Download - Significant Digits
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Significant Digits
By Michelle Lamary and
Caitlin Ostrowski
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Counting Significant Digit Rules
1. All non-zero digits are significant(725 , 2, 12)
2. Trapped zeros are significant(101, 2003)
3. Ending zeros are significant only if the decimal point can be seen
(100. , 1.10, 100, 20)
4. Leading (beginning) zeros are never significant
(0.001, 0.9)
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Example 1
401700.0900
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Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits
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Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros
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Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 ending zeros
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Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown
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Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown Rule 4 – 0 beginning zeros
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Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown Rule 4 – 0 beginning zeros
10 Significant Digits
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Example 2
0.007050
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Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers
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Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero
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Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 3 – 1 ending zero
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Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal
point is shown
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Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal
point is shown Rule 4 – beginning zeros are not significant (3
beginning zeros)
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Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal
point is shown Rule 4 – beginning zeros are not significant (3
beginning zeros)
4 significant digits
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Example 3
700.
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Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number
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Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros
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Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros
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Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown
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Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown Rule 4 – 0 leading zeros
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Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown Rule 4 – 0 leading zeros
3 significant digits
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Example 4
8500
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Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers
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Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros
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Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 2 ending zeros
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Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal
point is NOT shown)
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Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal
point is NOT shown) Rule 4 – 0 beginning zeros
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Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal
point is NOT shown) Rule 4 – 0 beginning zeros
2 significant digits
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Example 5
8500.
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Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits
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Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros
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Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros
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Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown
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Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown Rule 4 – 0 beginning zeros
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Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal
point shown Rule 4 – 0 beginning zeros
4 significant digits
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Example 6
0.0000001
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Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number
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Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros
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Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros
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Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point
is shown)
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Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7
non significant beginning zeros)
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Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7
non significant beginning zeros)
1 significant digit
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Example 7
200009
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Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers
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Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros
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Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros
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Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point
NOT shown)
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Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point
is NOT shown) Rule 4 – 0 beginning zeros
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Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 4 – 0 beginning zeros
6 significant digits
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Example 8
10
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Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number
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Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros
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Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 1 ending zero
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Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but
decimal point is NOT shown)
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Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but
decimal point is NOT shown) Rule 4 – 0 leading zeros
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Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but
decimal point is NOT shown) Rule 4 – 0 leading zeros
1 significant digit
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Example 9
1000.000
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Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number
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Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros
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Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 ending zeros
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Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal
point shown
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Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal
point shown Rule 4 – 0 leading zeros
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Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal
point shown Rule 4 – 0 leading zeros
7 significant digits
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Example 10
1136
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Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers
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Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros
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Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros
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Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros (Decimal point is NOT
shown)
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Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 4 – 0 leading zeros
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Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 4 – 0 leading zeros
4 significant digits
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Extra Practice
1. 20
2. 20.
3. 101
4. 0.0071
5. 3333
6. 4567.
7. 1001.
8. 0.00005
9. 21
10.1000
11.1010
12.1550
13.0.0010790
14.9999990
15.1
16.5.
17.90000009
18.0.91000270
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Extra Practice Answers
1. 1
2. 2
3. 3
4. 2
5. 4
6. 4
7. 4
8. 1
9. 2
10.1
11.3
12.3
13.5
14.6
15.1
16.1
17.8
18.8