Approximations and Accuracy

Rounding up and down of numbers to significant figures, decimal places and nearest whole numbers are practical applications of approximations to everyday life

 

  1. Percentage error

 

When rounding to any number of significant figure

Look at the first unwanted digit

Use the rules of approximations

Keep the number about the right size

 

Note: The zero between two significant digits is significant. For example, in the number 306, the 0 between 3 and 6 is significant, whole in the number 0-00692, the zeros area not significant

 

Example:

16418.39 = 16400 to 3 s.f

16418.39 = 16000 to 2 s.f

16418.39 = 16420 to 4 s.f

 

Percentage error = error           x         100

measurement                 1

 

Relative error = maximum absolute error

Actual value

= Precision  

Measurement

 

 

  1. Sequence and series I and II
  2. Arithmetic progression (A.P) calculating the nth term of an A.P, common difference and first
  3. Solving problems of arithmetic mean of A.P
  • Sum of an A.P

 

A.p :- a = first term

d = common difference gotten from 2 minus first, 3rd – 2nd etc

Un = 1 + (n – 1) d

:. Nth of an Ap = a + (n – 1) d

Sum of Ap => n/2 {2a + (N – 1)d}

 

  1. Geometrical Progression (G.P)
  2. Definition of Geometric Progression (G.P), fian, first term (a), common ratio (r) and nth term of a G.P
  3. Calculation nth term, Geometric mean and sum of terms of G.P
  • Sum of infinity of G.P

 

r = common ration, a = first term

r is gotten by dividing any term by its percentage term

2nd term = 3rd term

First term    2nd term

:. Tn = arn-1

Sum of an nth term of a G.P

Sn = a(1 – rn)                                    (1)

  • – r)

 

Sn = a(rn – 1)                                    (2)

(r – 1)

Note: if r < 1, formula (1) is advisable to be used

                        If r > 1, formula (2) is advisable to be used

Sum to infinity

S =      a__

(1 – r)

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