simply look at the difference (absolute value) between the exponents of the unit you are converting from and the unit you are converting to. For example, suppose that you want to convert 7.11 milligrams to kilograms. The difference between the exponent in kilograms

(+3) and the exponent in milligrams (-3) is 6. If the unit you are converting from is SMALLER than the unit you are converting to (as in the example), multiply the original value by 10negative

difference to convert to the new unit. If the unit you are converting from is LARGER than the new unit, multiply the original value by 10positive difference to convert to the new unit. Therefore, 7.11

milligrams is equal to 7.11×10-6 kilograms. In Excel, you would multiply 7.11 by 1E-6 to make the conversion. If the number you are converting is already in scientific notation, add the

difference between the exponents to the existing exponent if you are converting to a smaller unit, or subtract the difference if converting to a larger unit. Thus, converting 7.11×102

milligrams to kilograms will give you 7.11×10-4 kilograms (the original exponent of 2 minus the difference of 6).

One of the biggest advantages of the metric system is that you do not need to use complicated ratios to change from one unit to another. All conversions are based on powers of 10, unlike the

English system, where conversions are quite cumbersome (12 inches/foot, 5280 feet/mile).

Explain how to perform the following conversions and record your answers.

1. 66 grams to centigrams

2. 7.524 kiloliters to microliters

3. 856 nanograms to milligrams

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Temperature conversions

Your dorm room is 55 degrees Celsius. Should you get

facilities to help you?

The equations that allow you to convert between

Fahrenheit and Celsius temperatures are:

F = (9/5)× C+32 andC = (5/9×(F-32))

You can answer this question by building a spreadsheet containing a formula converting Fahrenheit to Celsius.

= cell with a number in it

= cell with a formula in it

Start this spreadsheet by creating the series of Fahrenheit numbers in Column B. Remember, Excel will recognize this pattern for you so you just have to copy the first three cells in Column B through

Row 36. Create the formula needed for the conversion to Celsius in Cell C4 and copy the formula through Row 36.

Recreate this spreadsheet.

What is the approximate Fahrenheit equivalent of 55 degrees Celsius? Should you call facilities? Record your answer.

B C23 Fahrenheit Celsius4 -10 -23.335 -5 -20.566 0 -17.787 5 -158 10 -12.229 15 -9.44410 20 -6.66711 25 -3.88912 30 -1.11113 35 1.666714 40 4.444415 45 7.222216 50 1017 55 12.77818 60 15.55619 65 18.33320 70 21.11121 75 23.88922 80 26.66723 85 29.44424 90 32.22225 95 3526 100 37.77827 105 40.55628 110 43.33329 115 46.11130 120 48.88931 125 51.66732 130 54.44433 135 57.22234 140 6035 145 62.77836 150 65.556

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Volume conversions

As before, use a spreadsheet to convert to familiar units.

Create a column of milliliters, starting with 5 mls and

incrementing by 5 mls till you have 150 mls.

There are 16 tablespoons in a cup, 4 cups in a quart, 4 quarts in a gallon, and 1 liter is equal to 1.06 quarts.

Your next door neighbor offers you 25

milliliters of Sam Adams for $5.00. Will

you have a good party?

So, how many tablespoons are in 25 mls? Will you invite this neighbor to

your party?

= Cell with a number = Cell with a formula

Recreate this spreadsheet, starting on a new sheet.

B C D E F G H2 milliliters liters microliters quarts gallons cups tablespoons3 5 0.005 5000 0.0053 0.00133 0.0212 0.33924 10 0.01 10000 0.0106 0.00265 0.0424 0.67845 15 0.015 15000 0.0159 0.00398 0.0636 1.01766 20 0.02 20000 0.0212 0.0053 0.0848 1.35687 25 0.025 25000 0.0265 0.00663 0.106 1.6968 30 0.03 30000 0.0318 0.00795 0.1272 2.03529 35 0.035 35000 0.0371 0.00928 0.1484 2.3744

