Significant Figures
Significant Figures
Some numbers are so big or so small, that to write them in standard form with all the zeros would be time consuming and tedious. For example, the number 602,000,000,000,000,000,000,000 is a number quite often used in chemistry. It would be helpful if there were a shorter way to write this number. To speed up the process, scientists and mathematicians have developed a way to omit any zeros that are place holders.
When writing numbers, some zeros are not significant, and are used simply as place holders, to make the number smaller or bigger. So which zeros are significant (important) and which are not. The following six rules will help to determine the significant zeros.
Rules for Significance:
1) All non-zero numbers are significant.
Examples:
Some numbers are so big or so small, that to write them in standard form with all the zeros would be time consuming and tedious. For example, the number 602,000,000,000,000,000,000,000 is a number quite often used in chemistry. It would be helpful if there were a shorter way to write this number. To speed up the process, scientists and mathematicians have developed a way to omit any zeros that are place holders.
When writing numbers, some zeros are not significant, and are used simply as place holders, to make the number smaller or bigger. So which zeros are significant (important) and which are not. The following six rules will help to determine the significant zeros.
Rules for Significance:
1) All non-zero numbers are significant.
Examples:
Number
12 24.56 |
Significant Figures
2 4 |
2) Any zero between non-zero numbers is significant (trapped zero rule).
Examples:
Examples:
Number
107 40.002 |
Significant Figures
3 5 |
3) Any zeros preceding a non-zero number are not significant (decimal rule).
Examples:
Examples:
Number
0.006 0.00903 |
Significant Figures
1 3 |
4) Any zero after a decimal point and after a non-zero number is significant.
Examples:
Examples:
Number
9.00 150 0.00600 0.080 54300 54300. |
Significant Figures
3 2 3 2 3 5 |
Notice that in the rule above, it does not matter whether the decimal or the non-zero number comes first. If both conditions are satisfied, trailing zeros are significant. In addition, notice that if a decimal is not present, trailing zeros are not significant. Look at the last two numbers. Although they look like they are the same number, they are not. By putting the decimal point 54300., the person measuring insures that the number is exact, meaning the person measuring took the time to check that it was exactly 54300 units. However, in 54300, where there is no decimal point, the number is an approximation. The person measuring is saying "Oh, it's around 54300 units." Which means it could actually be 54289, but time was not taken to properly measure the value.