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MATHEMATICS FOR INTERIOR DESIGN GSC1105
Lecture notes # 1
Topic : Estimation
Content : Approximation and estimation including rounding off number to a required number of decimal
or significant figure.
Learning objectives
This week’s sessions are designed so that you will be able to:
1. Make estimates of numbers, quantities, sizes, capacity and lengths.
2. Approximate the numbers to a specified number of significant figures (s.f) and decimal places
(d.p).
3. Round off to the reasonable accuracy in the context of the problems.
What is estimation?
1. To calculate approximately (the amount, extent, magnitude, position, or value of something).
2. A tentative evaluation or rough calculation, as of worth, quantity, or size.
3. A statement of the approximate cost of work to be done, such as a building project or doing
renovation.
Here it can be concluded that estimation is the mathematical idea of representing calculation or
measurement such as distance, size, cost etc in a non-exact value. The estimated value or measurement is
rounded off to a required number of decimal or significant figures.
Purpose of Estimating: (some of them)
1. To give a reasonably accurate idea of the cost
An estimate is necessary to give the owner a reasonably accurate idea of the cost to help him decide
whether the work can be undertaken as proposed or needs to be curtailed or abandoned, depending upon
the availability of funds and prospective direct and indirect benefits.
2. Estimating Materials (include the estimated measurement of the materials)
From the estimate of a work it is possible to determine what materials and in what quantities will be
required for the work so that the arrangements to procure them can be made.
3.Estimating Time
The estimate of a work and the past experience enable one to estimate quite closely the length of time
required to complete an item of work or the work as a whole.
Rounding off to Decimal places and Significant figure
Estimation by can be done by rounding off the values into appropriate number of significant figures (s.f)
or number of decimal places (d.p). Problems below:
Value
$578.83
456.652 cm
Round of to decimal
places
$579.80 ( to 1 d.p)
456.65 cm ( to 2 d.p)
Value
$578.83
456.652 cm
Round of to
significant figure
$600 ( to 1 s.f)
460 cm ( to 2 s.f)
Beside the idea of estimation by rounding off the decimal places and the significant figure, estimation can
also be sometimes by rounding off the place value such as to the nearest ten, hundreds, thousands, tenth,
hundredth and so on.
Problems :
1. Round off the following numbers to the degree of accuracy shown in the brackets.
a)
b)
c)
d)
e)
f)
2841 ( nearest 100)
7286 (nearest 10)
3.84 ( 1 s.f)
0.00451 (1 s.f)
63.084 ( 2 d.p)
0.0567 (3 d.p)
a)
b)
c)
d)
e)
f)
2800
7290
4.00 or 4
0.005
63.08
0.057
Solution 1 :
2. Estimate the value of 10 900 x 0.0442, giving your answer correct to 1 significant figure.
Solution 2:
a. Round off all the values into 2 significant figure. (higher than being specified in order not
to lost the accuracy significantly)
b. 10 900  11,000 and 0.0442  0.044
c. Evaluate to get value of 484 and estimated as 500.
3. A rectangle plank of wood with measurement of 1.53m by 2.52m. Estimate the area of the plank
correct to 1 significant figure.
Solution 3:
a. Multiply 1.5m with 2.5m to obtain the area of the rectangle.
b. Round off the answer (3.75m2) to 1 s.f
c. Answer is 4 m2
4. A box with 3.751m long, 8.19m wide and height of 0.125m. Estimate, correct to 1 decimal place ,
the volume of the box.
Solution 4:
a. Round off all the values into 2 decimal places.
b. 3.751  3.75, 8.19  8.19 and 0.125  0.13
c. Finding the volume as 3.992625.. and estimated to 1 decimal place as 4 m2
5.
The diagram represent a cuboid with 9cm, 10.4cm and
2.2cm on the respective side.
Using your own degree of accuracy, Estimate the
volume of the cuboid.
Solution 5:
1. Use the value 9cm  10cm, 10.4cm  10cm and 2.2cm  2cm. Multiplying all  200cm3.
2. Use 9cm, 10.4cm  10cm and 2.2cm  2cm. Multiplying all become 180cm  200cm3 (1 s.f)
Thinking skill :
Rahman is measuring a cubical box with sides of 13.45cm. He needs to round off his measurements to
a) one decimal place.
b) Two decimal place
c) 1 significant figure
d) Nearest tenth.
Rahman also need to buy 100 units of this cubical box. If one box cost $1.85. Estimate the total cost of
buying 100 units of this box. (Estimate to 1 significant figure).