Approximations are linked to terms such as decimal places,
significant figures, standard form and so on. It is a method of assuming
precise values to figures. It is also a method of counting to the nearest whole
numbers.
Common terms used in Approximations are decimal places (d.p)
and significant figures (sigfig) or (s.f).
Note;
Before you can approximate any number, the following rule
must be fully understood;
0
|
0
|
1
|
0
|
2
|
0
|
3
|
0
|
4
|
0
|
5
|
1
|
6
|
1
|
7
|
1
|
8
|
1
|
9
|
1
|
The table above simply suggest that during approximation,
figures from 0-4 becomes 0 while figures from 5-9 becomes 1. Without knowing
this rule it will be difficult for you to approximate any number.
Example 1; Correct
0.00630427 to 7 decimal places.
Solution
To do this, follow these steps;
Count 7 numbers after the decimal point. The seventh figure
is ‘2’ and beside it is ‘7’ which falls between 5-9 so it becomes ‘1’ according
to the rule in the table above. Add this ‘1’ to the seventh figure which is ‘2’,
that gives 3.
The result is; 0.0063043. (Answer)
Example 2; Correct
15.300649 to 3 decimal places.
Solution
Count 3 numbers after the decimal point. The third number is
‘0’ and beside it is ‘6’ which falls between 5-9 so it becomes ‘1’ according to
the rule above. Add this ‘1’ to the third number which is ‘0’, that gives 1.
The result is; 15.301000. This can also be written as
15.301. (Answer)
Note
All other numbers are rounded down and will become zero.
It’s a rule!
Example 3; Express
0.006457 to 3 significant figures.
Solution
Applying the rule to significant figures is just a little
bit different because here zeros are not counted unlike decimal places. In
order to do this, follow the steps below;
Count 3 “non-zero” figures after the decimal point. The
third figure is ‘5’ and beside it is ‘7’ which falls between 5-9 so it becomes
‘1’. Add this ‘1’ to the third figure which is ‘5’, that gives 6.
The result is; 0.00646. (Answer)
Example 4; Express
2.00584 to 4 sigfig.
Solution
A very important thing to note here is zeros that are found
in between non-zero significant figures are counted as being significant.
Count 4 significant figures from the beginning of the number.
The fourth figure will be ‘5’ and beside it is ‘8’ which falls between 5-9 so
it becomes ‘1’. Add this ‘1’ to the fourth figure which is ‘5’, that gives 6.
The answer is 2.006.
Example 5; Round
off 241.863 to the nearest whole number.
Solution
This is a little different from decimal places and
significant figures but the same rule applies here as well.
To the nearest whole number means no decimal point should be
found in the answer. This is how you do it;
Consider the figure after decimal point, which is ‘8’ and
falls between 5-9 so it becomes ‘1’. Add this ‘1’ to the last figure before
decimal point which is also 1 (1+1) that gives 2.
Therefore, the result is 242.
Example 6; Round
off 2.2 hours to the nearest hours.
Solution
Follow the same step in example 5;
Consider the figure after decimal point which is ‘2’ and
falls between 0-4 so it becomes ‘0’ according to the rule. Add this ‘0’ to the
last figure before the decimal point which is 2 (0+2) that gives 2.
Answer is 2 hours.
Example 7; Take
173.245 to the nearest hundred.
Solution
In order to do this, you must follow place value counting system;
H T U
173.245
H stands for hundred
T stands for tens
U stands for units.
To the nearest hundred means; Consider the hundredth value
which is ‘1’ beside it is ‘7’ which falls between 5-9 so it becomes ‘1’. Add
this ‘1’ to the hundredth value which is also 1 (1+1), that gives 2.
The answer is 200. (Remember all the other values becomes
zero)
Example 8; Express
92,681 in the nearest thousand.
Solution
Apply place value counting system;
TTH
TH H T U
92,681
To the nearest thousand means; Consider the thousandth value
which is ‘2’ beside it is ‘6’ which falls between 5-9 so it becomes ‘1’. Add
this ‘1’ to the thousandth value (2+1) that gives 3.
93,000. (Answer)
Practice these
questions below;
1. Correct the following figures to the number of decimal
places indicated.
(a) 3.0561 (2d.p)
(b) 0.008153 (1d.p)
(c) 0.09634 (3d.p)
(d) 0.0006005 (4d.p)
