Home MATHEMATICS TOPIC 5: APPROXIMATIONS | MATHEMATICS FORM 1

TOPIC 5: APPROXIMATIONS | MATHEMATICS FORM 1

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Geometry Points and Lines

Measurements
can be rounded to a certain number of significant
figures.Approximation- is a process of rounding numbers to a certain
degree of accuracy.A number can be rounded to a certain required place
value such as to the nearest ten, hundred, and thousand

Rounding off Whole Numbers to Given Place Values
Round off whole numbers to given place values
STEPS
  • When
    rounding a number, stand at the digit of the required place value, then
    look at the next digit to the right; if it is or more, round up (i.e,
    increase the digit of the required place value by 1) and if it is or
    less, do not change the digit of the required place value
  • Replace all the remaining digits to the right of the required place value with the zeros
Example 1
The population of Tanzania in a census of 2002 was 42,850,671. Round this to the nearest
  1. million
  2. ten million
Solution
  1. The
    million digit is 2, since the next digit to the right is greater than
    5, then we can increase 2 by 1 and put the remaining digits to the right
    of 2 zeros. There fore;42,850,671 ≈ 43,000,000
  2. The ten million
    digit is 4, since the next digit to the right is less than 5, then we do
    not change 4 but we put the remaining digits to the right of 4 zeros.
    There fore;42,850,671 ≈ 40,000,000
Decimals to a Given Number of Decimal Place
Round off decimals to a given number of decimal place
STEPS
  • When
    rounding a decimal, stand at the digit of the required decimal place,
    then look at the next digit to the right; if it is or more, round up
    (i.e increase the digit of the required decimal by 1) and if it is or
    less, do not change the digit of the required decimal place
  • Replace all the remaining digits to the right of the required decimal place with the zeros
NOTE
  • The
    first digit after the decimal point is the first decimal place, the
    second digit after the decimal point is the second decimal place e.t.c
  • Example 0.568 is the first decimal place and is the second decimal place
Example 2
Round 0.24736 to the nearest
  1. 1 decimal place
  2. 2 decimal places
  3. 3 decimal places
Solution
  1. 0.24736≈ 0.02 (1 d.p)
  2. 0.24736≈ 0.025 (2 d.p)
  3. 0.24736≈ 0.0247 (1 d.p)

 

 

The Knowledge of Rounding Off of Numbers in Computations Involving Large Numbers and Small Numbers
Use the knowledge of rounding off of numbers in computations involving large numbers and small numbers
Approximation
can be used in operation to check whether a calculation is correct or
not, i.e in addition, subtraction, multiplication and divisione.g 446 x
45 = 20 070
The
above calculation can be checked quickly whether it is correct or not
by rounding each number to 1 significant figure and then multiply i.e
400 x 50 = 20 000
Therefore,
the approximation of 20 000 is close to 20 0070 is correct.Before
carrying an operation, each number in a calculation is rounded to 1
significant figure
Example 5
Find the approximate value of
Example 6
A
school trip of 32 people went to a tour, which costs a transport fee of
580/- each people. What was the approximate total transport cost?
Solution
32 × 580 ≈30×600 = 18 000
The approximate transport cost was 18 000/- 

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