Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. \(\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)\) e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

Short Answer

Expert verified
a. \(188.28\) b. \(11.6\) c. \(4.21\times10^{-6}\) d. \(6.1\times10^{-26}\) e. \(4.894\) f. \(0.22\%\)

Step by step solution

01

Calculate each fraction individually

First, we calculate each fraction and round the result to the correct number of significant figures: \(\frac{2.526}{3.1} = 0.8151613\) (rounded to 3 significant figures) \(\frac{0.470}{0.623} = 0.7544081\) (rounded to 3 significant figures) \(\frac{80.705}{0.4326} = 186.7087\) (rounded to 4 significant figures)
02

Add the three results

Now, we add the results obtained in Step 1: \(0.815 + 0.754 + 186.71 = 188.279\)
03

Round the final result

Finally, we round the result to the correct number of significant figures: \(188.279\) (rounded to 5 significant figures) a. Answer: \(188.28\) b. \((6.404 \times 2.91) /(18.7-17.1)\)
04

Perform the subtraction

First, we perform the subtraction: \(18.7 - 17.1 = 1.6\)
05

Perform the multiplication

Next, we perform the multiplication: \(6.404 \times 2.91 = 18.63524\)
06

Divide the results

Now, we divide the result of the multiplication by the result of the subtraction: \(\frac{18.63524}{1.6} = 11.6464\)
07

Round the final result

Finally, we round the result to the correct number of significant figures: \(11.6464\) (rounded to 3 significant figures) b. Answer: \(11.6\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\)
08

Subtract the terms

We subtract the given terms: \(6.071 \times 10^{-5} - 8.2\times10^{-6} - 0.521\times10^{-4} = 0.00006571 - 0.00000940 - 0.00005210 = 0.00000421\)
09

Round the final result

Finally, we round the result to the correct number of significant figures: \(0.00000421\) (rounded to 3 significant figures) c. Answer: \(4.21\times10^{-6}\) d. \(\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)\)
10

Add the terms in parentheses

First, we add the terms in each parenthesis: \(3.8 \times 10^{-12} + 4.0 \times 10^{-13} = 3.84 \times 10^{-12}\) \(4 \times 10^{12} + 6.3 \times 10^{13} = 6.304 \times 10^{13}\)
11

Perform the division

Next, we perform the division: \(\frac{3.84\times10^{-12}}{6.304\times10^{13}} = 6.093\times10^{-26}\)
12

Round the final result

Finally, we round the result to the correct number of significant figures: \(6.093\times10^{-26}\) (rounded to 2 significant figures) d. Answer: \(6.1\times10^{-26}\) e. \(\frac{9.5+4.1+2.8+3.175}{4}\)
13

Add the numbers

First, add the four numbers: \(9.5 + 4.1 + 2.8 + 3.175 = 19.575\)
14

Divide the sum by 4

Now, divide the result obtained in Step 1 by 4: \(\frac{19.575}{4} = 4.89375\)
15

Round the final result

Finally, we round the result to the correct number of significant figures: \(4.89375\) (rounded to 4 significant figures) e. Answer: \(4.894\) f. \(\frac{8.925-8.905}{8.925} \times 100\)
16

Subtract the numbers

First, subtract the numbers in the fraction: \(8.925 - 8.905 = 0.020\)
17

Perform the division

Now, perform the division: \(\frac{0.020}{8.925} = 0.002241\)
18

Multiply the result by 100

Now, multiply the result obtained in Step 2 by 100: \(0.002241 \times 100 = 0.2241\)
19

Round the final result

Finally, we round the result to the correct number of significant figures: \(0.2241\) (rounded to 2 significant figures) f. Answer: \(0.22\%\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

To determine the volume of a cube, a student measured one of the dimensions of the cube several times. If the true dimension of the cube is \(10.62 \mathrm{~cm}\), give an example of four sets of measurements that would illustrate the following. a. imprecise and inaccurate data b. precise but inaccurate data c. precise and accurate data Give a possible explanation as to why data can be imprecise or inaccurate. What is wrong with saying a set of measurements is imprecise but accurate?

A thermometer gives a reading of \(96.1^{\circ} \mathrm{F} \pm 0.2^{\circ} \mathrm{F}\). What is the temperature in \({ }^{\circ} \mathrm{C}\) ? What is the uncertainty?

Which of the following statements is(are) true? a. A spoonful of sugar is a mixture. b. Only elements are pure substances. c. Air is a mixture of gases. d. Gasoline is a pure substance. e. Compounds can be broken down only by chemical means.

Convert the following Fahrenheit temperatures to the Celsius and Kelvin scales. a. \(-459^{\circ} \mathrm{F}\), an extremely low temperature b. \(-40 .^{\circ} \mathrm{F}\), the answer to a trivia question c. \(68^{\circ} \mathrm{F}\), room temperature d. \(7 \times 10^{7 \circ} \mathrm{F}\), temperature required to initiate fusion reactions in the sun

Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. \(212.2+26.7+402.09\) b. \(1.0028+0.221+0.10337\) c. \(52.331+26.01-0.9981\) d. \(2.01 \times 10^{2}+3.014 \times 10^{3}\) e. \(7.255-6.8350\)

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free