Rounding off, significant figures

There are three significant figures in the denominator and two in the numerator. The answer should have two significant figures round off the average speed to be... 

In this case the answer must have two significant figures. Rounding off, 26.832 becomes 27—no decimals at all ... 

Returning to the original problem, when you divide 5.31 by 8.568, you get 0.61974789915966386554621848739496 on your calculator. However, because you used the mathematical operation division, your answer must have just three significant figures. Rounding off 0.6197 becomes 0.620. 

The use of the arithmetic functions is fairly obvious, but you should use powers of ten except in trivial cases. To enter 96 500 for instance, consider it 9.65 x 104 and enter 9.65 EE4. (On most calculators F.F4 means x 104). The calculator keeps track of the decimal point and provides an answer between one and ten times the appropriate power of ten. It will usually display many more figures than are significant, and you will have to round off the final result. If at least one factor was entered as a power of ten, the power-of-ten style will prevail in the display, and you need not fear running off scale, nor will any significant figures disappear off scale. 

Round off the following quantities to the indicated number of significant figures. 

Note When doing these calculations, do not round off your answers until the end. The answers here are rounded after each step to illustrate the concept of significant figures. 

Note When doing an extensive calculation, keep all the numbers in your calculator. The answers here are rounded off to the appropriate number of significant figures after each step only to illustrate the concept of... 

Note To find e-95 66, take the inverse In of-95.66 on your calculator, inv In of-95.66 = 2.85 x 10 42. Keep one more significant figure and round off to three significant figures at the end, particularly when working with logarithms. 

For multiplication and division problems, round off the answer to the same number of significant figures in the measurement with the fewest significant figures. 

In this book, we will tend to be very strict in rounding off the final answer to the correct number of significant figures. Your instructor will tell you just how strict she or he wishes you to be. 

Dimensional analysis, sometimes called the factor label (unit conversion) method, is a method for setting up mathematical problems. Mathematical operations are conducted with the units associated with the numbers, and these units are cancelled until only the unit of the desired answer is left. This results in a setup for the problem. Then the mathematical operations can efficiently be conducted and the final answer calculated and rounded off to the correct number of significant figures. For example, to determine the number of centimeters in 2.3 miles ... 

The answer will be rounded off to 2 significant figures based upon the 2.3 miles, since all the other numbers are exact ... 

Know how to determine the number of significant figures in a number, the rules for how many significant figures are to be shown in the final answer, and the round-off rules. 

Make sure your units cancel, leaving you with the units desired in your final answer. Round off your final numerical answers to the correct number of significant figures. Remember, most molecular compounds—compounds containing only nonmetals—do not ionize in solution. Acids are the most common exceptions. 

Be sure to round your answer off to the correct number of significant figures. 

In rounding off quantities to the nearest correct number of significant figures, add one to the last figure retained provided the following figure is either 5 or over. Hence, the average of 0.6526, 0.6521, and 0.6524 is 0.6525 (0.65237). 

Note Values calculated from the basic limits shall be rounded off to two (2) significant figures. 

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