10 40 0.04 40000 0.0424 0.0106 0.1696 2.713611 45 0.045 45000 0.0477 0.01193 0.1908 3.052812 50 0.05 50000 0.053 0.01325 0.212 3.39213 55 0.055 55000 0.0583 0.01458 0.2332 3.731214 60 0.06 60000 0.0636 0.0159 0.2544 4.070415 65 0.065 65000 0.0689 0.01723 0.2756 4.409616 70 0.07 70000 0.0742 0.01855 0.2968 4.748817 75 0.075 75000 0.0795 0.01988 0.318 5.08818 80 0.08 80000 0.0848 0.0212 0.3392 5.427219 85 0.085 85000 0.0901 0.02253 0.3604 5.766420 90 0.09 90000 0.0954 0.02385 0.3816 6.105621 95 0.095 95000 0.1007 0.02518 0.4028 6.444822 100 0.1 100000 0.106 0.0265 0.424 6.78423 105 0.105 105000 0.1113 0.02783 0.4452 7.123224 110 0.11 110000 0.1166 0.02915 0.4664 7.462425 115 0.115 115000 0.1219 0.03048 0.4876 7.801626 120 0.12 120000 0.1272 0.0318 0.5088 8.140827 125 0.125 125000 0.1325 0.03313 0.53 8.4828 130 0.13 130000 0.1378 0.03445 0.5512 8.819229 135 0.135 135000 0.1431 0.03578 0.5724 9.158430 140 0.14 140000 0.1484 0.0371 0.5936 9.497631 145 0.145 145000 0.1537 0.03843 0.6148 9.836832 150 0.15 150000 0.159 0.03975 0.636 10.176

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Mass conversions

Will 60 grams of sodium chloride make my French fries salty?

You can answer this question by building a

spreadsheet that allows you to convert grams to

more familiar units of mass like ounces or

pounds, (or vice versa).

There are 454 grams in 1 pound, and 16 ounces in a pound. You also need to

use the values for the metric prefixes given in

Slide 8.

Again, start by creating a series of numbers in column B to represent grams. Create and copy formulas to convert these values to pounds in Column C, and subsequently pounds to ounces in Column D. Remember, you can also “chain” your conversion factors in your formulas

= Cell with a number = Cell with a formula

Next, use the relationships between the metric prefixes to convert grams to kilograms, milligrams, and nanograms

in Columns E, F, and G. Format the numbers appropriately. (see slide 6)

Recreate this spreadsheet on a new sheet, print it, and record how many ounces and

nanograms are in 65 grams.

B C D E F G23 grams pounds ounces kilograms milligrams nanograms4 5 0.011 0.176 0.005 5000 5.00E+095 10 0.022 0.352 0.010 10000 1.00E+106 15 0.033 0.529 0.015 15000 1.50E+107 20 0.044 0.705 0.020 20000 2.00E+108 25 0.055 0.881 0.025 25000 2.50E+109 30 0.066 1.057 0.030 30000 3.00E+1010 35 0.077 1.233 0.035 35000 3.50E+1011 40 0.088 1.410 0.040 40000 4.00E+1012 45 0.099 1.586 0.045 45000 4.50E+1013 50 0.110 1.762 0.050 50000 5.00E+1014 55 0.121 1.938 0.055 55000 5.50E+1015 60 0.132 2.115 0.060 60000 6.00E+1016 65 0.143 2.291 0.065 65000 6.50E+1017 70 0.154 2.467 0.070 70000 7.00E+1018 75 0.165 2.643 0.075 75000 7.50E+1019 80 0.176 2.819 0.080 80000 8.00E+1020 85 0.187 2.996 0.085 85000 8.50E+1021 90 0.198 3.172 0.090 90000 9.00E+1022 95 0.209 3.348 0.095 95000 9.50E+1023 100 0.220 3.524 0.100 100000 1.00E+1124 105 0.231 3.700 0.105 105000 1.05E+1125 110 0.242 3.877 0.110 110000 1.10E+1126 115 0.253 4.053 0.115 115000 1.15E+1127 120 0.264 4.229 0.120 120000 1.20E+1128 125 0.275 4.405 0.125 125000 1.25E+1129 130 0.286 4.581 0.130 130000 1.30E+1130 135 0.297 4.758 0.135 135000 1.35E+1131 140 0.308 4.934 0.140 140000 1.40E+1132 145 0.319 5.110 0.145 145000 1.45E+1133 150 0.330 5.286 0.150 150000 1.50E+1134 155 0.341 5.463 0.155 155000 1.55E+1135 160 0.352 5.639 0.160 160000 1.60E+1136 165 0.363 5.815 0.165 165000 1.65E+1137 170 0.374 5.991 0.170 170000 1.70E+1138 175 0.385 6.167 0.175 175000 1.75E+1139 180 0.396 6.344 0.180 180000 1.80E+1140 185 0.407 6.520 0.185 185000 1.85E+1141 190 0.419 6.696 0.190 190000 1.90E+1142 195 0.430 6.872 0.195 195000 1.95E+1143 200 0.441 7.048 0.200 200000 2.00E+11

