Nonzero digits

The significant digits of a number are tlie digits from tlie first nonzero digit on tlie left to eitlier (a) the last digit (whetlier it is a nonzero or zero) on tlie right if tliere is a decimal point, or (b) tlie last nonzero digit of the number if tliere is no decimal point. For example ... 

In scientific notation, a number is written as A x 10 7. Here A is a decimal number with one nonzero digit in front of the decimal point and a is a whole number. For example, 333 is written 3.33 X 102 in scientific notation, because 102= 10x 10 = 100 ... 

The number of 10s is the number of places in 665 000 that the decimal point must be moved to the left to get one (nonzero) digit to the left of the decimal point. 

The zeros in 0.0222 m do not indicate anything about the accuracy with which the measurement was made they are not significant. (They are important, however.) In a number reported properly, all nonzero digits are significant. Zeros are significant only when they help to indicate the accuracy of the measurement. The following rules are useful to determine when zeros are significant in a properly reported number ... 

All zeros to the left of the first nonzero digit are not significant. The zeros in 0.01 and 007 are not significant (except perhaps to James Bond). 

All zeros to the right of the decimal point and to the right of the last nonzero digit are significant. The zeros in 1.000 and 3.0 are significant. 

If the first digit to be dropped is greater than 5, or is equal to 5 and there are nonzero digits after it to be dropped, the last digit retained is increased by 1 ... 

For numbers less than 1, only zeros that are at the end of the number and zeros that are between nonzero digits are significant. 0.02Q = 2 s.f. 

Zeroes to the left of the first nonzero digit are not significant. 

Any zero to the left of nonzero digits is not significant unless it is also covered by rule 2. 

Any zero to the right of nonzero digits and also to the right of a decimal point is significant. 

Any zero to the right of nonzero digits and to the left of a decimal point and not covered by rule 2 may or may not be significant, depending on whether the zero is a placeholder or actually part of the measurement Such a number should be expressed in scientific notation to avoid any confusion. 

Any nonzero digit is significant. So 6.42 contains three significant figures. 

Zeros sandwiched between nonzero digits are significant. So 3.07 contains three significant figures. 

When a number has no decimal point, any zeros after the last nonzero digit may or... 

If the first digit you remove is 5 and there are more nonzero digits following, round up. Thus, 5.664525 becomes 5.665 when rounded to four significant figures, because there are nonzero digits (2,5) after the 5. 

If the leftmost digit to be removed is a five that is followed by nonzero digits, then round up. The last remaining digit increases by one. 

Captive zeros are trapped between two nonzero digits, as in 5.006. Captive zeros are always significant. In 5.006 there are four significant figures. 

F, T While 5,007 has three different digits, there are four significant figures present because both zeros between the nonzero digits are significant. 

Zeros between nonzero digits are significant. These zeros are holding places between the other digits. An example is 403. Here all three digits are significant. The 4 tell you the number of hundreds, the 0 tells you the number of tens, and the 3 tells you the number of ones. 

In rounding off numbers, (a) increase the last retained digit by 1 if the leftmost digit to be dropped is more than 5, or is 5 followed by any nonzero digits ... 

Zeros between nonzero digits are significant figures. 

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