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Then you proceed with the multiplication and/or division and adjust the number of significant figures in the final result according to rule #2 . However, when you adjust the number of significant figures, you should include the number of significant figures fromyour note in the decision process. If that is the smallest number of significant figures of all the factors, you should use it as the number of significant figures forthe final result.
An exercise involving combined operations
Evaluate the following expression and display the final result with the correct number of significant figures.
(169.01 + 3294.6372) * (0.00365 - 29.333)
Please copy the code from Listing 3 into an html file and open it in your browser.
| Listing 3 . An exercise involving combined operations. |
|---|
<!-- File JavaScript03.html --><html><body><script language="JavaScript1.3">//Compute, fix the number of decimal places,
// and display the sum of two numbers.var a1 = 169.01
var a2 = 3294.6372var aSum = (a1 + a2).toFixed(2)
document.write("aSum = " + aSum + "<br/>")
//Compute, fix the number of decimal places,// and display the difference between two
// other numbers.var b1 = 0.00356
var b2 = 29.333var bDiff = (b1 - b2).toFixed(3)
document.write("bDiff = " + bDiff + "<br/>")
//Compute and display the product of the// sum and the difference.
var product = aSum * bDiffdocument.write("product = " + product + "<br/>")
//Round the product to the correct number// of significant figures based on the least
// number of significant figures in the// factors.
var final = product.toPrecision(5)document.write("final = " + final + "<br/>")
//Display a final line as a hedge against// unidentified coding errors.
document.write("The End")</script></body></html> |
When you open your html file in your browser, the text shown in Figure 5 should appear in the browser window.
| Figure 5 . Screen output from Listing #3. |
|---|
aSum = 3463.65
bDiff = -29.329product = -101585.39085000001
final = -1.0159e+5
The End |
The more stringent procedure
The code in Listing 3 implements the more stringent procedure , not because it is necessarily the correct one. Rather, it is simpler toimplement in a script.
Do addition and subtraction first
Listing 3 begins by adding two numbers, adjusting the precision to the least precise of the two numbers, and saving the result in the variable named aSum .
Then Listing 3 subtracts one number from another number, adjusts the precision to the least precise of the two numbers, and saves the result in thevariable named bDiff .
Display to get information on significant figures
Both results are displayed immediately after they are obtained. This is necessary for me to know which one has the least number of significant figures.I need to know that to be able to properly adjust the number of significant figures in the final product.
In other words, it was necessary for me to write and execute the addition/subtraction portion of the script in order to get the informationrequired to write the remainder of the script.
Do the multiplication
Then Listing 3 multiplies the sum and difference values and displays the result in the default format with far too many significant figures as shown bythe third line of text in Figure 5 .
Finally Listing 3 adjusts the number of significant figures in the product based on the number of significant figures in bDiff and displays the final result with five significant figures in normalized scientific(exponential) notation.
I encourage you to run the scripts that I have presented in this lesson to confirm that you get the same results. Copy the code for each script into atext file with an extension of html. Then open that file in your browser. Experiment with the code, making changes, and observing the results of your changes. Makecertain that you can explain why your changes behave as they do.
This section contains a variety of miscellaneous information.
Financial : Although the Connexions site makes it possible for you to download a PDFfile for this module at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should be aware thatsome of the HTML elements in this module may not translate well into PDF.
I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.
In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.comshowing me as the author. I neither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, pleasebe aware that it is a copy of a module that is freely available on cnx.org and that it was made and published without my prior knowledge.
Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.
-end-
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