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Create an XY scatter graph and add a trendline

Hint: Highlight the columns indicated in green to make your graph. Click

control at the top of each column and drag over it vertically to highlight the correct range. Then select the chart

wizard icon to make your graph.

Create an XY scatter plot of the highlighted ranges. Select the

graph subtype just displaying the data points without a connecting line. Add a title for the graph and

the axes.

You can add a trendline to this graph by clicking on the graph, then selecting “add trendline” from the chart menu. Select

“linear“ in the type submenu, and check “set intercept = 0” and “display equation on chart” in the options submenu. Remember,

the equation of a line is in the form y = mx + b, where m is the slope of the line and b is y-intercept.

Record the equation of the line. Why should the b term be equal to 0? What does the m term tell you?

B C D E F G23 grams pounds ounces kilograms milligrams nanograms4 5 0.011 0.176 0.005 5000 5.00E+095 10 0.022 0.352 0.010 10000 1.00E+106 15 0.033 0.529 0.015 15000 1.50E+107 20 0.044 0.705 0.020 20000 2.00E+108 25 0.055 0.881 0.025 25000 2.50E+109 30 0.066 1.057 0.030 30000 3.00E+1010 35 0.077 1.233 0.035 35000 3.50E+1011 40 0.088 1.410 0.040 40000 4.00E+1012 45 0.099 1.586 0.045 45000 4.50E+1013 50 0.110 1.762 0.050 50000 5.00E+1014 55 0.121 1.938 0.055 55000 5.50E+1015 60 0.132 2.115 0.060 60000 6.00E+1016 65 0.143 2.291 0.065 65000 6.50E+1017 70 0.154 2.467 0.070 70000 7.00E+1018 75 0.165 2.643 0.075 75000 7.50E+1019 80 0.176 2.819 0.080 80000 8.00E+1020 85 0.187 2.996 0.085 85000 8.50E+1021 90 0.198 3.172 0.090 90000 9.00E+1022 95 0.209 3.348 0.095 95000 9.50E+1023 100 0.220 3.524 0.100 100000 1.00E+1124 105 0.231 3.700 0.105 105000 1.05E+1125 110 0.242 3.877 0.110 110000 1.10E+1126 115 0.253 4.053 0.115 115000 1.15E+1127 120 0.264 4.229 0.120 120000 1.20E+1128 125 0.275 4.405 0.125 125000 1.25E+1129 130 0.286 4.581 0.130 130000 1.30E+1130 135 0.297 4.758 0.135 135000 1.35E+1131 140 0.308 4.934 0.140 140000 1.40E+1132 145 0.319 5.110 0.145 145000 1.45E+1133 150 0.330 5.286 0.150 150000 1.50E+1134 155 0.341 5.463 0.155 155000 1.55E+1135 160 0.352 5.639 0.160 160000 1.60E+1136 165 0.363 5.815 0.165 165000 1.65E+1137 170 0.374 5.991 0.170 170000 1.70E+1138 175 0.385 6.167 0.175 175000 1.75E+1139 180 0.396 6.344 0.180 180000 1.80E+1140 185 0.407 6.520 0.185 185000 1.85E+1141 190 0.419 6.696 0.190 190000 1.90E+1142 195 0.430 6.872 0.195 195000 1.95E+1143 200 0.441 7.048 0.200 200000 2.00E+11

