Transcript Rounding to 1 Significant Figure

Learning Objective:
I will learn…
How to round to whole
numbers , decimal
places and significant
figures.
Key words:
Square
My Learning Outcome…
Triangle
I will apply my learning I will evaluate
my
trapezium
by…
learning by…
Rounding .
Explaining to your
partner how to round
to 1 significant figure?
L7:
Application Tasks…
L4
Rounding to nearest 10 or
100.
L5
Rounding to decimal
places. L6
Rounding to significant
figures.
Be bale to understand
standard form.
Learn
L4
Rounding – to the nearest 10
4832
No
5 or
more?
4830
4837
Yes
5 or
more?
4840
195
Yes
5 or
more?
200
Apply
15823
5 or
1
No
5872
15820
0  Copy &
5900
Yes
more?
Your Turn
L4
Rounding – to the nearest 100
Number
complete
this table:
89
5 or
more?
Yes
5 or
more?
100
To nearest
10 37520
To nearest
100 37500
37 521
To nearest
1000
38000
274500
274500
274 503
275000
7630920
7630900
7631000
9880
450
9900
10000
500
0
7 630
918
9 875
452
Learn
Rounding to 1 Decimal Place (1DP)
4.832
5 No 5 or
4.842
5 No 5 or
4.8
4.8
4.87
5.2671
4 Yes 5 or
more?
Yes
4.9
5 or
more?
more?
4.852
Yes
5 or
more?
4.9
more?
5.3
L5
1.967
Yes
2.0
5 or
more?
Learn
L5
Rounding to Decimal Places: 2DP
4.832
5 No 5 or
4.846
4.83
4.85
more?
Yes
5 or
more?
more?
4.8
1.694
9 No 5 or
5.267
1 Yes 5 or
1.69
5.27
more?
4.8595
1 Yes 5 or
6
1.897
Yes
more?
1.9
0
5 or
more?
Learn
L5
Rounding to Decimal Places: 3DP
4.832
5 Yes 5 or
4.846
2 No 5 or
4.859
5 Yes 5 or
4.833
4.846
4.86
more?
more?
1.694
2 No 5 or
5.262
7 Yes 5 or
1.694
5.263
more?
more?
0
1.999
9 Yes 5 or
more?
more?
2.00
0
Rounding to Decimal Places
Apply
4.852
5 or
more?
Yes
4.9
Your Turn
1DP
1.694
9 No 5 or
more?
1.69
 Copy &
Number
complete
this table: 63.4721
D
2DP
5.262
7 Yes 5 or
3DP
more?
5.263
To 1DP
To 2DP
To 3DP
63.5
63.47
63.472
87.6564
87.7
87.66
87.656
149.9875
150.0
149.99
149.988
3.54029
3.5
3.54
3.540
0.59999
0.6
0.60
0.600
L6
Learn
Significant Figures: Important Zeros in Numbers
a.
5 2 0
0 0
b.
5 .
2
0 0
c.
0 .
0
5 0
d.
0 2
.
5 0
Which zeros
matter?
Are there any
we could get
rid of and still
have the same
value?
When dealing with
Significant Figures, you
need to keep any zeros
that tell us the value of a
number
Learn
Rounding to 1 Significant Figure (1SF)
0.076
5 Yes 5 or
0.001
2 No 5 or
0.08
0.001
more?
241
No
L6
5 or
more?
200
more?
587
Yes
5 or
more?
600
1.009
5 No 5 or
more?
1
75
Yes
5 or
more?
80
Learn
Rounding to 2 Significant Figure (2SF)
1472
Yes
5 or
more?
1500
42728
Yes
L6
5 or
more?
43000
1.427
9 No 5 or
0.053
5 Yes 5 or
more?
more?
1.4
0.05
20447
8 No 5 or
4
0.069
6 Yes 5 or
more?
more?
200000
0.07
0
Learn
Rounding to 3 Significant Figure (3SF)
0.0267
1 No 5 or
3.294
9 No 5 or
0.026
7
13798
3.29
more?
Yes
L6
5 or
more?
13800
34728
No
more?
5 or
more?
3470
97497
8 Yes 5 or
more?
975000
0
12.06
9 Yes 5 or
more?
12.1
Rounding to Significant Figures
Apply
0.076
5 Yes 5 or
1SF
2SF
42728
more?
Your Turn
0.08
more?
43000
 Copy &
Number
complete
6.3528
this table:
C
5 or
more?
Yes
12.06
9 Yes 5 or
To 1SF
3SF
12.1
To 2SF
To 3SF
6.35
6.4
6
34.026
34.0
34
30
0.005708
0.00571
0.0057
0.006
150.932
151
150
200
0.0000783
5
0.0000784
0.000078
0.00008
You need to understand about powers of
Learn
10.
Try these to test your previous knowledge.
10-1
102
101
106
105
103
10-2
10-3
Remember this?
104
100
se the worksheet “powers of ten” for further explanation
Learn
Standard Form is used a lot in maths and
science as a convenient way of writing very
large, or very small numbers
for example:
The distance from the earth to the sun is
149 000 000 km
huge!
A hydrogen atom has a diameter of about
0.000 000 2 mm
microscopic!
Learn
Let’s deal with large numbers first.
Look at how these numbers have been broken dow
500
= 5 × 100
= 5 × 102
5000 = 5 × 1 000
= 5 × 103
50 000 = 5 × 10 000
= 5 × 104
you know how to write
these as powers of 10
Learn
What about these?
= 5.5 × 102
550
= 5.5 × 100
5 500
= 5.5 × 1 000 = 5.5 × 103
4
=
5.5
×
10
000
=
5.5
×
10
55 000
Learn
Put these numbers into standard form:
6 000
400
80 000
9 000
=6×
103
4 000 = 4 × 103
= 4×
102
450
= 8×
104
= 9 × 103
4 00 000 = 4 ×
105
= 4.5 × 102
= 5.5 × 104
55000
3500 = 3.5 × 103
750 000= 7.5 × 105
Learn
Standard form is:
a number
between 1
and 10
×
a power
of ten
Apply
Now try writing these numbers in standard form
5 000 000
= 5 × 106
5 500 000
= 5.5 × 106
5 250 000
= 5.25 × 106
5 100 000
= 5.1 × 106
5 156 342
= 5.156342 × 106
Learn
Reverse!
Change each of these numbers
to an ordinary number
6×
102
2.8 × 101
2×
103
9.9 × 1010
5×
107
7.1 × 104
9×
108
3.97 × 102
3.7 ×
109
8.172 × 102
Learn
The next stage is to write very
small numbers, i.e. numbers less than 1
Check that you understand about
negative powers of 10
0.001 =
0.1 = 1 = 10-1
10
0.00001 =
0.01 =
0.0001 =
Apply
Write in standard form:
0.007
0.006 7
0.04
0.000 000 002 34
0.000 000 005
0.006 7
0.0234
0.3
0.000 002 3
0.000 045
*
3.5 × 10-1
4.5 × 10-4
7.2 × 10-5
6.1 × 10-3
1.17 × 10-10
Apply
Change each of these to a large or small number:
5.5 ×
10-6
1.115 × 104
6.5 ×
10-8
1.412 × 10-3
3.2 ×
105
7.2 × 101
2.9 ×
102
9.01 × 10-2
3.167 ×
10-11
1.17 × 106
Apply
* How do you round to the nearest Significant
figure?
*