Significant Digits

 

RULES FOR DETERMINING SIGNIFICANT DIGITS

 

1.         All non-zero digits are always significant.

2.         Captive zeros are always significant.

3.         Trailing zeros are significant if there is a decimal point.

4.         Leading zeros are never significant.

 

 

Examples:

1.         All non-zero digits are always significant.

            3.76 has 3 significant digits.

            37.6 has 3 significant digits.

            175.624 has 6 significant digits.

 

2.         Captive zeros are always significant.

            4008 has 4 significant digits.

            30.9 has 3 significant digits.

            8.101 has 4 significant digits.

 

3.         Trailing zeros are significant if there is a decimal point.

                        1.0 has 2 significant digits.

            10 has 1 significant digit. (The trailing zero is not after the decimal.)

            5.200 has 4 significant digits.

            5200 has 2 significant digits. (The trailing zeros are not after the decimal.)

            25.0 has 3 significant digits.

 

4.         Leading zeros are never significant.

                        0.017 has 2 significant digits.

                        0.000594 has 3 significant digits.

                        0.06030 has 4 significant digits.

 

Additional Practice A

 

How many significant digits are contained in each of the following numbers?

1.                  10.42

2.                  12.00

3.                  0.0015

4.                  604

5.                  200.

6.                  0.0000078

7.                  0.250

8.                  0.7009

9.                  0.0102030


 

            In science classes we commonly obtain numerical data in the lab and then use these numbers in calculations. This begs the question: How are significant digits handled in calculations? The answer depends on whether you are (a) adding and subtracting or (b) multiplying and dividing.

 

ADDITION AND SUBTRACTION

            The answer should be rounded off so as to contain the same number of decimal places as the least precise value.

 

Examples:

              17.15             2 digits after the decimal

               -4.170           3 digits after the decimal

              12.98             2 digits after the decimal

 

              12.7               1 digit after the decimal

                4.716           3 digits after the decimal

            +13.85             2 digits after the decimal

              31.3               1 digit after the decimal

 

MULTIPLICATION AND DIVISION

            The answer should be rounded off so as to contain the lowest number of significant digits, regardless of the decimal point.

 

Examples:

                3.17             3 significant digits

             x 5.186           4 significant digits

              16.4               3 significant digits

 

              18.35             4 significant digits

               0.717             3 significant digits

 

           = 25.6               3 significant digits


 

 

Additional Practice B

Perform the following operations. Copy this assignment on a separate sheet of paper. Circle your answers.

 

10.              67.73 + 709.3 + 4.622

11.              416.3 51.903

12.              236.401 + 90.72 + 16.3

13.              47.30 20.60

14.              65.10 x 3.10

15.              21.0 / 61.00

16.              3.40 x 8.00

17.              0.00570 / 0.510

 

 

 

 

 

Answers to Additional Practice A

1.                  4

2.                  4

3.                  2

4.                  3

5.                  3

6.                  2

7.                  3

8.                  4

9.                  6

 

Answers to Additional Practice A

10.              781.7

11.              364.4

12.              343.4

13.              26.70

14.              202

15.              0.344

16.              27.2

17.              0.0112