significant digits by michelle lamary and and caitlin ostrowski
TRANSCRIPT
Significant Digits
By Michelle Lamary and
Caitlin Ostrowski
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)
Example 1
401700.0900
Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits
Example 1 - Answer
401700.0900 Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros
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
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
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
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
Example 2
0.007050
Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers
Example 2 - Answer
0.007050 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero
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
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
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)
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
Example 3
700.
Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number
Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros
Example 3 - Answer
700. Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros
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
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
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
Example 4
8500
Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers
Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros
Example 4 - Answer
8500 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 2 ending zeros
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)
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
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
Example 5
8500.
Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits
Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros
Example 5 - Answer
8500. Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros
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
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
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
Example 6
0.0000001
Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number
Example 6 - Answer
0.0000001 Rule 1 – 1 sig dig non-zero number Rule 2 - 0 sig digs trapped zeros
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
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)
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)
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
Example 7
200009
Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers
Example 7 - Answer
200009 Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros
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
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)
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
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
Example 8
10
Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number
Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros
Example 8 - Answer
10 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 3 – 1 ending zero
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)
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
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
Example 9
1000.000
Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number
Example 9 - Answer
1000.000 Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros
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
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
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
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
Example 10
1136
Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers
Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros
Example 10 - Answer
1136 Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros
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)
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
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
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
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