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

- 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

- Sequence and series I and II
- Arithmetic progression (A.P) calculating the nth term of an A.P, common difference and first
- 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, 3^{rd} – 2^{nd} etc

Un = 1 + (n – 1) d

:. Nth of an Ap = a + (n – 1) d

Sum of Ap => n/2 {2a + (N – 1)d}

- Geometrical Progression (G.P)
- Definition of Geometric Progression (G.P), fian, first term (a), common ratio (r) and nth term of a G.P
- 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 = ar^{n-1}

Sum of an nth term of a G.P

Sn = __a(1 – r ^{n})__ (1)

- – r)

Sn = __a(r ^{n} – 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)