Significant digit zeros

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 ... 

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 between significant digits are significant. The 0 in 1.01 is significant. 

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. 

A recorded volume of 2.8 L represents two significant figures. If this same volume were written 0.028 m3, it would still contain only two significant figures. Zeroes appearing as the first digits of a number are not significant, since they merely locate the decimal point. 

This value must be rounded off to three total significant digits because this is the lower precision of the numerator and the denominator. The first insignificant digit is a 5. In this case there are additional non-zero digits after the 5, so rounding occurs upwards to 2.79 g/ml (answer B). 

All zeros that are located between two non-zero numbers are significant. 408 has three significant digits. 25 074 has five significant digits. 

Zeros that are located to the right of a value may or may not be significant. 22 700 may have three significant digits, or it may have five significant digits. See the box below to find out why. 

What if you were able to measure the volume of water in the Great Lakes You could verify the value of 22 700 km3. Then all five digits (including the zeros) would be significant. Here again, scientific notation lets you show clearly the five significant digits 2.2700 x 104 km3. 

Do not drop significant digits, even zeros, during... 

It implies that they are all significant digits. Yet the nonfinal zeros to the right of the decimal point in the mass of an H20 molecule are used as placeholders. They are not significant digits. There are only three significant digits in... 

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. 

Any zeros between significant digits (for example, in 903) are significant. 

The 6 is certainly significant. The zeros to the right of all other digits in an integer are uncertain they may reflect the precision or just the magnitude of the number. Without further information, it is impossible to tell (rule 4). 

The answer is 3.00 g/cm. It must have three significant digits because both the dividend (4.92) and the divisor (1.64) have three significant digits. In this case, add two zeros to the answer given by the electronic calculator (3) to get the correct number of significant digits. 

How many significant digits are in the value 0°F (The zero is not left of all other digits, right of all other digits, or between all other digits.) How many are there in its Celsius equivalent ... 

We must apply the rules wheu reportiug the answer. For example, the reciprocal of 9.00 is really 0.111, but the calculator displays something like 0.111111111. Similarly, dividing 5.34 by 1.78 should yield 3.00, but the calculator displays 3. We must report only the three significant digits in the first example and must add the two significant zeros in the second example. 

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