# Mathematical measurements assignment help

Mathematical measurements assignment help

Title: Mathematical measurements assignment help

Laboratory Report Sheet

Name: Date:

Email:

Laboratory Instructor:

Course Nbr.: CHEM 101 Distance

Section:

Experiment Nbr.: 1 – Home-based Lab

Experiment Title: LABORATORY MEASUREMENT

Purpose:

Concepts related to the textbook:

Conclusion:

Experiment 1 – LABORATORY MEASUREMENT

The following is to be completed at home.

For background:

• Read the information on significant figures and dimensional analysis in your textbook.

Some of the measurement techniques described in your manual may be done at home with varying degrees of accuracy, while others will need to be done in the laboratory where the needed instruments are available. You will also see most of these measurement techniques and instruments in the demonstrations that appear in the videotapes.

The purpose of this experiment is to familiarize you with the proper way to take and record measurements using a meter stick (ruler). Additionally, it is to help you learn to apply significant figure rules when combining measurements and to learn what is implied by and what the difference between precision and accuracy is.

In this experiment, all the numbers in parentheses refer to lines on the attached data sheet where your measurements and/or answers are to be recorded.

I. AREA OF A RECTANGLE

Use the rectangle below to do the following measurements.

A B

C D

Using a ruler, measure and record (1) the length (line AB) and (2) width (line AC) of the rectangle drawn above in cm. Be sure to record the measurement as accurately as possible in order to attain the maximum number of significant figures. Record these lengths to 2 decimal places, e.g., 1.20 cm. For example, some line might be 8.55 cm….that means, the line ended between the calibrated (marked) 8.5 and 8.6 lines on your ruler…… and you estimated its very end to be closer to the 8.6 and therefore estimated the next/last number………and recorded the measurement to be 8.55 cm. If a line ended exactly on the 8.6 calibration, you would record 8.60 cm.

You will recall that the area of a rectangle is equal to the length times the width (A=LW). Use your calculator and the formula given to find the area of the rectangle (3). Record all the digits provided by your calculator. Note that cm x cm = cm2; the units of area are always a squared unit.

Record the area (4) rounded to the proper number of significant figures based on your original measurements. In science, it is often necessary to report or use a measurement in units other than that in which it was originally recorded (conversions). In order to practice this type of conversion: Show the set-up (5) to convert the area of this rectangle from cm to m . [Recall that 100 cm = 1m. Therefore, (100cm) = (1m) or 10000cm = 1 m ].

Convert the value to square meters and report the area (6). Report the area one final time using scientific notation (and the correct number of significant figures) (7).

As an additional practice, suppose a student had measured the length and width of a different rectangle in inches and had calculated the area as 150 square inches. What would the area be in square feet? (8) [Recall that 12 inches = 1 foot. Therefore, (12 inches) = (1 foot) or 144 in =1ft .]

Convert this area from square inches into square centimeters (2.54 cm = 1inch) (9).

Be certain to report the result to the proper number of significant figures.

II. AREA OF A TRIANGLE

Area of triangle = one-half x base x height or A=1/2 bh

A

B

D C

You are going to calculate the area of this triangle using two different sets of measurements. The point is to show that the resulting calculation of area depends on the precision with which you take the original measurements and effects the final calculation. The application of significant figure rules to the results of calculations is supposed to prevent these discrepancies! Let’s see if it does.

Use the ruler provided (10).

In the first set, record the length of the base “ABC” and its height “DB” in cm.

In the second set, record the length of the base “DC” and its height “AD” in cm.

Calculate the area of the triangle in square centimeters in each case. First, record the area answers using all the digits provided by your calculator and then rewrite the calculated area answers using the significant figure rules.

How do the values of the original calculator areas compare: Are they exactly the same before rounding/applying significant figure rules, yes or no (11)? If NO, explain why not (12). Are the 2 original calculated areas close or very different (13)?

After rounding to the proper number of significant figures, are the two answers for the area of this triangle the same (yes or no)? (14)

III. PRECISION AND ACCURACY

Use your textbook or a dictionary for reference, if necessary. This topic is also discussed on the World of Chemistry #3 videotape.

What is meant by the precision of a set of measurements (15)?

What is meant by the accuracy of a set of measurements (16)?

Suppose a student determined a certain triangle to have an area of 26.5 cm2 by one set of measurements and 26.7 cm2 by a second set of measurements and 26.8 cm2 by a third set of measurements. What is the average (mean) value of these three areas (17)? By comparing the 3 individual areas to the mean/average, how would you describe the student’s precision (18) and accuracy (19)?

IV. MEASUREMENT

Units of measurement are a means of communication.

What things do you measure every day, in the kitchen, bathroom, workplace, etc.?

List at least 4 things (20).

How do you know that the scale at the grocery store is accurate or that the pump at the gasoline station measures the volume accurately (21)?

Find an empty 1 or 2 liter bottle. (Soda is a common bottle found around the house). Fill your empty bottle with water. Using any measuring device that you have in your kitchen, measure the number of ounces equivalent to your bottle (22). (Recall that 1 cup =8 oz.)

DATA TABLES – Submit with the Lab Report Sheet

I. Area of Rectangle (A=LW)

Answers Units

(1) Length of rectangle (AB) cm

(2) Width of rectangle (AC) cm

(3) Area (A=LW) – Calculator Answer cm2

(4) Area – Rounded (significant figures) cm2

(5) Conversion setup – cm2 to m2

m2

(6) Area – Calculator Answer m2

(7) Area – Rounded (significant figures) m2

(8) Area – in2 to ft2 ft2

(9) Area – converted to cm2 cm2

II. Area of Triangle (A=1/2bh)

(10) Triangle Data

Base (ABC) cm

Height (BD) cm

Area – Original (a) cm2

Area – Rounded cm2

Base (DC) cm

Height (AD) cm

Area – Original (b) cm2

Area – Rounded cm2

(11) Are the original (a + b) calculator areas exactly the same before rounding (yes or no)?

(12) Explain if No.

(13) Are the two original calculated areas close or very different? Explain

(14) After rounding to the proper number of significant figures, are the two answers for the area of this triangle the same (yes or no)?

III Precision and Accuracy

(15) Precision

(16) Accuracy

(17) Average (mean) of (3) Areas

(18) Describe the student’s precision.

(19) Describe the student’s accuracy.

IV Measurement

(20) Identify four items you measure each day (kitchen, bathroom, workplace, etc.): 1

2

3

4

(21) How do you know that the scale at the grocery store is accurate or that the pump at the gasoline station measures the volume accurately?

(22) Empty 1 or 2 liter bottle

(1 cup = 8 oz) Size (L)

oz

mL

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Mathematical measurements assignment help Mathematical measurements assignment help Mathematical measurements assignment help