how to find significant figures in chemistry?
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How to Count Significant Figures
Rule 1 (for non-zeroes):
All non-zero digits are significant. This rule should be simple, if the digit is not zero, count it as significant.
Exercise 1: The number 643 has how many significant figures?
643 All digits are non-zero, all digits are significant.
The number 643 has 3 significant figures.
Exercise 2: The number 8.9 has how many significant figures?
8.9 All digits are non-zero, all digits are significant.
The number 8.9 has 2 significant figures.
This rule is simple enough. What students usually find confusing are the zeroes because they may or may not be significant. Let’s focus on them now.
Rule 2 (for sandwiched zeroes):
Zeroes sandwiched between two significant digits are significant.
Exercise 3: The number 1005 has how many significant figures?
1005 The non-zeroes are significant.
1005 The sandwiched zeroes are significant.
The number 1005 has 4 significant figures.
Exercise 4. The number 9.01 has how many significant figures?
9.01 The non-zeroes are significant.
9.01 The sandwiched zero is significant.
The number 9.01 has 3 significant figures.
This rule should not be confusing either. If it’s a sandwiched zero, there is no reason to doubt that it is significant. What most students find difficult to remember the rules for the leading zeroes (like in 0.0056) or trailing zeroes (like in 1.20 or 750). Let’s move on to those.
Rule 3 (for zeroes at the beginning):
Zeroes at the beginning of a number are never significant.
Exercise 5: The number 0.432 has how many significant figures?
0.432 The non-zeroes are significant.
0.0432 The leading zeroes are not significant.
The number 0.432 has 3 significant figures.
Exercise 6: The number 0.0000006 has how many significant figures?
0.0000006 The non-zero is significant.
0.0000006 The leading zeroes are not significant.
The number 0.0000006 has 1 significant figure.
Exercise 7: The number 0.02108 has how many significant figures?
0.02108 The non-zeroes are significant.
0.02108 The sandwiched zero is significant.
0.02108 The leading zeroes are not significant
Answer: The number 0.02108 has 4 significant figures.
Exercise 8: The number 0.00801008 has how many significant figures?
0.00801008 The non-zeroes are significant.
0.00801008 The sandwiched zeroes are significant.
0.00801008 The leading zeroes are not significant.
Answer: The number 0.00801008 has 6significant figures.
All of the rules we have discussed so far are definitive. Non-zeroes are always significant. Sandwiched zeroes are always significant. Zeroes at the beginning are never significant.
Zeroes at the end, which is covered in the last guideline, may or may not be significant.
Rule 4 (for zeroes at the end):
Zeroes at the end of a number are significant if there is a decimal point.
Exercise 9: The number 3.80 has how many significant figures?
3.80 The non-zeroes are significant.
3.80 The trailing zero is significant (decimal point present).
The number 3.80 has 3 significant figures.
Exercise 10: The number 250 has how many significant figures?
250 The non-zeroes are significant.
250 The trailing zero is not significant (no decimal point).
The number 250 has 2 significant figures.
Exercise 11: The number 4080 has how many significant figures?
4080 The non-zeroes are significant.
4080 The sandwiched zero is significant.
4080 The trailing zero is not significant (no decimal point).
The number 4080 has 3 significant figures.
Exercise 12: The number 2.050 has how many significant figures?
2.050 The non-zeroes are significant.
2.050 The sandwiched zero is significant.
2.050 The trailing zero is significant (decimal point present).
The number 2.050 has 4 significant figures.
Exercise 13: The number 0.01200 has how many significant figures?
0.01200 The non-zeroes are significant.
0.01200 The beginning zeroes are not significant.
0.01200 The ending zeroes are significant (decimal point present).
The number 0.01200 has 4 significant figures
Rule 1 (for non-zeroes):
All non-zero digits are significant. This rule should be simple, if the digit is not zero, count it as significant.
Exercise 1: The number 643 has how many significant figures?
643 All digits are non-zero, all digits are significant.
The number 643 has 3 significant figures.
Exercise 2: The number 8.9 has how many significant figures?
8.9 All digits are non-zero, all digits are significant.
The number 8.9 has 2 significant figures.
This rule is simple enough. What students usually find confusing are the zeroes because they may or may not be significant. Let’s focus on them now.
Rule 2 (for sandwiched zeroes):
Zeroes sandwiched between two significant digits are significant.
Exercise 3: The number 1005 has how many significant figures?
1005 The non-zeroes are significant.
1005 The sandwiched zeroes are significant.
The number 1005 has 4 significant figures.
Exercise 4. The number 9.01 has how many significant figures?
9.01 The non-zeroes are significant.
9.01 The sandwiched zero is significant.
The number 9.01 has 3 significant figures.
This rule should not be confusing either. If it’s a sandwiched zero, there is no reason to doubt that it is significant. What most students find difficult to remember the rules for the leading zeroes (like in 0.0056) or trailing zeroes (like in 1.20 or 750). Let’s move on to those.
Rule 3 (for zeroes at the beginning):
Zeroes at the beginning of a number are never significant.
Exercise 5: The number 0.432 has how many significant figures?
0.432 The non-zeroes are significant.
0.0432 The leading zeroes are not significant.
The number 0.432 has 3 significant figures.
Exercise 6: The number 0.0000006 has how many significant figures?
0.0000006 The non-zero is significant.
0.0000006 The leading zeroes are not significant.
The number 0.0000006 has 1 significant figure.
Exercise 7: The number 0.02108 has how many significant figures?
0.02108 The non-zeroes are significant.
0.02108 The sandwiched zero is significant.
0.02108 The leading zeroes are not significant
Answer: The number 0.02108 has 4 significant figures.
Exercise 8: The number 0.00801008 has how many significant figures?
0.00801008 The non-zeroes are significant.
0.00801008 The sandwiched zeroes are significant.
0.00801008 The leading zeroes are not significant.
Answer: The number 0.00801008 has 6significant figures.
All of the rules we have discussed so far are definitive. Non-zeroes are always significant. Sandwiched zeroes are always significant. Zeroes at the beginning are never significant.
Zeroes at the end, which is covered in the last guideline, may or may not be significant.
Rule 4 (for zeroes at the end):
Zeroes at the end of a number are significant if there is a decimal point.
Exercise 9: The number 3.80 has how many significant figures?
3.80 The non-zeroes are significant.
3.80 The trailing zero is significant (decimal point present).
The number 3.80 has 3 significant figures.
Exercise 10: The number 250 has how many significant figures?
250 The non-zeroes are significant.
250 The trailing zero is not significant (no decimal point).
The number 250 has 2 significant figures.
Exercise 11: The number 4080 has how many significant figures?
4080 The non-zeroes are significant.
4080 The sandwiched zero is significant.
4080 The trailing zero is not significant (no decimal point).
The number 4080 has 3 significant figures.
Exercise 12: The number 2.050 has how many significant figures?
2.050 The non-zeroes are significant.
2.050 The sandwiched zero is significant.
2.050 The trailing zero is significant (decimal point present).
The number 2.050 has 4 significant figures.
Exercise 13: The number 0.01200 has how many significant figures?
0.01200 The non-zeroes are significant.
0.01200 The beginning zeroes are not significant.
0.01200 The ending zeroes are significant (decimal point present).
The number 0.01200 has 4 significant figures
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