Significant Digits. In Chemistry, because numbers (i.e. data) are connected with making measurements, they carry a measure of uncertainty based on the accuracy of the measuring instrument and/or the measuring skill of the chemist.
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In Chemistry, because numbers (i.e. data) are connected with making measurements, they carry a measure of uncertainty based on the accuracy of the measuring instrument and/or the measuring skill of the chemist.
Therefore, we must use the concept of significant digits when doing mathematical processes and when reporting numerical values.
1) All non-zero digits ARE significant. (ex. 1-9)
2) Zeroes between two significant digits ARE significant.
(ex. 203 or 2.0008)
3) Zeroes beyond the decimal point and at the end of a number ARE significant.
(ex. 0.0007100 The two zeroes at the end ARE significant.)
1) Zeroes after a non-zero number when there is NO decimal are
(ex. 1203000 The three zeroes at the end are NOT significant.
They are only place holders because the number can be written
as 1.203 x 106.)
2) Zeroes after the decimal point but before the first non-zero digit are NOT significant.
(ex. 0.0007010 or .0007010 The first three zeroes after the
decimal are NOT significant. They are only place holders because the number can be written as 7.010 x 10-4.)
Think about the United States.
Yes, that’s the United States
The Pacific Ocean is to your LEFT.
The Atlantic Ocean is to your RIGHT.
If a decimal is PRESENT (PACIFIC) count from the LEFT until you reach the first non-zero digit. The rest of the digits will be significant.
If a decimal is ABSENT (ATLANTIC)
count from the RIGHT until you reach the first non-zero digit. The rest of the digits will be significant.
How many significant digits are in each of the following numbers?
The rule is that the right-most significant position in the answer is that which is common to all the numbers being added and/or subtracted.
Report as: 16.996
Report as: 5410
The rule is your answer should be limited to the lowest number of significant digits of the values that are used to determine the final answer.
Report as: 2100
Ex. 4350.25 / 15.5 =
Report as: 281