Sem-2_Roundings concept. Details..details description about

rounding

1. Sem2 GEOA (2020)
Rounding off & Angular
Measurement
Chandan Surabhi Das
Barasat Govt.College

2. Definition: Rounding
•Rounding means making a numbersimplerbut keeping its
value close to what it was.The result is less accurate, but
easier to use.
•Example: 7.3 rounds to 7
Because 7.3 is closer to 7 than to 8
•But what about7.5?
Is it closer to 7 or closer to 8? It is half-way in between, so
what should we do?
Negative Numbers
•-7.4 rounds up to -7
•-7.5 rounds down to -8
•-7.6 rounds down to -8

3. Rounding to Tens, Tenths, Whatever ...
•Example:
"Half Round Up" totens(nearest 10):
25 rounds up to 30
24.97 rounds down to 20
•Example
•"Half Round Up" tohundredths(nearest 1/100):
•0.5168 rounds up to 0.52
•1.41119 rounds down to 1.41

4. Rounding Decimals
•Rounding totenthsmeans to leaveone numberafter the
decimal point.
•Rounding tohundredthsmeans to leavetwo numbersafter
the decimal point.
EX: 3.1416 rounded to hundredths is 3.14, as the next digit (1)
is less than 5
EX: 3.1416 rounded to thousandths is 3.142, as the next digit
(6) is more than 5
EX: 1.2735 rounded to 3 decimal places is 1.274, as the next
digit (5) is 5 or more

5. Rounding Whole Numbers
•We may want to round to tens, hundreds, etc, In this case we
replace the removed digits with zero.
EX: 134.9 rounded to tens is 130, as the next digit (4) is
less than 5
EX: 12,690 rounded to thousands is 13,000, as the next
digit (6) is 5 or more
EX: 15.239 rounded to ones is…………?
EX: 16.556 rounded to ones is…………?
EX: 10.999 rounded to ones is…………?
EX: 105.9 rounded to tens is………….?
EX: Round 97,870 to the nearest thousand……..?

6. Rounding to Significant Digits
To round to "so many" significant digits,count digits from
left to right, and then round off from there.
EX: 1.239 rounded to 3 significant digits is 1.24, as
the next digit (9) is 5 or more
EX: 134.9 rounded to 1 significant digit is 100, as
the next digit (3) is less than 5
EX: 0.0165 rounded to 2 significant digits is 0.017,
as the next digit (5) is 5 or more (0 is not a
significant number)

7. For example
1,654 to the nearest thousand is ………... To
the nearest 100 it is ……………. To the nearest
ten it is …………….
Express 0.4563948 to three decimal
places………………….

8. Measurement: Linear, Angular
•TheLinear Measurementincludesmeasurementsof
length, diameters, heights and thickness
TheAngular measurementincludes
themeasurementof angles.
•Angle is ameasurementthat we
canmeasurebetween the two line which meets at
one point.Angular measurementsare playing a
very crucial role inmeasurements.
•The most contemporary units are the degree ( °)
andradian(rad)
•SI unit of angular measure is theradian

9. •Angle Measurement –Degree Measure
•A complete revolution, i.e. when the initial and terminal
sidesare in the same position after rotating clockwise or
anticlockwise, is divided into 360 units calleddegrees. So, if
the rotation from the initial side to the terminal side is
(1360)thof a revolution, then the angle is said to have a
measure of one degree. It is denoted as 1°.
•We measure time in hours, minutes, and seconds, where 1
hour = 60 minutes and 1 minute = 60 seconds. Similarly, while
measuring angles,
•1 degree = 60 minutes denoted as 1°= 60′
•1 minute = 60 seconds denoted as 1′ = 60″

10. Angle Measurement –Radian Measure
•Radian measure is slightly more complex than the degree
measure. Imagine acirclewith a radius of 1 unit. Next,
imagine an arc of the circle having alengthof 1 unit. The
angle subtended by thisarcat the centre of the circle has
a measure of 1 radian. Here is how it looks:

11. Radian Measure
•n a circle of radius r, an arc of length r subtends an angle of 1
radian at the centre.Hence, in a circle of radius r, an arc of
lengthlwill subtend an angle = \( \frac{l}{r} \) radian.
Generalizing this, we have, ina circle of radius r, if an arc of
lengthlsubtends an angle θ radian at the centre, then
•θ =lr
:
•Radian measure =π180°x Degree measure
Degree measure =180°πx Radian measure
:

12. Example 1
•Convert 40°20′ into radian measure.