Significant figures multiplication

Most measured quantities are not end results in themselves. Instead, they are used to calculate other quantities, often by multiplication or division. The precision of any such derived result is limited by that of the measurements on which it is based. When measured quantities are multiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. 

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. 

Multiplication and division the answer should not contain a greater number of significant figures than the number in the least precise measurement. 

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

Check your answers. Try to finish a little early so that you can read through your answers. Make sure your answers are complete. It is easy to make simple errors. Check for any missing answers to parts of questions, especially multiple-choice questions. Make sure your answers make scientific sense, and in numerical answers check that you have included units and considered significant figures. 

No problem. Follow the normal order of operations, doing multiplication and division first, followed by addition and subtraction. At each step, follow the simple significant-figure rules, and then move on to the next step. 

Significant figures are discussed in Chapter 3. For multiplication and division, the number with the fewest digits determines how many digits should be in the answer. The number 91 kcal at the beginning of this problem limits the answer to 2 digits. 

In multiplication and division, we are normally limited to the number of digits contained in the number with the fewest significant figures ... 

Multiplication or division. The product or quotient should be rounded off to the same number of significant figures as the least accurate number involved in the calculation. Thus, 0.00296 x 5845 = 17.3, but 0.002960 x 5845 = 17.30. However, this rule should be applied with some discretion. For example, consider the following multiplication ... 

Different rounding off rules are needed for addition (and its reverse, subtraction) and multiplication (and its reverse, division). In both procedures we round off the answers to the correct number of significant figures. 

Multiplication and division When multiplying or dividing, the number of significant figures in the result should be the same as the smallest number of significant figures in the data. 

In nearly all practical chemical calculations, a precision of only two to four significant figures is required. Therefore the student need not perform multiplications and divisions manually. Even if an electronic calculator is not available, an inexpensive 10-in slide rule is accurate to three significant figures, and a table of 4-place logarithms is accurate to four significant figures. 

Let s try a multiplication example. Evaluate the following expression and report the answer to the proper number of significant figures. 

For multiplication or division, the result has the same number of significant figures as the term with the least number of significant figures. 

The manipulation of significant figures in multiplication, division, addition, and subtraction is important. It is particularly important when using electronic calculators which give many more digits than are useful or significant. If you keep in mind the principle that the final answer can be no more accurate than the least accurate measurement, you should not go wrong. A few examples will demonstrate this. 

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