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Approximation (Significant Figure, Decimal Places And Rounding Off)

APPROXIMATION: 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

• 7562 (b)907235 (c)8991

SOLUTION

• 7562 = 7560 (nearest ten)

= 7600 (nearest hundred)

=8000 (nearest thousands)

• 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

• 78602 (b) 702.976 (c) 0.000057849

SOLUTION

• 78602 = 80000  (1s.f),   79000 (2s.f), 78600(3s.f)
• 976  = 700 (1s.f), 700(2s.f)  703 (3s.f)
• 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

• 3994 (b) 0.00749

SOLUTION

• 3994 = (i) 67.40(2d.p) ,  (ii) 67.399(3d.p)
• 00749  = (i) 0.01(2d.p),  (ii) 0.007(3d.p)