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Significant Digits Notes
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Purpose: Significant digits (or significant figures) is a communication tool to express where you rounded any particular number.
Question (do not need to copy):
If you won one million dollars, where would you want that rounded?
The person paying would want to round it at the millions place, then they only have to pay you $500,000. Significant digits communicates where the rounding occurred! (end of do not need to copy)
In science we round for our measurements. We always estimate a digit between the lines on a measurement tool, and with significant digits we can communicate how accurate a measurement tool we used.
The Four Rules for Significant Digits:
The Four Rules for Significant Digits:1) All nonzero digits are significant
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs
.400000 ← these zeros are sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs
.400000 ← these zeros are sig digs
Nonexamples: 400000 ← these zeros are NOT sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs
.400000 ← these zeros are sig digs
Nonexamples: 400000 ← these zeros are NOT sig digs
.000004 ← these zeros are NOT sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significantExamples: 4.00000 ← these zeros are sig digs
.400000 ← these zeros are sig digs
Nonexamples: 400000 ← these zeros are NOT sig digs
.000004 ← these zeros are NOT sig digs
Mixed: .00400 ← only 2 of these zeros are sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significantExamples: 4000005 ← these zeros are sig
digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs
400.0005 ← these zeros are sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs
400.0005 ← these zeros are sig digs
.4000005 ← these zeros are sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs
400.0005 ← these zeros are sig digs
.4000005 ← these zeros are sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs
400.0005 ← these zeros are sig digs
.4000005 ← these zeros are sig digs
Nonexample: 0.0000045 ← these zeros are NOT sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significantExamples: 4000005 ← these zeros are sig digs
400.0005 ← these zeros are sig digs
.4000005 ← these zeros are sig digs
Nonexample: 0.0000045 ← these zeros are NOT sig digs
Mixed: 0.004005 ← only 2 of these zeros are sig digs
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significant4) Any other zeros are NOT signficiant digits, but
still MUST be shown to keep the decimal place correct
The Four Rules for Significant Digits:1) All nonzero digits are significant2) Zeros that are after a decimal and after a
nonzero digit (or vice versa) are significant3) Zero between significant digits (zeros or
nonzeros) are also significant4) Any other zeros are NOT signficiant digits, but
still MUST be shown to keep the decimal place correct
Example : 1,000,000 ← only the “1” is a sig dig, so the one is where the rounding occurred (could have been 4,000,000 rounded down or 500,000 rounded up - we don’t know, but we know where it was rounded)
Self-Check (do not need to copy):
How would you write one million to be as sure as possible of getting all your money?
Significant Digits Practice
Copy down these numbers, then circle the sig digs in each of them:84.100.03910077.66700.06078008.528000.000900.006
7080300500.020640004009200001600.005000.000000100200
Copy down these numbers, then round them to the stated amount of sig digs:84.10 to 3 S.D.84.10 to 1 S.D.0.039100 to 2 S.D.0.9876 to 3 S.D.
0.9876 to 1 S.D.7080 to 3 S.D.30050 to 3 S.D.500 to 2 S.D.
How many Significant Digits is in:
84.10
How many Significant Digits is in:
84.10
4
How many Significant Digits is in:
0.039100
How many Significant Digits is in:
0.039100
5
How many Significant Digits is in:
77.6670
How many Significant Digits is in:
77.6670
6
How many Significant Digits is in:
0.060
How many Significant Digits is in:
0.060
2
How many Significant Digits is in:
78000
How many Significant Digits is in:
78000
2
How many Significant Digits is in:
8.52800
How many Significant Digits is in:
8.52800
6
How many Significant Digits is in:
0.00090
How many Significant Digits is in:
0.00090
2
How many Significant Digits is in:
0.006
How many Significant Digits is in:
0.006
1
How many Significant Digits is in:
7080
How many Significant Digits is in:
7080
3
How many Significant Digits is in:
30050
How many Significant Digits is in:
30050
4
How many Significant Digits is in:
0.0206
How many Significant Digits is in:
0.0206
3
How many Significant Digits is in:
4000400
How many Significant Digits is in:
4000400
5
How many Significant Digits is in:
9200001
How many Significant Digits is in:
9200001
7
How many Significant Digits is in:
600.00
How many Significant Digits is in:
600.00
5
How many Significant Digits is in:
500
How many Significant Digits is in:
500
1
How many Significant Digits is in:
0.000000100200
How many Significant Digits is in:
0.000000100200
6
Round the following number to the amount of Significant Digits:
84.10 to 3 S.D.
Round the following number to the amount of Significant Digits:
84.10 to 3 S.D.
84.1
Round the following number to the amount of Significant Digits:
84.10 to 1 S.D.
Round the following number to the amount of Significant Digits:
84.10 to 1 S.D.
80
Round the following number to the amount of Significant Digits:
0.039100 to 2 S.D.
Round the following number to the amount of Significant Digits:
0.039100 to 2 S.D.
0.039
Round the following number to the amount of Significant Digits:
0.9876 to 3 S.D.
Round the following number to the amount of Significant Digits:
0.9876 to 3 S.D.
0.988
Round the following number to the amount of Significant Digits:
0.9876 to 1 S.D.
Round the following number to the amount of Significant Digits:
0.9876 to 1 S.D.
1
Round the following number to the amount of Significant Digits:
7080 to 3 S.D.
Round the following number to the amount of Significant Digits:
7080 to 3 S.D.
7080
Round the following number to the amount of Significant Digits:
30050 to 3 S.D.
Round the following number to the amount of Significant Digits:
30050 to 3 S.D.
30100
Round the following number to the amount of Significant Digits:
500 to 2 S.D.
Round the following number to the amount of Significant Digits:
500 to 2 S.D.
5.0 x 102
