Week 5 – SS1 First Term General Mathematics Notes

 WEEK 5

STANDARD FORM AND APPROXIMATION

STANDARD FORM: Is a convenient way of writing very large or small numbers. It is the product of the numbers in powers of 10 to determine the position of the decimal pointand it´s writing between 1 and 9 i.e. a X . Where ais the number between 1and 9 and n is the position of the decimal point.
EXAMPLE:
Express the following numbers in standard form;

1. 9 (b) 54.6 (c) 570200

   SOLUTION.

   1. 9 = 9 x (b) 54.6 = 5.46 x (c) 570200 = 5.702 x

      NEGATIVE POWERS (NUMBERS LESS THAN 1 )
      Express the following numbers in standard form;

      1. 0.02 (b) 0.000175

         SOLUTION

         1. 0.02 = 2 x (b) o.000175 =1.75 x .

ADDITION AND SUBTRACTION OF NUMBERS IN STANDARD FORM    

Simplify the following;

1. 5.14 x + 2.842 x (b) 5.24 x 4.33 x

SOLUTION

1. 5.14 x = 5.14 x 10x10x10x10x10x10x10 = 51400000

   2.842 x = 2.842 x 10x10x10x10x10 = 284200 +
   51684200
   51684200 =5.16842 x

2. 5.24 x = 5.24 x= = 0.0000524

    4.33 x = 4.33 x = = 0.00000433
   0.0000524 0.00000433 =0.00004803
   0.00004807 =4.807 x
   MULTIPLICATION AND DIVISION OF STANDARD FORM
   Simplify the following:

   1. 8.222 x x 6.32 x (b) 2.8 x 1.5 x

      SOLUTION

      1. (8.222 x 6.32) x () = 51.96304 x

         5.196304 x =5.196304 x

(b) (2.8 1.5) x ( ) = 1.86667 x
1.86667 x

APPROXIMATION (SIGNIFICANT FIGURE, DECIMAL PLACES AND ROUNDING OFF)

PPROXIMATION: Is calculating values or numbers only to a certain degree of accuracy.
SIGNIFICANT FIGURE: Is a process in which each of the digits in a number that are needed to a given accuracy is presented.
DECIMAL: is the writing of numbers to a required fractional part.
EXAMPLE:
Approximate the following to the nearest (i) ten (ii) hundred (iii) thousand

1. 7562 (b)907235 (c)8991

SOLUTION

1. 7562 = 7560 (nearest ten)

   = 7600 (nearest hundred)
   =8000 (nearest thousands)

2. 907235 = 907240 (nearest ten)

   = 907200 (nearest hundred)
   =907000 (nearest thousand)

© 8991 = 8990 (nearest ten)
= 9000 (nearest hundred)
= 9000(nearest thousands)
SIGNIFICANT FIGURE: Express the following numbers to (i) 1s.f (ii) 2s.f (iii) 3s.f

1. 78602 (b) 702.976 (c) 0.000057849

SOLUTION

1. 78602 = 80000 (1s.f), 79000 (2s.f), 78600(3s.f)
2. 702.976 = 700 (1s.f), 700(2s.f) 703 (3s.f)
3. 0.000057849 = 0.00006(1s.f), 0.000058(2s.f), 0.0000578(3s.f)

DECIMAL PLACES: Express the following numbers to ; (i) 2d.p (ii)3d.p

1. 67.3994 (b) 0.00749

SOLUTION

1. 67.3994 = (i) 67.40(2d.p) , (ii) 67.399(3d.p)
2. 0.00749 = (i) 0.01(2d.p), (ii) 0.007(3d.p)

ASSESSMENT: Solve the following questions;

1. Write the following in standard form:
   1. 7560 (ii)7560000000 (iii) 0,00756 (iv) 0.000000756
2. Find each of the following ,leaving your answers in standard form:
   1. (4 x ) x (2.6 x ) (ii) (6.4 x (8 x
3. Evaluate (9.05 x ) + (6.5 x ) – (6.5 x ) giving your answer in standard form.
4. Express each of the following numbers to : (i) 1s.f, (ii) 3s.f, (iii) 2d.p (iv) 3d.p
5. 799.8094 (b) 6.3006 (c) 0.0014698

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