A figure within a number is significant if it is there to indicate precision. If, instead, it is there just to indicate the size of the number, it is not significant. Thus, a zero to the right of the decimal at the end must always be significant, because that zero does nothing to indicate the size of the number. The numbers 10 and 10.0 are the same size, so the last zero in 10.0 must have been put there to indicate that the measuring device actually went out to the tenths place. On the other hand, a number like 0.9 has only one significant figure because the zero that starts the number is simply there to indicate the size of the number. If a number is a decimal, we always write a “0.” in front of it to indicate that the number is less than one. In proper math, the number “.9” is not correct. A decimal must always be preceded by a number. Thus, “0.9” is the only way to write it, and the first zero simply indicates size. That’s why a number like 2,500 has only 2 significant figures.

A few more examples:

1. How many significant figures are in 12,300.0?
As soon as a zero is to the right of the decimal point, it becomes significant. Thus, the last zero in this number is significant. The other two zeros are therefore between significant figures, making them significant. As a result, there are 6 significant figures in that number.

2. How many significant figures are in 34,000,000?
There are only 2 significant figures.

3. How many significant figures are in 0.3400?

0.3400 has 4 significant figures, because zeros to the right of the decimal are always significant. Since they are not necessary to indicate the size of the number, they must be there for precision However, the first zero is not between significant figures and is not to the right of the decimal, so it is not significant.

4. How many significant figures are in 3.0400?

3.0400 has 5 significant figures, because zeros to the right of the decimal are always significant. Since they are not necessary to indicate the size of the number, they must be there for precision.

5. How many significant figures are in 30.400?

30.400 has 5 significant figures, because the zeros to the right of the decimal are significant. Since they are not necessary to indicate the size of the number, they must be there for precision. Since they are significant, the zero after the 3 is significant because it is between two significant figures.