';
truevalue5[0]='25.14';
truevalue5a[0]='25.15';
truevalue5b[0]='25.16';
sigfig5[0]='4';
question5[1]='';
truevalue5[1]='25.14';
truevalue5a[1]='25.15';
truevalue5b[1]='25.16';
sigfig5[1]='4';
question5[2]='
';
truevalue5[2]='0.675';
truevalue5a[2]='0.676';
truevalue5b[2]='0.677';
sigfig5[2]='3';
question5[3]='
';
truevalue5[3]='0.00934';
truevalue5a[3]='0.00933';
truevalue5b[3]='0.00935';
sigfig5[3]='3';
question5[4]='
';
truevalue5[4]='501';
truevalue5a[4]='500';
truevalue5b[4]='502';
sigfig5[4]='3';
question5[5]='
';
truevalue5[5]='5593';
truevalue5a[5]='5592';
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window.document.write('A. Uncertainty in Measurements:
Measurements are an important tool for the chemist to study the nature of matter. Frequently we need to determine the mass of an object, or its volume, or its length. When we record a measurement, we write down a numerical value, and then a unit. Normally the metric system is used when we make measurements, and the following units are usually used.
| Mass: | grams |
| Volume: | milliliters |
| Length: | centimeters |
Let´s try making a measurement of the length of an object in centimeters. The value we record will depend on the accuracy of the ruler that we employ for the measurement. Let´s use two different rulers for our measurement.
What is the reading of the length of the rectangle using Ruler A? The length of the rectangle is clearly between 4 and 5 centimeters. If you envision the distance from 4 to 5 being divided into 10 parts, you can estimate another digit. Does it look like the rectangle goes about 8/10ths of the way to the 5 division? Since we try to avoid using fractions in chemistry (they are too difficult to work with), we should write this measurement as 4.8 centimeters.
Now try using Ruler B to make the same measurement. Since this ruler has smaller divisions, we should be able to get a more accurate reading. The rectangle appears to go slightly past the 4.8 division. Again we can estimate a digit if we imagine the distance between 4.8 and 4.9 being divided into 10 parts (it´s not easy sometimes, but do your best). Does it look like 4.84 centimeters? If it does not look exactly like 4.84 centimeters, that´s ok. Your value may be just a bit different. Here´s why this variation in measurements is quite common.
In both of these measurements, we had to estimate the last digit. This estimation results in an uncertainty in the measurement. What is the uncertainty in the two measurements? Frequently the uncertainty is expressed as ± one unit of the estimated division.
The uncertainty of the measurement using Ruler A would be 0.1 centimeter. Thus, the measurement would sometimes be expressed as 4.8 ± 0.1 centimeters. The uncertainty of the measurement using Ruler B would be 0.01 centimeter. Thus, the measurement would sometimes be expressed as 4.84 ± 0.01 centimeters.
The measurement using Ruler A has two significant figures, while that obtained by using Ruler B has three significant figures. What are significant figures, how they are determined, and why they are important in chemistry will be discussed in the next and subsequent sections.
'); window.document.write('B. Reading a Scale and Determining the Significant Figures:
When you read a scale in chemistry, the major divisions are frequently subdivided into ten parts. Thus, you can determine a digit from the major divisions and from the subdivisions. One more digit can be determined if you imagine the distance between the subdivisions further divided into ten parts. This will be an estimated division. All of these digits that you write down for the measurement are termed significant digits (or more commonly, significant figures).
Try to read the following scale as accurately as possible, enter its value, and then the number of significant figures.
 | |
| Value of Measurement | Number of Significant Figures |
That was easy. Let´s try this one.
 | |
| Value of Measurement | Number of Significant Figures |
Notice that the zero before the decimal point is not a significant figure. Now try this one.
 | |
| Value of Measurement | Number of Significant Figures |
Let´s try a scale with large numbers.
 | |
| Value of Measurement | Number of Significant Figures |
Let´s try one more.
| ' + question5[index5] + ' | |
| Value of Measurement | Number of Significant Figures |
C. Determination of Significant Figures in a Number:
What if you are not personally making a measurement, but rather reading the results of someone else´s work? How do you know the number of significant figures in their values? Nonzero digits are always significant. The problem lies with zeros. Sometimes they are significant, and sometimes they are not significant. Here´s how you can easily tell.
| Significant Figures | |
 | 7 |
 | 5 |
 | 3 |
 | 5 |
 | 7 |
| Significant Figures | |
 | 5 |
 | 1 |
 | 6 |
 | 2 |
Try another example
| ' + question6[index6] + ' |
D. Why Are Significant Figures Important?
The use of significant figures allows us to round off the answer we get from a calculation in a uniform and reasonable fashion. In the next section, we will look at the use of significant figures in the process of rounding off the answer of a calculation.