This document provides information about units, prefixes, and scientific notation used in the metric system. It defines the seven base SI units for mass, length, time, electric current, temperature, amount of substance, and luminous intensity. It also describes the prefixes that are multiplied with the base units to indicate decimal multiples and submultiples, such as kilo, mega, milli, and micro. Several examples are provided to demonstrate converting between numeric values and scientific notation with prefixes.
2. – F ˆ F www.schoolDD.com 1
1
ˈ F ʽ F F
F F F F F F
F F F F F
F F F F F ˈ F ʽ F
1.1 ʽ F F
ʽ F F F
F ʽ F ˈ F
F F F F F F F ˈ F
F
F F F F F F
F F F F F
F F F F F
ʽ F ˈ F F F
1.2 F SI
F 7 F F F (m), (kg), (s), F (A), (K),
(mol) (cd)
F F F F F F (N) = kg.m/s2
, (J) = N.m = kg.m2
/s2
1.3 F F (Prefix)
F F F F F F F F
F F 1 F F 1000 ˈ F F
F F 1000 103
F F F F F F F
(1012
), (10-12
), (109
), (10-9
), (106
), (10-6
)
(103
), (10-3
), (102
), (10-2
), (101
), (10-1
)
F F F F F ˈ F ˈ F F , ,
, , , F F F
3. – F ˆ F www.schoolDD.com 2
F F F F 103
F F 103
F 106
109
1012
F F F 101
F
102
101
F F ˈ F F ... F ˈ ....
1012
10-12
109
10-9
106
10-6
103
10-3
102
10-2
101
10-1
F 1
F
. 4,700,000,000 F ˈ
F F F 1 = 106
F ˈ (10-6
x 106
) F
F 1 F F F ...
∴ 4,700,000,000 x (10-6
x 106
) = 4,700 x 106
= 4,700 Mm Ans
. F F F F 0.0004 F
1 = 10-3
∴ 0.0004 x (103
x 10-3
) = 0.4 x 10-3
= 0.4 mm Ans
. 0.5
1 = 103
∴ 0.5 = 0.5 x 10-3
= 0.5 x 10-3
x (10-3
x 103
)
= 0.5 x 10-6
x 103
= 0.5 x 10-6
kg Ans
. 1 ,
1 = 10-2
∴ (1 )2
= (10-2
)2
= 10-4 2
1 = 10-4
Ans
4. – F ˆ F www.schoolDD.com 3
1 F F 101
(1 )2
= (101
)2
= 102 2
1 = 102
Ans
F F F Hard Disk F , F F
?
1.4 F
1.
F F F F F F F F F F
s = ut +
ଵ
ଶ
at2
F F m =
୫
ୱ
x s +
୫
ୱమ
x s2
F m = m + m
2.
F F F ˈ F F F F
F F
F a =
୴ି୳
୲
F F
୫
ୱమ
=
ౣ
౩
ି
ౣ
౩
ୱ
F
୫
ୱమ
=
୫
ୱమ
F F F F T = 2πට
ℓ
F F s = ට
୫
ౣ
౩మ
= √sଶ
F s = s
1.5 F F
(error) F F
F F
F A ˈ F F A ˈ F + A
ˈ A + A
F F F F F 70 + 0.2 F F
ˈ F F F 69.8 70.2
5. – F ˆ F www.schoolDD.com 4
- F
F R = A +/- B
R = A + B
