Science defines the world that we live in. Anything from making a salad to constructing roller coasters requires the involvement of science. But we as humans have not created a way to completely eradicate the error of a measurement reading. Even with all of the advancements we have made in regard to technology and scientific resources, there is no way of getting an exact measurement. This is extremely apparent when looking at chemistry laboratories. When looking at a 50 mL graduated cylinder for example, each member of the group could gain a different reading of how much liquid is inside of the cylinder. Each reading could be 2 mL off from one another, and because of this, uncertainty must be taken into account when recording measurements. Even though, now, it may seem that there is no possible way of gaining an exact recording, there is an accepted rule across science: significant figures. There are actually five rules that come along with using significant figures, or sig figs for short. The first rule is that all non-zero numbers are significant. For example, in the number 123.456, there are six significant figures. In short, all of the numbers in that example are significant. If the number is 987, there are three significant figures. One of the most confusing parts of a number in regard to how many significant figures it has is the zeros it contains. The second rule is that all zeros that are in between non-zero numbers are significant. A problem that could be on a test is, “Given the number 654078, find the number of significant figures.” Based on the first rule, one would already know that 6, 5, 4, 7, and 8. But is that zero in the middle considered significant? The answer is yes. This is because in order to make a measurement decision on the 4 and the 7, one must make a decision on the hundred 's place. That is why there are six significant figures in this number. For that reason, the zero in between two significant figures is considered significant as well. This also goes for zeros with decimal places. If given a number like 5.0091, there are a total of five significant figures. Now what about when zeros are not in between non-zero numbers? Well, this is where it gets slightly more complicated. In the number 0.0067, there are a total of two significant figures. This shows that it does not matter how many zeros are in front of the non zero numbers, they are not significant. Now if the number given is .300, one would quickly assume based on the previous rule that there is only one significant figure. But this is actually not the case. There are three significant figures based on the rule that trailing zeros to the right of a decimal point are significant. The fifth rule states that measured values with trailing zeros preceding the decimal point are ambiguous. In order to understand their significance it is important to express these values in scientific notation. In another example problem, one may be
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There are known numerical values that are not subject to fractional error, and therefore do not affect the number of significant figures in a calculation. These are called “exact numbers.” Some examples include: 1 foot = 12 inches, 100 years in a century, 2.54 cm in an inch. Therefore, if a number is considered exact, it does not affect the accuracy of a calculation. When taking significant figures into account for a problem, exact numbers will not affect them either.
When performing a measurement on a digital instrument, read and record all of the numbers as displayed, including zeros after the decimal point. But on a scaled instrument, estimate one more figure than you can actually read from the scale. This accounts for the inaccuracies and errors that occur naturally.
Accuracy is “a measure of the deviation of the measured value from the true or accepted value.” Precision is “a measure of the agreement of experimental measurements with each other.” Significant figures relate to precision rather than accuracy. The more precisely a measurement is performed, the more significant digits one can have. If given a measured value, assume that the number of digits given reflect the precision of the measurement. When given a value, the answer cannot be more precise than the data that is
There are known numerical values that are not subject to fractional error, and therefore do not affect the number of significant figures in a calculation. These are called “exact numbers.” Some examples include: 1 foot = 12 inches, 100 years in a century, 2.54 cm in an inch. Therefore, if a number is considered exact, it does not affect the accuracy of a calculation. When taking significant figures into account for a problem, exact numbers will not affect them either.
When performing a measurement on a digital instrument, read and record all of the numbers as displayed, including zeros after the decimal point. But on a scaled instrument, estimate one more figure than you can actually read from the scale. This accounts for the inaccuracies and errors that occur naturally.
Accuracy is “a measure of the deviation of the measured value from the true or accepted value.” Precision is “a measure of the agreement of experimental measurements with each other.” Significant figures relate to precision rather than accuracy. The more precisely a measurement is performed, the more significant digits one can have. If given a measured value, assume that the number of digits given reflect the precision of the measurement. When given a value, the answer cannot be more precise than the data that is