Home MATHEMATICS TOPIC 5: APPROXIMATIONS | MATHEMATICS FORM 1

TOPIC 5: APPROXIMATIONS | MATHEMATICS FORM 1

October 20, 2020

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TOPIC 5: APPROXIMATIONS | MATHEMATICS FORM 1

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 Numbers

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

million
ten million

Solution

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
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 decimal place
2 decimal places
3 decimal places

Solution

0.24736≈ 0.02 (1 d.p)
0.24736≈ 0.025 (2 d.p)
0.24736≈ 0.0247 (1 d.p)

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 it is between the first and the last

Examples

13 – has two significant figures
709.43 – has five significant figures
0.0004001 – 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 (i.e 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

Example 3

Given the number 45.274 round to

1 first significant figure
2 significant figure
significant figure

Solution

50
45
45.3

Example 4

Round 146 400 to

2 first significant figure
4 significant figure
3 significant figure

Solution

150 000
146 400
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

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