F = ( A +/- B ) + ( A + B )
F R = A +/- 2B
R = A + 2 B
F = ( A +/- 2B ) + ( A + 2 B )
- F F (%) F F F (%)
F
F R = A x/ൊ B
R = (
x100 +
x100 ) %
F = ( A x/ൊ B ) + (
x100 +
x100 ) %
F R = A x/ൊ B2
R = (
x100 +
ଶ
x100 ) %
F = ( A x/ൊ B2
) + (
x100 +
ଶ
x100 ) %
F R = A x/ൊ √B
R = (
x100 +
ଶ
x100 ) %
F = (A x/ൊ √B ) + (
x100 +
ଶ
x100 ) %
F 2
F 12.44 + 0.01 . F ˈ 2 F F 4.52 + 0.02 F
F
F F R = A B
F F R = ( A B ) + ( A + B )
6. – F ˆ F www.schoolDD.com 5
= ( 12.44 - 4.52 ) + ( 0.01 + 0.02 )
R = 7.92 + 0.03
∴ F F = 7.92 + 0.03 . Ans
F 3
F ˈ F F 1.20 + 0.01 ˈ F F
ˈ F F
V = W x L x H
F F V = (W x L x H ) + (
x100 +
x100 +
ୌ
ୌ
x100 ) %
= (1.20 x 1.20 x 1.20) + (
.ଵ
ଵ.ଶ
x100 x 3 )%
= 1.73 + 2.5 %
V = 1.73 + (
ଵ.ଷ ୶ ଶ.ହ
ଵ
)
F V = 1.73 + 0.043 3
Ans
+ 0.043 ˈ 2.5 % Ans
F 4
F F F (ℓ) ˈ 40.0 + 0.2 . F F F
T = 2πට
ℓ
F F ( g = 10 m/s2
)
T = 2πට
ℓ
F F T = 2πට
ℓ
+ (
ℓ
ଶℓ
x 100 ) %
= 2 x (22/7) x ට
.ସ
ଵ
+ (
.ଶ
ଶ୶ସ
x 100 ) %
= 1.256 + 0.25 %
T = 1.256 + (
ଵ.ଶହ ୶ .ଶହ
ଵ
)
F F T = 1.256 + 0.003 s Ans
7. – F ˆ F www.schoolDD.com 6
F 5
F F F 1.00 + 0.01 F F ˈ
F F
V = 4/3 x π x (d/2)3
F F V = 4/3 x π x (d/2)3
+ (
ଷ ୢ
ୢ
x 100 ) %
= 4/3 x (22/7) x (1.00 /2 )3
+ (
ଷ ୶ .ଵ
ଵ.
x 100 ) %
= 0.523 + 3 %
V = 0.523 + (
.ହଶଷ ୶ ଷ
ଵ
)
V = 0.523 + 0.02 m3
Ans
ˈ 3 % Ans
1.6
F
. + .
F F F
F 6 F 4.25 + 0.01 .
F F 4.2
( ) 5
0.1 .
F 0.01 .
F ˈ F F F 4.24 . 4.26 .
1 2 3 4 5 6
F F 4.2 + F 0.05
= 4.25
8. – F ˆ F www.schoolDD.com 7
1. F F F F F 0 F F
F 0.671 , 4.03 , 0.043 , 20.00 , 0.40 , 0.0003 3 , 3 , 2 , 4 , 2
1
2. F F F F F F 0 F F 15 , 136 , 4245 , 70324 ,
2001 2 , 3 , 4 , 5 4
3. F F F F 0 F A x 10n
1 A ൏ 10 10n
F ˈ F 12000 F ˈ 1.2 x 104
, 1.20 x 104
, 1.200 x 104
, 1.2000
x 104
2, 3, 4, 5
F F F
F F
3.21 + 4.156 = 7.366 ˈ 7.37 ( F 3 5
ˆ F F 5 ˆ )
5354 - 21.6 = 5332.4 ˈ 5332
F F F
F F
2.34 x 100.9 = 236.106 ˈ 236
7.3 ÷ 874 = 0.0083524 ˈ 0.0084
537.13 x 4.5 = 2417.085 ˈ 2.4 x 103
1.7 F
F F F F ˈ F
F F y = mx + c x ˈ y ˈ
ˈ y ˈ x F m = y/ x c ˈ y (y x
F y2
, y½
, 1/y x2
, x ½
, 1/x F )
F F F F F ˈ F F F
F F F F F F
c
x
