2. Required Basic Mathematical Skills
Rounding off whole
numbers to a specified
place value
Round off 1 688 to the
nearest hundred
1off 430 618 to the
700
Round
nearest thousand
431 000
3. Round off 30 106 correct to
the
nearest hundred.
0
3 0106
0<5
4. Round off 14.78
to the nearest whole number
+1
15. 7 8
4
Add I the decimals
Drop all to digit 4
Understand !!!
The first digit on the
right is greater than 5
5. Required Basic Mathematical Skills
Rounding off whole
numbers to a
specified number of
decimal places
Express 1.8523 to
three decimal places
1.852 to
Express 0.4968
two decimal places
0.50
6. Round off 5.316
to 1 decimal place
5 . 3 1 6
Do not
The first digit on the
change
Underline digit 3
right is less than 5
digit 3
st
(1 decimal place)
7. Round off 4.387
to 2 decimal places
+1
9
4.38 7
Add 1 todigit on
The first digit 8
Underline
8
the right is more
(2 nd decimal 5
than place)
12. FIX, SCI, RND
(Fix)
: Number of Decimal Places
1
(Sci)
2
: Number of Significant
Digits
(Norm) : Exponential of significant
Digits
3
13. Round off 5.316
to 1 decimal place
5x
MODE
Fix
1
1
Fix 0 ٨ 9 ? 1
5 . 3
= 5.3
1
6
14. Round off 5.316
to 2 decimal place
5x
MODE
Fix
1
1
Fix 0 ٨ 9 ?
5 . 3
= 5.32
5.32
1
6
2
15. Round off 4.387
to 2 decimal place
5x
MODE
Fix
1
1
Fix 0 ٨ 9 ?
4 . 3
= 4.39
4.39
8
7
2
16. Round off 4.387
to 1 decimal place
5x
MODE
Fix
1
1
Fix 0 ٨ 9 ?
4 . 3
= 4.4
4.4
8
7
1
17. Required Basic Mathematical Skills
Law of Indices
10m x 10n = 10m + n
10 ÷ 10 = 10
m
n
m -n
Simplify the following
103 x 10-5
10-2
102 ÷ 106
10-4
18. Very large and very small numbers are conveniently
rounded off to a specified number of significant figures
The concept of significant figures is another way
of stating the accuracy of a measurement
ignificant figures refer to the relevant digits in an integer
or a decimal number which has been rounded off to
a given degree of accuracy
20. The rules for determining the
number of significant figures in
a number are as follows:
All non-zero digits are significant
figures
2.73 has 3 significant figures
1346 has 4 significant figures
21. The rules for determining the
number of significant figures in
a number are as follows:
All zeros between non-zero are
significant figures
2.03 has 3 significant figures
3008 has 4 significant figures
22. The rules for determining the
number of significant figures in
a number are as follows:
In a decimal, all zeros after any
non-zero digit are significant
figures
3.60 has 3 significant figures
27.00 has 4 significant
figures
23. The rules for determining the
number of significant figures in
a number are as follows:
In a decimal, all zeros before
the first non-zero digit are
not significant
0.0032 has 2 significant figures
0.0156 has 3 significant
figures
24. The rules for determining the
number of significant figures in
a number are as follows:
All zeros after any non-zero
digit in a whole number are not
significant unless stated other
wise
1999 = 2000 ( one s.f )
25. The rules for determining the
number of significant figures in
a number are as follows:
All zeros after any non-zero
digit in a whole number are not
significant unless stated other
wise
1999 = 2000 ( two s.f )
26. The rules for determining the
number of significant figures in
a number are as follows:
All zeros after any non-zero
digit in a whole number are not
significant unless stated other
wise
1999 = 2000 ( three s.f )
27. State the number of significant figures in
each of the following
(a)
4 576
(b)
603
(c)
25 009
(d)
2.10
(a)
0.0706
(f)
0.80
4
3
5
3
3
2
32. hod of rounding off to a specified number of significant figur
Identify the digit (x) that is to be rounded off
Is the digit after x greater than or equal to 5
YES
Add 1 to x
NO
x remains unchanged
Do the digit after x lie before the decimal point?
