Basic Mathematics Form One Notes – Approximation
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+ 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
a million
b. ten million
Solution
a 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
b. 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 itis or more, round up (i.e increase the digit of the required decimal
by 1) and ifitis 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.¢
+ Example 0.568 is the first decimal place and is the second decimal place
Example 2
Round 0.24736 to the nearest
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aI decimal place
b. — 2decimal places
©. 3decimal places
Solution
a 0.24736= 0.02 (1 dp)
b. 0.24736= 0.025 (2d.p)
© 0.24736= 0.0247 (I dp)
Significant Figures
Significant figures of a number – are the significant digits, counted from left of the number. The
first significant figure must be non-zero; following significant figures may take any value
A Number to a Given Number of Significant Figures
Write a number to a given number of significant figures
Is the number of significant digits including 0 if itis between the first and the last
Examples
a 13 ~has two significant figures
b. 709.43 —has five significant figures
© 0.000401 —has four significant figures
STEPS
+ When rounding a number to a certain significant figure, stand at the digit of the required
significant figure, then look at the next digit to the right; if it is or more, round up (ie increase
the digit of the required significant figure by 1) and if it is or less, do not change the digit of the
required significant figure
+ Replace all the remaining digits to the right of the required significant figure with the
zeros
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Example 3
Given the number 45.274 round to
a. | first significant figure
b. 2 significant figure
©. significant figure
Solution
a 50
b 4s
© 453
Example 4
Round 146 400 to
a 2 first significant figure
b. 4 significant figure
©. 3 significant figure
Solution
a 150000
b. 146400
146 000
Approximations in Calculations
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
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Approximation can be used in operation to check whether a calculation is correct or not, ie in
addition, subtraction, multiplication and divisione.g 446 x 45 = 20070
The above calculation can be checked quickly whether it is correct or not by rounding each
number to I significant figure and then multiply ie 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 | significant figure
Example 5
Find the approximate value of
(a) 22.1 + 4.77
(b) 127-79
(c) 0.53 x 0.68
(d) 423 +19
(e) 535 +1121
Solution
(a) 22.1 +4.77~20 + 5=25
(b) 127-79 = 100 — 80 = 20
(c) 0.53 x 0.68 0.5 x 0.7 =0.35
(d) 423 +19 = 400+ 20 = 20
(e) 535 +1121 + 500+ 1000 =0.5
Example 6
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A school trip of 32 people went to a tour, which costs a transport fee of $80/- each people. What
was the approximate total transport cost?
Solution
32 « $80 =30%600 = 18 000
The approximate transport cost was 18 000/-
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