y = mx + c
y
F
y = mx + c
x
xy = k y =
୩
୶
y
F
y =
௫
k F
9. – F ˆ F www.schoolDD.com 8
1.8 F ʽ F
ʽ F F F F F F ʽ F F F
F ˈ ˈ F F F ˆ F ʽ F F F F
ˈ ʽ F
1.8.1 F F F F F F F
F
F
C
c
F 2 F ോോ F F F
a
a
a
∆ F F = 180/3=60°
a/b = A/B
a/c = A/C
b/c = B/C
B
A
θ
b
a
θ
θ
θ
θ
θ
α
α
α
α
∆ F 180°
θ
90-θ
θ
θ
θ
θ
10. – F ˆ F www.schoolDD.com 9
1.8.2 F
α
θ
b
a
c
F sin , cos , tan
sinθ =
ୟ
ୡ
sinα =
ୠ
ୡ
cosθ =
ୠ
ୡ
cosα =
ୟ
ୡ
tanθ =
ୟ
ୠ
tanα =
ୠ
ୟ
tanθ =
ୱ୧୬
ୡ୭ୱ
sin2
θ + cos2
θ = 1
√2
60
30
√3
1
2
45
1
1
53
37
4
3
5
(slope) =
୷మି୷భ
୶మି୶భ
= tan θ
x
y
(+)
x
y
(-)
x
y
x
y
1>2>3
3 =0
4 ˈ -
4
3
2
1
x
y
x
y
F =(k)xy
c2
= a2
+b2
c = √aଶ bଶ
x
y
y =mx + c F
c
y
θ
(x1 , y1)
(x2 , y2)
x
y
11. – F ˆ F www.schoolDD.com 10
1.8.3 F
1.
ଵ
ୟ౮
= a-x
, ax
.ay
= a(x + y)
,
ୟ౮
ୟ౯
= ax
.a- y
= a(x - y)
, a0
= 1
2. F log a = x F a = 10x
F ln a = x F a = ex
log(a.b) = log a + log b
log(a/b) = log a - log b
1.8.4
1. F ax2
+ bx + c = 0 F x =
ିୠേ√ୠమିସୟୡ
ଶୟ
2. F x2
a2
= 0 (x a)(x + a) = 0 F x = +a x = -a
3. F (x a)2
= 0 x2
2ax + a2
= 0 (x a)(x - a) = 0 F x = +a
4. F (x + a)2
= 0 x2
+ 2ax + a2
= 0 (x + a)(x + a) = 0 F x = -a
5. F x2
- 4 x - 12 = 0 (x - 6)(x + 2) = 0 F x = 6 , -2
1.8.5 F
1. 5 = (3+t)2
5-3 = 2t or
2. y = 3x + 2√3 x
y = 5√3 x or
3. 2x3
= 4x2
- (3x + x2
)x x F ?
4. y = 3x + 2 x y F ?
1.8.6 F F
1. F a ן b
ୟభ
ୟమ
=
ୠభ
ୠమ
2. F a ן
ଵ
ୠ
ୟభ
ୟమ
=
ୠమ
ୠభ
3. F A x B = C x D A < C F B > D
4. D
ଡ଼
= P F F F X F F F F ?
5. A
ହమ
େିଵ
= (N
ଵ
ଶ
) X A
ଷమ
େିଵ
= (6 - N) Y F N = 3 F X ˈ F Y ?
12. – F ˆ F www.schoolDD.com 11
1.8.7 F F F ˈ F
F ˆ F F F F F F F F ˆ
F F F F ˈ F ʾ F ˈ 44 ʾ
F F F 5 ʾ F F 2 ʾ F ˆ F F
F ˆ = A ʾ
F = B ʾ
= C ʾ
ʾ F ˈ 44 ʾ F ˆ ˈ
44+1+1+1 = 47 ʾ
F F F A + B + C = 47 ----(1)
F F F 5 ʾ
F F F B - A = 5 ----(2)
F F 2 ʾ
F F F B - C = 2 ----(3)
F F F F F 3 3 F F F F
F F 3 A C F B
(1) + (2) + (3) , (A+B+C) + (B-A) + (B-C) = 47 + 5 + 2
3B = 54
B = 18
F B (2) F A F B - A = 5
18 - A = 5
18 - 5 = A
A = 13
F B (3) F C F B - C = 2
18 - C = 2
18 - 2 = C
C = 16
ˆ F 13, 18 16 ʾ Ans
F F F F F F F ˇ F ʽ F F
! F F F F F F F F F F ˆ
ʽ F F