Significant digits subtraction

Rule II. The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing —10 after the result. 

Case Amount c Subtracted Digits Typed in Number of Significant Digits... 

We must report the results of our calculations to the proper number of significant digits. We almost always use our measurements to calculate other quantities and the results of the calculations must indicate to the reader the limit of accuracy with which the actual measurements were made. The rules for significant digits as the result of additions or subtractions with measured quantities are as follows ... 

There arc only two significant digits since the subtraction yields an answer with two significant digits. That answer limits the final volume to two significant digits. 

Add, subtract, multiply, or divide. Round off your answer, and express it in scientific notation to the correct number of significant digits. 

Review the rules for significant digits when adding, subtracting, multiplying, and dividing numbers. 

When we add or subtract numbers in exponential notation, the exponents must be the same. (This rule is related to the rule that requires numbers being added or subtracted to have their decimal points aligned.) The answer is then the sum or difference of the coefficients times the same exponential part as in each number being added or subtracted. (The calculator does this operation automatically, but we must know what is happening in order to report the proper number of significant digits [see Section 2.4].)... 

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. 

Because two different rules are used for the subtraction and division, note that the numerator of part (b) has only two significant digits, as shown in part (a). Therefore the quotient has only two significant digits. 

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

Addition and subtraction do not depend on the number of significant digits. Consider the following example ... 

When we do calculations in science, we must round properly and according to the rules of significant digits. We will follow one rule when adding and subtracting and another when multiplying and dividing. These two important rules are shown here. 

If you do this problem in one step, the subtraction still yields a value with three significant digits, so the density has only three significant digits. 

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