significant digits

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