Rounding
10/100/1000
http://www.youtube.com/watch?v=UP7YmXJc7Ik
(rounding to the nearest 10, 100, 1000, 10000)
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Rounding
We do not always need to know the exact value of a number.
For example,
There are 1432
pupils at Eastpark
Secondary School.
There are about one
and a half thousand
pupils at Eastpark
Secondary School.
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Rounding whole numbers
Example
Round 34 871 to the nearest 100.
Look at the digit in the hundreds position.
Write down every digit (from the left) up to this digit i.e. 348.
Look at the digit in the tens position i.e. 7
If this digit is 5 or more round up the digit in the hundreds
position.
OR
If this digit is 4 or less replace with zeros
Solution:34871 = 34900 (to the nearest 100)
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Rounding whole numbers
Complete this table:
to the nearest
1000
to the nearest
100
to the nearest
10
37521
38000
37500
37520
274503
275000
274500
274500
7630918
7631000
7630900
7630920
9875
10000
9900
9880
452
0
500
450
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Answers
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Answers
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Decimal Places (dp)
http://www.youtube.com/watch?v=JPhrIl_TiqY
(rounding dp)
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6.88945
1st decimal place
1 dp
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2nd decimal place
2 dp
3rd decimal place
3 dp
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Rounding decimals
Example
Round 2.75241302
1342.75241 to one decimal place.
Look at the digit in the first decimal place i.e. 7
We need to write down every digit up to this i.e. 1342.7
Look at the digit in the second decimal place i.e. 5.
If this digit is 5 or more then we need to round up the digit
in the first decimal place OR
If this digit is a 4 or less, delete all digits after the 1dp
1342.75241 to 1 decimal place is 2.8
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Rounding to a given number of decimal places
Complete this table:
to the nearest
whole number
to 1 d.p.
to 2 d.p.
to 3 d.p.
63.4721
63
63.5
63.47
63.472
87.6564
88
87.7
87.66
87.656
149.9875
150
150.0
149.99
149.988
3.54029
4
3.5
3.54
3.540
0.59999
1
0.6
0.60
0.600
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Answers
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Significant Figures (sf)
http://www.youtube.com/watch?v=MK5C1N9e3vw&feature=relmfu
(rounding sf)
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Rounding to significant figures
Numbers can be rounded to any given number of significant
figures.
The first significant figure of a number is the first digit (from
the left) which is not a zero.
E.g.
4 890 351
First significant figure
and
0.0007506
First significant figure
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Rounding to significant figures
The second, third and fourth significant figures are the
digits immediately following the first significant figure,
including zeros.
For example,
4 890 351
This
is
the
first
significant
figurefigure
This
This
This
is is
the
isthe
the
second
third
fourth
significant
significant
significant
figure
figure
and
0.0007506
This
is
first
significant
figure
This
This
This
isthe
is
the
isthe
the
second
third
fourth
significant
significant
significant
figure
figure
figure
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Rounding to significant figures
Complete this table:
to 3 s. f.
to 2 s. f.
to 1 s. f.
6.3528
6.35
6.4
6
34.026
34.0
34
30
0.005708
0.00571
0.0057
0.006
150.932
151
150
200
0.0000784
0.000078
0.00008
0.00007835
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Answers
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Rounding
(upper and lower limits)
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Whenever a number is rounded using dp, sf, or to the nearest
1/10/100/1000 a margin of error is created.
118.49
117.5
117
118
119
A plank of wood measures 118 cm to the nearest centimetre.
Where on the diagram could the plank be?
What is the minimum length of the wood (lower limit)?
117.5 cm
What is the maximum length of the wood (upper limit)?
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118.49 cm
Upper and lower limits
Example
What are the limits of $1700 if rounded to the nearest $100
$1650
$1 7 0 0
$ 1 74𝟗
Lower limit:
Look at the digit in the hundreds position.
Reduce this digit by 1
Take the position to the right and change to a 5
Upper Limit
After the hundreds position change to 49
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Your Turn:
Fill in the upper and lower limits for these rounded numbers
Number
137
46800
75420
658000
5.75
0.056
96000
Rounded to
Nearest 1
Nearest 100
Nearest 10
Nearest 1000
2 d.p.
3d.p.
2 s.f.
Lower limit Upper limit
136.5
137.49
46750
46849.9
75415
75424.9
657500
658499.9
5.745
5.7549.9
0.0555
0.05649.9
95500
96499.9
Using inequalities the first pair of answers can be written
as 136.5 ≤ x < 137.5
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ANSWERS
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