Multiplication, significant digits

The division of two numbers of s significant digits each can yield results that require nearly any number of digits (only a few if one number is a simple multiple of the other, many if one or both numbers are irrational) usually the number of bytes the computer displays or uses for calculation... 

There are logarithms for all numbers, not just whole multiples of 10. What is the pH of a solution if [H3O+] = 0.004 76 mol/L Enter 0.00476. Press the [LOG] key and then the [+] key. The answer is 2.322. This result has three significant digits—the same number of significant digits as the concentration. 

You only need to worry about these on the free-response portion of the test. On the multiple-choice portion, they do not try to trick you by having two answers that differ only by the number of significant digits. 

For multiplication and division, the number of significant digits in the factor with the fewest significant digits limits the number of significant digits in the answer. For example, let s multiply 4.1 cm by 21.07 cm ... 

If a problem has both addition or subtraction and multiplication or division, the part that is done first must have its significant digits noted before the next operation is performed, because the rules are different for determining which digits are retained. 

The rules for significant digits in addition and subtraction are different from those in multiplication and division. 

The same information is obtained if consecutive decisions are reached between choices with different values of m, either as alternatives or as multiple choice questions (Fig. 3.3-11). This allows to calculate how much information a certain analytical procedure may supply or how much information is needed to solve a particular analytical problem. An analytical measure, such as a melting point or a refractive index with 3 significant digits, may supply Id 999 = 9.96 = 10 bit. In order to identify one compound in a spectral collection of N different samples, Id N bit are required to identify one out of 100 000 spectra, at least 16.61 bit are needed. 

Rule for multiplication and division When multiplying or dividing, our answer must show the same number of significant digits as the measurement in the problem with the least number of significant digits. 

Now, our answer no longer claims to be more accurate than the measurements that it was based on. Figure 2-4b illustrates the rule for rounding after multiplication. Each of the measurements showed only three significant digits, so the calculated volume could only show three significant digits. 

There are several useful rules of thumb that allow you to determine the proper number of significant digits in the result of a calculation. For multiplication of... 

Multiplication and Division Rules When multiplying or dividing numbers, the result of the calculation should be recorded with the least number of significant digits given by any of the numbers used in the calculation. For example,... 

What limits the number of significant digits in a calculation involving only multiplication and division ... 

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