Conversion of grams to ounces

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

0 50 100 150 200 250

Grams

Ou

nces

Recreate this graph

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Using trendlines to look at temperature conversions; the TREND function

Refer back to the spreadsheet you created to convert Fahrenheit temperatures to Celsius. Make a copy of the Fahrenheit column by highlighting from B4 through

B36. Select copy from the edit menu, place the cursor on Cell D4 and select paste from the edit menu. Highlight Cells C4 through D36 and create an XY scatter

graph as before. Your x-axis is the Celsius data and the y-axis is composed of the Fahrenheit equivalents. Add the linear trendline and display the equation on

the graph. DO NOT set the intercept = 0. (Why?)

Record the equation of the line. Where have you seen a similar equation in this module?

Now highlight Cells B4 through C36 and create an XY scatter graph as before. Your x-axis is now the Fahrenheit data and the y-axis is composed of the Celsius equivalents.

Add the trendline and display the equation. Record the equation of the line. Why is this equation not exactly the same as the second conversion formula (Celsuis from

Fahrenheit) given on Slide 10? Why is the value of the intercept 17.78?

Optional activity: Excel can give you a value for one unit from the other unit if you use the built-in TREND function. The format of this function is:=TREND(range of y values, range of x-values, x-value to convert)

If you want to determine the Celsius equivalent of 350 degrees Fahrenheit, enter: =TREND(C4:C36,B4:B36,350) in any open cell in the spreadsheet.

Record the value you obtain.

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Turn in your answers to these questions.1. Given the following formulae, write the corresponding Excel

equations.a. 12 x 2b. Column B row 3 divided by 56c. 1.55 x 106 multiplied by 1.8 x 10-3

2. Convert the following numbers to decimal notation and Excel notation.a. 3.94 x 1012

b. 7.234 x 10-4

3. In the country Gogobee, the currency is lemons. There are 62.9 lemons in a dollar. You want to buy some items. a. If shoes cost 580 lemons, how many dollars do you have to part

with to wear them?b. You need bandages for the blisters from your new shoes. They

cost $2.49. How many lemons is this?4. A perceived advantage of the metric system is that the conversions

are based on powers of ten. Explain what this means to you. Do you agree or disagree that the metric system offers advantages?

End of Module Assignments

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End of Module Assignments

5. You are planning a road trip through Canada, where speed limits are posted in kilometers/hour. You have a lead foot, but don’t want to get stopped for speeding, so you need to get a sense for the relationship between miles/hour (mph) and kilometers/hour. a. In one column of a spreadsheet, create a list of speeds in

miles/hour starting with 5 mph and ending with 100 mph in increments of 5.

b. In a second column, create and copy a formula to convert miles/hour to kilometers/hour. The relationship between miles and kilometers is 1.609 kilometers per mile.

c. Create an XY scatter graph of these data. Be sure to label the axes. Add the trendline and display the equation of the line on the chart. Print the table and graph and turn them in.

6. Optional question: 2.17 grams of NaCl (table salt) occupies a volume of 1 cubic centimeter (1 cc3 – a small cube 1 centimeter on each side). What volume in cc3 is occupied by 60 grams of salt? Would this make French fries salty? Answer this question using a conversion ratio.

7. Optional question: Refer back to the mass spreadsheet. Using the TREND function, determine the milligram equivalent of 2.5 pounds.

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Pretest

1. Convert the following numbers to decimal notation and Excel notation.a. 6.345 x 105

b. 8.5 x 10-4

2. What is the relationship between:a. A kilogram and a gram?b. A liter and a milliliter?

3. Convert 55 millimeters to kilometers.4. How would you write the following mathematical formulae as Excel

equations?a. 7.3 multiplied by the contents of cell column A row 6b. 5.2 + 4 + (10 divided by 7)