Grade 7 REGULAR MATH SIGNIFICANT FIGURES

LESSON 3           Significant Figures

Rounding off is part also of the significant figures. Let us consider the height of the Mount Everest. Accordingly, the height is 8 847.93 m including the snow.

The height of this mountain can be expressed as:

1.   8 847.9 (correct to 5 significant figures)

2.   8 848 (correct to 4 significant figures)

3.   8 850 (correct to 3 significant figures)

4.   8 900 (correct to 2 significant figures)

5.   9 000 (correct to 1 significant figure)

Example 1. Round off 3 245.72 to

(a)        5 significant digits                (b)    4 significant digits

(b)        3 significant digits                (d)    2 significant digits

(e)        1 significant digit

Solution: In these cases, what we are doing here is like rounding off.

(a)        5 significant digits is 3 245.7          
(b)    4 significant digits is 3 246

(c)         3 significant digits is 3 250              
(d)    2 significant digits is 3 300

(e)        1 significant digit is 3 000

Example 2.  Round off 0.004 018 48 to

(a)        5 significant digits                (b)    4 significant digits

(c)    3 significant digits                (d)    2 significant digits

(e)     1 significant digit

Solution:    (a) 5 significant digits is 0.004 018 5    
                (b) 4 significant digits is 0.004 019

(c) 3 significant digits is 0.004 02         
(d) 2 significant digits is 0.00 40

(e) 1 significant digit is 0.00 4

Rules on Approximation to a given number of a Significant Digit

1.   All non-zero digits are SIGNIFICANT wherever they are recorded.

Example: The number 33.2 has THREE significant figures because all of the digits present are non-zero.

2.   Zeros that lie between non-zero digits are SIGNIFICANT.

Example: 20.51 has FOUR significant figures. The zero is between a 2 and a 5.

3.   Zeros, which are not preceded by a non-zero digit, are NOT SIGNIFICANT. This is most evident in decimals.

Example: The number 0.54 has only TWO significant figures. 0.0032 also has TWO significant figures. All of the zeros are leading.

4.   Zeros that occur after the decimal point but are not followed by a non-zero digit are also SIGNIFICANT.

Example: 38.700 has 5 significant figures. 16.00 has 4 significant figures.

5.   The zeros at the end of a whole number are NOT SIGNIFICANT.

Example: 4 500 has only 2 significant figures. 290 has only 3 significant figures.

Example 3. David bought a bag which costs ₱388.50, two shirts cost ₱1,325.75 and a pair of shoes amounted to ₱1,455.00. Find the sum of the prices, correct to a.   4 significant figures      b. 3 significant figures      c. 2 significant figures

Solution:

   ₱    388.50          a. ₱3,169 (correct to 4 significant figures)

   ₱ 1,325.75           b. ₱3,170 (correct to 3 significant figures)

+ ₱ 1,455.00           c. ₱3,200 (correct to 2 significant figures)

        ₱ 3,169.25

Exercise

A.   Round off the following values to (a) 4 significant figures (b) 3 significant figures and (c) 2 significant figures.

1. 348.15                                   4. 0.067 473 21

a. _________ ans. 348.2              a. _________    

b. _________ ans. 348                 b. _________            

c. _________ ans. 350                 c. _________     

               

2. 29.138 56                               5. 0.000 051 146

a. _________                             a. _________                    

b. _________                             b. _________                    

c. _________                              c. _________

3. 1.109 78                                6. 4 269.61

a. _________                             a. _________                    

b. _________                             b. _________                    

c. _________                              c. _________

B.   Indicate how many significant figures there are in each of the following measured values.

1.   1 057   ________                                6. 0.000 489 _________

2.   3.002   ________                                7. 32.913     _________

3.   19.249  ________                               8. 7.003       _________

4.   8.01     ________                                9. 61.017     _________

5.   20.001  ________                               10. 178.00   _________

C.   Solve the problem.

The mass of a watch glass was measured four times. The masses were 99.997 g, 100.008 g, 100.011 g, and 100.005 g. What is the average mass of the watch glass? (correct to 6 significant figures)

Activity Sheet on Significant Figures (Reg. Math 7)

Name: _______________________________

Section:______________________________

A.   Indicate how many significant figures there are in each of the following measured values.

1. 246.32   _____          6. 0.00340  _____         11. 0.0001    _____

2. 107.854 _____           7. 14.600    _____        12. 0.0001    _____

3. 100.3     _____          8. 700000   _____         13. 9010.0    _____

4. 0.678     _____          9. 350 670  _____         14. 14.002    _____

5. 1.008     _____          10. 1.0000  _____         15. 1 006.80 _____

B.   Round off the following values to (a) 4 significant figures (b) 3 significant figures and (c) 2 significant figures.

1. 4 030.5                                  2. 13.018 6                        3. 0.008 707

a. _________                             a. _________                     a. _________

b. _________                             b. _________                     b. _________

c. _________                             c. _________                     c. _________

C.   Find the values of the following expressions, correct to 3 significant digits.

1.   395 + 872                                      2. 724.73 – 120.48 + 68.5

3.   48 × 14.5                                       4. 20.4 ÷ 62.8

D.  Solve the following problems. Show your solution.

1.   There are ₱6,785.65 and ₱13,826.58 in Robin’s two saving accounts. Find the total amount in his two saving account, correct to 5 significant figures.

2.   A can of milk weighs 684 g. What is the total weight of 38 cans of milk in kg? (Give your answer correct to 3 significant digits)