YES (BEFORE)
Replace each digit with zero
NO (AFTER)
Drop the digits
Write the number according to the specified number of significant figures
33. Round off 30 106 correct to
three
significant figures.
0
3 0106
0<5
34. Round off 30 106 correct to
three
significant figures.
5x
MODE
3
=
Sci
2
0
2
1
Sci 0 ٨ 9 ?
0
3.01 x 10 44
3.01 x 10
30 100
30 100
6
3
35. Round off 0.05098 correct to
three
significant figures.
1 0 +1
0. 0 5098
8>5
00
0 . 0 51 9 8
36. Round off 0.05098 correct to three
significant figures.
5x
MODE
0
=
Sci
2
.
2
0
Sci 0 ٨ 9 ?
5
5.10 x 10-2
5.10 x 10-2
0.0510
0.0510
0
3
9
8
37. To clear the Sci specification……
5X
Press
MODE
Norm
3
Norm 1 ⱱ 2 ?
3
1
To continue the Sci specification……
ON
Press
38. Round off 0.0724789 correct to
four significant figures.
+1
8
0. 0 724789
8>5
8
0. 0 724789
39. Round off 0.0724789 correct to
four significant figures.
5x
MODE
Sci
2
2
Sci 0 ٨ 9 ?
0
.
=
7.248 x 10 -2
7.248 x 10 -2
0
7
0.07248
0.07248
2
4
4
7
8
9
40. Complete the following table (Round off to)
Number
3 sig. fig.
2 sig. fig.
1 sig. fig.
47 103
47100
47000
50 000
20 464
20 500
20 000
20 000
1 978
1 980
3.465
3.47
2 000
3.5
2
0003
70.067
70.1
70
70
4.004
4.00
4.0
4
0.04567
0.0457
0.046
0.05
0.06045
0.0605
0.060
0.06
0.0007805
0.000781
0.00078
0.0008
41. We usually use standard form for writing very large a
very small numbers
A standard form is a number that is written as the
product of a number A (between 1 and 10) and
a power of 10
A x 10n, where 1 ≤ A < 10, and n is an integer
42. Positive numbers greater than or equal
to 10 can be written in the standard form
A x 10n , where 1 ≤ A ≤ 10 and n is the
positive integer, i.e. n = 1, 2, 3,………
Example 58 000 000 = 5.8 x 107
43. Positive numbers less than or equal
to 1 can be written in the standard form
A x 10n , where 1 ≤ A ≤ 10 and n is the
negative integer, i.e. n = …..,-3, -2, -1
Example 0.000073 = 7.3 x 10-5
44. Express 431 000 in standard form
Express the number as a product of
A (1 ≤ A < 10) and a power of 10
A
Power of 10
431 000 = 4.31 x 100 000
4.31 x 105
=
431 000 = 4 3 1 0 0 0
4.31 x 105
=
5 is the number of places, the decimal point
is moved to the left
45. Express 431 000 in standard form
5x
MODE
4
=
Sci
2
3
2
1
Sci 0 ٨ 9 ?
3
0
0
4.31 x 1055
4.31 x 10
0
46. Express 0.000709 in standard form
Express the number as a product of
A (1 ≤ A < 10) and a power of 10
Power of 10
A
1
0.000709 = 7.09 x
10000
1
= 7.09 x
4
10
7.09 x 10-4
=
47. Express 0.000709 in standard form
0.000709 = 0 . 0 0 0 7 0 9
= 7.09 x 10-4
-4 is the number of places, the decimal point
is moved to the right
48. Express 0.000709 in standard form
5x
MODE Sci
2
2
Sci 0 ٨ 9 ?
0
.
