S1T1 Approximation and Significant Digits

Rounding is about approximating a number to a given value or number of decimal places.

Round Off Numbers

If the digit is LESS than 5, Round DOWN [drop all digits to the right]

If the digit is GREATER/EQUAL to 5, Round UP [ADD 1 to left, drops all digits to right]

Method

Step1: Underline the required Rounding place value. <round-off to 10, 8456>

Step2: ( ) right number and Compare :

           If  equal or greater than 5 (5, 6,7,8,9), ROUND-UP, ADD

           If less than 5 (4,3,2,1,0), ROUND-DOWN, NO CHANGE

Step 3: Change the numbers to the right to 0

Example: 

(1)       Round 36.586 to nearest 1 decimal place.

            36.546             (Step 1 : Underline round off)

            36.5(4)6           (Step 2 : 2^nd decimal 4 is less than 5, drop all to right] )

            = 36.5 (1 d.p)   (Step 3: Change the numbers to the right to 0)

Example

(2)       Round 36.875 to nearest 2 decimal places.

            36.875 = 36.88 (2 d.p) [third decimal 5, add one to 7, and drop all to right]

Significant Digits                            

Number is Significant for

            1.         Every non-zero                                          : 42549          (5 sig digits)

            2.         Zeros in between digits                            : 1001, 1.003 (4 sig digits)

            3.         Zeros at end of numbers with decimals  : 300.100 (6 sig digits)

Number is not significant for

            1.         Zeros to left of numbers                           : 00003467 (4 sig digits)

            2.         Zeros at end of non-decimal numbers    : 823000 (3 sig digits) 

            3.         Zeros to right of decimal number < 1      : 0.0005 (1 sig digits)

[ For Decimal, remember to put a trailing zero for specified significant figure. 

            Eg: 0.200 is 3 significant figures]

Round Off Numbers to Significant Figures

1.  Start counting from first significant figure (number other than 0), 

2.  Check the digit to the right of the rounding digit

3.  Apply the rounding rule, and replace all digits to right with 0.

Example:      

            Round off 81267 to 3,2,1 significant figure/s.

Step1: Look at significant figure => 3, count 3 sig fig numbers from left and underline.

             << 8 1 2 6 7 are the 3 significant figures >>

Step2: Round off number to right 

            << 8 1 2 6 7 (round off 4^th ,  number 6 => +1 to 2,  8 1 3).  >>

Step3: Replace number to right with 0

              8 1 3 0 0 (to 3 sig fig)

To 2 significant figure:  81000 (2 sig fig)

To 1 significant figure: 80000 (1 sig fig)

Example:

            Round 52.8975 to 4 significant figures

                     52.8975.      (Step 1 : 4 s.f at 9)            

      => change 52.8 to 52.9      (Step 2 : Round off number to right , 5th - 7)

            52.90            (Step 3 - Put trailing 0)

            52.8297 ~ 52.90 (4 sig fig)

More Examples

(1)  00384.12 has 5 significant digits.

(2)  56.045 has 5 significant digits

(3)  3.0120 has 5 significant digits (the 0s are to be counted)

(4)  00036540 has 5 significant digits (36540) [Zeros to left are not counted]

(5) 0.0006 has 1 significant digits [Decimal number less than 1]

(6) 4 significant digits: 12.34, 01.234, 01234, 1.002, 4.020, 0.001234

Practice

1.         Round off each of the following numbers to 1 decimal place, 2 decimal places and 3 decimal places.

(a)       36.7247         (b)       2.8734                       (c)       100.283

(d)       1.0049                       (e)       0.9999                       (f)        9.959

(f)        0.2139                       (g)       5.3027                       

2.         Round off each of the following numbers to 2 significant figures, 3 significant figures and 4 significant figures.

(a)       483.86                       (b)       248999                      (c)       15.795

(d)       0.59 974                    (e)       18932                        (f)        37.649