#electrical engineering notes

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Measurements 22.1 and 22.10 imply different levels of accuracy. The first suggests that the measurement was made by an instrument only accurate to the tenths place; the latter was obtained with an instrument capable of reading to the hundredths place. The use of zeros in a number, therefore, must be treated with care and the implications must be understood.

There are two types of numbers: exact and approximate. Exact numbers are precise to the exact number of digits presented, just as we know there are 12 apples in a dozen, not 12.1.

A battery of 100V can be written as 100.0V, 100.00V and so on, since it is 100V at any level of precision. Additional zeros were not included for clarity purposes.

In the lab environment, where measurements are continually taken, and the level of accuracy can vary from one instrument to another, it is important to understand how to work with the results.

Any reading obtained in a lab should be considered approximate. The analog scales with their pointers may be difficult to read, and even though the digital meter provides only specific digits on it’s display, it is limited to the number of digits it can provide.

Precision of a reading can be determined by the number of significant figured (digits) it can present. Significant digits are those integers (0-9) that can be assumed to be accurate for the measurements being made.

All non-zero numbers are considered significant, with zero only being significant some of the time.

Example: The zeros in 1005 are considered significant because they define the size of the number and are surrounded by non-zero numbers. In the number 0.4020 the zero to the left of the decimal isn’t significant but the other two zeros are because they define the magnitude of the number and the fourth place accuracy of the reading.

When adding approximate numbers, it is important to be sure that the accuracy of the reading is consistent throughout.

To add a quantity accurate only to the tenths place to a number accurate to the thousandths place will result in being accurate only the tenths place.

In addition or subtraction of approximate numbers, the entry with the lowest level of accuracy defines the solution.

For the multiplication and division of approximate numbers, the result has the same number of significant figures as the number with the least number of significant figures.

For approximate and exact numbers there is a need to round off the result; you must decide the appropriate level of accuracy and alter the result accordingly.

Note the digit following the last to appear in the rounded-off form, then add 1 to the last digit if greater than 5, and leave it alone if less. (Example: 3.186 = 3.19 = 3.2 depending on level of accuracy desired.)

Example 1.1 Preform the indicated operations with the following approximate numbers and round off the the appropriate level of accuracy: a) 532.6 + 4.02 + .036 = 536.656 = 536.7 b) .04 + .003 + .0064 = .0494 = .05

Example 1.2 Round off the following number to the hundredths place: a) 32.419 = 32.42 b) .05328 = .05

Most important rule: Use the correct units of measurement when substituting numbers into equations.

v=d/t v= velocity d= distance t= time

Assume, for the moment, that the following date are obtained for a moving object: d= 4000ft t= 1min And v is desired in miles per hour v=d/t = 4000ft/1min =/= 4000 mph As indicated above, the solution is totally incorrect. If desired in miles per hour, the unit of measurement for distance must be in miles, and that for time, in hours.

The numerical value substituted into an equation must have the unit of measurement specified by the equation

The next question is normally, “How do I convert the distance and time to the proper unit of measurement?” 1 mile= 5280 ft 4000 ft= .76 miles (3/4 miles, roughly) 1 minute= 1/60 hour or .017 hour v=d/t = .76mi/.017h = 44.71 mph

If a unit of measurement is applicable to a result or piece of data, then it must be applicable to the numerical value.

In review, before substituting numerical values into an equation, be sure of the following:

Each quantity has the proper unit of measurement as defined by the equation

The proper magnitude of each quantity as determined by the defining equation is substituted

Each quantity is in the same system of units (or as defined by the equation)

The magnitude of the result is of a reasonable nature when compared to the level of substituted quantities

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