=
7.09 x 10-4
7.09 x 10-4
0
0
0
3
7
0
9
49. Write the following numbers in standard
form
NUMBER
8765
32154
6900000
0.7321
0.00452
0.0000376
0.0000000183
STANDARD FORM
8.765 x 103
3.2154 x 104
6.9 x 106
7.321 x 10-1
4.52 x 10-3
3.76 x 10-5
1.83 x 10-8
50. Number in the standard form, A x 10n , can be
converted to single numbers by moving the decimal
point A
(a) n places to the right if n is positive
(b) n places to the left if n is negative
51. Express 1.205 x 104 as a single number
3.405 x 10
4
=3 . 4 0 5 0
Move the decimal point 4 places to the right
=34050
52. Express 3.405 x 104 as a single number
MODE
COMP
1
1
3 . 4 0
= 34 050
5
EXP
4
53. Express 7.53x 10-4 as a single number
7.53 x 10
-4
= 0 0 00 7.5 3
Move the decimal point 4 places to the left
= 0.000753
54. Express 7.53 x 10-4 as a single number
7 . 5 3
= 0.000753
EXP
(-)
4
55. Express the following in single numbers
STANDARD FORM
4.863 x 103
7.2051 x 104
4.31 x 106
5.164 x 10-1
1.93 x 10-3
2.04 x 10-5
9.16 x 10-8
NUMBER
4863
72051
4310000
0.5164
0.00193
0.0000204
0.0000000916
56. 3.25 X 105 = 325000
-5
7.14 X 10 = 0.0000714
4537000 = 4.537 X 106
0.0000006398 = 6.398 X 10-7
69. When two numbers in standard form are
multiplied or divided, the ordinary numbers
are multiplied or divided with each other
While their indices are added or subtracted
70. s
MA R T
a x 10 x b x 10
m+n
= (a x b) x 10
m
n
a x 10 ÷ b x 10
m-n
= (a ÷ b) x 10
m
n
71. 9.5 x 103 x 2.2 x 102
(9.5 x 2.2) x (103 x 102)
=
20.9 x 103+2
=
20.9 x 105
=
2.09 x 106
=
77. 1 km2 = (1000 x 1000) m2
= (103 x 103) m2
= 106 m2
78. The area of a piece of rectangular land is
6.4 km2. If the width of the land is 1600 m,
calculate the length, in m, of the land
Length of the land = Area
Width
6.4 x10 6
=
1.6x10 3
6.4
=
x103
1.6
3
= 4 x10 m
79. Round off 0.05098 correct to
three
significant figures.
+1
1 0
A
B
C
D
0.051
0.0500
0.0509
0.0510
0. 0 5098
8>5
00
0 . 0 51 9 8
80. Round off 0.05098 correct to three
significant figures.
5x
MODE
0
=
Sci
2
.
2
0
Sci 0 ٨ 9 ?
5
5.10 x 10 -2
5.10 x 10 -2
0.0510
0.0510
0
3
9
8
81. Round off 0.08305 correct to three significant
figures.
A
B
C
D
0.083
0.084
0.0830
0.0831
1 +1
0. 08305
5=5
0
0 . 0 8 31 5
82. Round off 0.08305 correct to three
significant figures.
5x
MODE
0
=
Sci
2
.
2
0
Sci 0 ٨ 9 ?
8
8.31 x 10-2
8.31 x 10-2
0.0831
0.0831
3
3
0
5
83. Round off 30 106 correct to
three
significant figures.
A
B
C
D
30 000
30 100
30 110
30 200
0
3 0106
0<5
84. Round off 30 106 correct to
three
significant figures.
A
B
C
D
30 000
30 100
30 110
30 200
5x
MODE
3
=
Sci
2
0
2
1
Sci 0 ٨ 9 ?
0
3.01 x 1044
3.01 x 10
30 100
30 100
6
3
85. Express 1.205 x 104 as a single number
A
B
C
D
1 205
12 050
1 205 000
12 050 000
MODE
COMP
1
1 2 0 50
1
1 . 2 0
= 12 050
5
EXP
4
86. Express 4.23 x 10-4 as a single number
A
B
C
D
0. 423
0. 0423
0. 00423
0. 000423
4 . 2 3
= 0.000423
EXP
(-)
4
87. Express 52 700 in standard form.
A
B
C
D
5.27 × 102
5.27 × 104
5.27 × 10−2
5.27 x 10-4
52 700
5x
MODE
5
=
Sci
2
2
2
7
Sci 0 ٨ 9 ?
0
5.27 x 1044
5.27 x 10
0
3