Significant figures counting number

One further point about significant figures Certain numbers, such as those obtained when counting objects, are exact and have an effectively infinite number of significant figures. For example, a week has exactly 7 days, not 6.9 or 7.0 or 7.1, and a foot has exactly 12 in., not 11.9 or 12.0 or 12.1. In addition, the power of 10 used in scientific notation is an exact number. That is, the number 103 is exact, but the number 1 X 103 has one significant figure. 

An exact number is a small number that can be reproducibly determined by counting or one that is defined to a particular value. Exact numbers have infinite precision and significant figures. Exact numbers are not obtained using measuring devices. 

Exact numbers. Often calculations involve numbers that were not obtained using measuring devices but were determined by counting 10 experiments, 3 apples, 8 molecules. Such numbers are called exact numbers. They can be assumed to have an unlimited number of significant figures. Exact numbers can also arise from definitions. For example, 1 inch is defined as exactly 2.54 centimeters. Thus in the statement 1 in. = 2.54 cm, neither 2.54 nor... 

Exact numbers. Some numbers are exact and have an infinite number of significant figures. Exact numbers occur in simple counting operations when you count 25 dollars, you have exactly 25 dollars. Defined numbers, such as 12 inches in 1 foot, 60 minutes in 1 hour, and 100 centimeters in 1 meter, are also considered to be exact numbers. Exact numbers have no uncertainty. 

Count the number of significant figures in the numerator and in the denominator the smaller of these two numbers is the number of significant figures in the quotient... 

For addition or subtraction, the limiting term is the one with the smallest number of decimal places, so count the decimal places. For multiplication and division, the limiting term is the number that has the least number of significant figures, so count the significant figures. 

Numbers from counting (for example, 1 kangaroo, 2 kangaroos, 3 kangaroos) or from defined quantities (say, 60 seconds per 1 minute) are understood to have an unlimited number of significant figures. In other words, these values are completely certain. 

The calibration curve of Figure 1 is a plot of (log A )6 vs. count number, Ng. The curve was corrected according to the procedure described above the new calibration curve is a plot of (log A )3 = log fi (log A )6 against N6. A use of this calibration curve is discussed later with the samples of the present study. Noteworthy is a significantly different performance of two GPC runs at the molecular lengths from 20,000 to 100,000. With the polystyrene standards alone such detailed difference could not be detected. To illustrate this point the molecular lengths of the polystyrene standards are indicated on the graph. 

Only measured quantities >f I may contain a measurement error, which limits the number of significant figures. In addition to counted objects (7 days =... 

It is important that you know how to count the number of significant figures in any measurement, as that shows you how to report the results of using a particular measuring device. The rules for determining the number of significant figures in a measurement are... 

Note, however, that this rule applies only to measured quantities or numbers calculated from measured quantities. If a quantity is known precisely—like a pure integer (2) or a counted rather than measured quantity (16 oranges)—its value implicitly contains an infinite number of significant figures (5 cows really means 5.0000... cows). 

You should ignore both count values and conversion factors when determining the number of significant figures in your calculated results. 

Counting numbers and defined constants have an infinite number of significant figures. 

The number to the left of the decimal point in a logarithm is called the characteristic, and the number to the right of the decimal point is called the mantissa. The characteristic only locates the decimal point of the number, so it is usually not included when counting significant figures. The mantissa has as many significant figures as the number whose log was found. 

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