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Significant Figures Part III

How Many Significant Figures or Decimal Places Are Correct?

The number of sig figs or decimal places that should be presented is often a decision to be made by the end user. In many instances, showing one or two sig figs is adequate; for example, in a simple comparison determining whether a result is less than or greater than a benchmark value. If the results will undergo substantial statistical evaluation or other arithmetic calculations, then more sig figs would be recommended. As a general rule, it is better to keep at least one additional sig fig through all calculations and round afterwards rather than rounding first.

One famous example for keeping extra sig figs and decimal places for calculations is the original “butterfly effect.” In 1961, a mathematician/meteorologist named Edward Lorenz was using a computer to simulate weather effects. He entered a value that had been rounded from six decimal places to only three, which represented about a 0.025% difference in the value. After he ran the program, he realized that the result represented a completely different weather pattern than if he had used all six decimal places. During later presentations, this effect took on its more popular meaning, which is still in use today.

At the other end of the spectrum, it is possible to provide far too many sig figs. Since computers and calculators became common, they have been used more and more frequently for data collection and analysis. If the data are being calculated using mathematical formulae (e.g., linear or quadratic regression), the computer could easily provide 32 or more sig figs in its evaluation. If this were presented as a single whole number, for example, it would be the equivalent of counting the number of grains of sand in a pile the size of Earth.

Some things to keep in mind when determining how many sig figs should be presented is how the data will be collected, limits in the ability to precisely measure a value, and if the data collected represents an exact measurement or is instead measuring a sample. For example, counting the number of children enrolled at each elementary, middle, and high school in a state is relatively straightforward. An exact count can be provided fairly easily, so a number that has six or seven sig figs would be appropriate.

On the other hand, counting the total number of people living in a state would be more challenging, since it would include births, deaths, and people moving into and out of the state. In addition, there may be a certain number of people who are temporary residents. Since all these changes can happen hundreds or even thousands of times per day, it would be more appropriate to provide only three or four sig figs for a statewide population count.

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From Our Accountant, To Your Accountant… Part III

Part III – “But, I have no clue what this report is telling me.”

Based upon my experience, I can attest that what gets accounting excited about a report is not necessarily what gets a project manager excited. “What’s the solution?” you may ask. We give our project managers the power to customize their own project information. Okay, so I am aware that accountants are pretty scared about giving much access to non-accounting people; however, if done properly, giving that access can save time, can make accounting’s job a little bit easier, and can help project managers feel empowered! It is a win–win! For example, almost all accounting and project management software has the capability to customize security on reports.   Providing views of various project-specific reports to project managers will allow them access to the administrative aspects of their projects and help them succeed in the technical aspects.

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Significant Figures, Decimal Places, and Rounding Part II

Part II Rounding Rules

When the data collected have more sig figs than needed, the results should be rounded. Rounding removes superfluous digits from a number and can make it easier to use in subsequent calculations and evaluations.

First, determine how many digits or decimal places the final result should be reported to, then find the next digit to the right. If its value is 0, 1, 2, 3, or 4, drop that digit and all subsequent digits. If the value is 6, 7, 8, or 9, increase the preceding digit (the last one that will be reported) by 1, and then drop all subsequent digits and decimal places from the number. If the last digit or decimal place to be reported is a 9, it will increase to a 0 and the next digit or decimal place to the left will be increased by 1. Follow the same rule for any additional 9s.

If the value is 5, then there are two possible rules to follow. Under standard rounding rules, the preceding digit or decimal place should be increased by one, with the same rules applying as if it were greater than 5. This is called the round-up rule. The alternate rule is that if the value is a 5, the last digit or decimal place to be reported should be left as-is if it is an even number and increased by 1 if it is an odd number. This is called the round-to-even rule.

Examples:

1.34 rounded to one decimal place would round to 1.3.

1.995 rounded to two decimal places would round to 2.00.

134 rounded to the 10’s place would round to 130.

1523 rounded to the 100’s place would round to 1500.

A note about spreadsheets: Spreadsheet programs (e.g., Excel) allow for the easy presentation and numerical evaluation of large quantities of data, which makes them very useful in a wide range of applications, including report preparation. If using Excel to perform rounding functions, there are two limitations the user should be aware of. First, Excel always rounds up and does not have a simple built-in round-to-even function. Second, Excel does not have a rounding function for integers (i.e., numbers cannot be rounded to the nearest 10s or 100s place) and puts trailing 0s in place of sig figs.

Examples:

1.25 in Excel will round to 1.3, as opposed to 1.2 by using the round-to-even rule.

1392 cannot be rounded any further in Excel, whereas it can be presented as 1390 by rounding to the nearest 10s place and as 1400 by rounding to the nearest 100s place.

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Grammar: Your vs. You’re

Do you know the difference between you’re and your? Just the fact that you’re reading this article could be your salvation and ensure you will never confuse the two words again.

Your shows possession, meaning it is used to present that something belongs to you. Because this four-letter word is an adjective, it is usually followed by a noun, but not always. 

          Your name is Tommy.

          Red is your favorite color. 

You're, on the other hand, is a contraction meaning "you are." It is often followed by a verb ending in “ing.” 

          You're moving too slowly and you’re going to be late for school.

          When you’re older, you’ll understand why your parents wanted you to be on time. 

To determine which version of the word is correct, try replacing it with “you are.” If the sentence still makes sense, then you’re is the form you want. If it doesn’t read properly, then you need to show possession and should use your.

 

 

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Keyboard Shortcuts

With all the down-sizing and funding cutbacks these days, many people have been forced to do their own typing and have no one to turn to for help with formatting issues.  If you’re in that position and are struggling with MS Word, you might appreciate knowing some of these basic keyboard shortcuts.  (You can get the full list of keyboard shortcuts by going to the Word help menu (F1) and searching for “keyboard shortcuts.”)

F1

 

Help

F4

 

Repeats your very last keystroke or command (works in other MS Office programs too).  You can use it multiple times in a row if you don’t press any other keys!  You must have your function keys locked on for this to work.

F7

 

Spell check

CTRL + C

 

Copy selection

CTL + X

 

Cut selection

CTRL + V

 

Paste selection

CTRL + E

 

Align center

CTRL + L

 

 Align left

CTRL + R

 

Aligh right

CTRL + F

 

 Find

CTRL + G

 

Go to (page number)

CTRL + H

 

Search and replace

CTRL + N

 

Creates a new blank page

CTRL + P

 

Brings up the "Print" menu

CTRL + S

 

Save (file update without exiting)

CTRL + Y

 

Redo

CTRL + Z

 

Undo

ALT + O, E

 

Brings up the "Change Case" menu

ALT + A, R

 

Brings up the "Table Properties" menu

ALT + O, P

 

Brings up the "Paragraph" menu

ALT + I, B

 

Brings up the insert "Break" menu (page break, section break, etc.)

Did you know?

 

When viewing a drop-down menu, you can execute a command without using the mouse.  Just hold the ALT key while pressing the key coinciding with the underlined letter in the command you want to use. 

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Blu Dove Support
Thanks for the tips!
Wednesday, 06 March 2013 23:05
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