Form 4 /Topic 1 - STANDARD FORM

1.    STANDARD FORM (Bentuk Piawai)

1.1  Significant Figures (s.f.) / Angka Bererti (a.b.)
Concept:  Rounding off numbers to the nearest figures/ Membundarkan nombor kepada nombor terdekat.
2 types of numbers : numbers >1  and numbers <1 (nombor lebih besar dari 1/lebih kecil dari 1)
Simple idea:  Let's say you have some money in the bank. Your bank accounts says you have RM 1987.96
How much money do you have approximately? You would say : RM2000 This is 1 significant figure.

Examples:
(i)  2359 = 2360 (3 s.f.)                  (ii)  48889 = 48900 (3 s.f.)
              = 2400 (2 s.f.)                                   = 49000 (2 s.f.)
              = 2000 (1 s.f.)                                   = 50000 (1 s.f.)

(iii)  0.00588 = 0.0059 (2 s.f.)       (iv)  0.9447 = 0.945 (3 s.f.)
                     = 0.006   (1 s.f.)                          = 0.94   (2 s.f.)
                                                                        = 1        (1 s.f.)

(v)  10.75  = 10.8  (3 s.f.)
                  = 11     (2 s.f.)
                  = 10     (1 s.f.)  ...... BUKAN 1 , tetapi 10 sebab nilai asal harus dikekalkan.


TRY THIS:
1.   Round off to 2 sig. figures:  (a)  6499 = ...............
                                                (b) 0.06499 = ...............
                                                (c) 1.6499 = ..............

2.  Round off to 3 sig. figure:   (a)  57455 = ............
                                              (b)  0.0057455 = ............
                                              (c)  12.57455 = .............

* Answers :
1(a)  6500
 (b)  0.065
 (c)  1.6

2 (a) 57500
  (b) 0.00575
  (c) 12.6


1.2  Standard Form / Bentuk Piawai
Concept: To change a number in normal form to Standard Form & vice versa.
               Standard Form is in the form of :  A x 10ⁿ   where 1 < A < 10  (A = 1.0 to 9.99) and n is an integer (positive/negative)
Basic knowledge:  10 = 10¹
                            100 = 10²
                          1000 = 10³
                        10000 = 10⁴

                            0.1 = 10^-1
                          0.01 = 10^-2
                        0.001 = 10^-3
                      0.0001 = 10^-4


Examples:
(i)      1200 = 1.2 x 10³        (v)  3.77 x 10⁴  = 37700
(ii)      234  = 2.34 x 10²     (vi)  9.23 x 10^-3 = 0.00923
(iii)     0.04 = 4 x 10^-2
(iv) 0.0056 = 5.6 x 10^-3

TRY THIS:
1.   Express the following in  Standard Form:
      (a)  667500 = ....................
      (b)  5460     = ....................
      (c)  0.0541  = ....................
      (d) 0.00088 = ...................

2.   Change the following into normal numbers:
     
      (a)  5.5 x 10^-7     = ....................
      (b) 1.76 x 10⁵     = ....................
      (c)  3.955 x 10^-2 = ....................


** Answers 
1 (a)  6.675 x 10 ⁵
   (b)  5.46 x 10 ³
   (c)  5.41 x 10 ^-2
   (d)  8.8 x 10 ^-4
2  (a)  0.00000055
   (b)  176000
   (c)  0.03955