This document provides information about units, prefixes, and formulas in the metric system. It includes: 1. Explanations of the seven base SI units - meter, kilogram, second, ampere, kelvin, mole, and candela. 2. Descriptions of the prefixes used to denote powers of ten when multiplying or dividing units, such as kilo (103) and milli (10-3). 3. Examples of calculations using prefixes to convert between units, like converting 4,700,000,000 meters to 4,700 kilometers. The document also contains sections on error analysis in measurements, kinematic formulas, and dimensional analysis.

1. www.schoolDD.com
1
SchoolDD.com  

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
ହ୆మ
େିଵ
= (N
ଵ
ଶ
) X A
ଷ୆మ
େି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