1. To approach the subject quantitatively
2. While selling or buying goods
3. During construction
4. For research

1. It gives one unit for one physical quantity.
2. It provides uniformity in measurement.

The relation between the horsepower (hp) and watt (W) is
1 hp = 746 Watt

=750 Watt (approx)

1. P =
2. P =
3. P = F x v ( v = velocity)
4. P =

Solution
(a) 500 mm = 500 /10 = 50 cm [10mm=1cm]

(b) 500 mm = 50
= 500/100 = 5m = 5x\(10^{-2}\) [100cm=1m]

(c)500 mm = 5x\(10^{-2}\)m
= 5x\(10^{-2}\)m / 1000 km = 5x\(10^{-6 }\) [1000m=1km]

10 kg = 10x1000 = 10000g= 1x \(10^{4}\) [1000gm=1kg]

Hence, 10 kg equals 1x \(10^{4}\)

2 hours, 10 minutes and 40seconds
= 2 x 60min+10min+40 s
= 120 min + 10min+40 s
= 130 x 60s + 40s
= 7800 + 40 s
= 7840 s
= 7.84 x \(10^{3}\) s

Hence, 2hr , 15 min and 30 sec equals 7.84 x \(10^{3}\) sec

Solution :
2,000,000,000,
= 2 x \(10^{9}\)

= 2.6 x \(10{^-9}\)

= 2 x 2.5 x \(10^{6}\) x \(10^{-3}\)

= 5.0 x \(10^{6-3 }\)

= 5 x \(10^{3}\)

= 3.5 x \(10^{12}\) x \(10^{-3}\) x \(10^{-3}\) x \(10^{-3}\) x \(10^{-3}\)\(km^{2}\) [1km= \(10^{3}\)m]

= 3.5\(km^{2}\)


Thus, 3.5 x \(10^{12}\)\(mm^{2}\) is equal to 3.5\(km^{2}\) .

= 4.91 x \(10^{4}\) x \(10^{3}\) x \(10^{3}\) x \(10^{3}\)\(m^{3}\)
= 4.91 x \(10^{13}\) x \(10^{2}\)x \(10^{2}\) x \(10^{2}\) x \(cm^{3}\)
= 4.91 x \(10^{19}\)\(cm^{3}\)


Thus, 4.91 x \(10^{4}\)\(km^{3}\) is equal to4.91 x \(10^{19}\)\(cm^{3}\)

Given,
Diameter of the volleyball (d) = 80cm
Radius of the volleyball (r) = \(\frac{80}{2}\) = 40cm = 0.4m
Volume of the volleyball (V) = ?

We know that,
V = \(\frac{4}{3}\ \pi\ r^{3}\)
= \(\frac{4}{3}\ \times\) \(\frac{22}{7}\) \(\times\) [ 0.4\(^3\) ]
= \(\frac{5.632}{21}\)
= 0.271
= 2,71 \(\times\) \(10^{-2}\) m\(^3\)

Hence, the volume of the volleyball is 2,71 \(\times\) \(10^{-2}\) m\(^3\)

Here.

Length = 22mm
Breadth = 155mm
Height = 10mm
We Know
Volume of rectangular Object = L \(\times\) B \(\times\) H
= 22 \(\times\) 155 \(\times\) 10
= 3.41 \(\times\) \(10^5\) \(m ^ -5\)


Again,

Area of book = Length \(\times\) breadth
= 3.41\(\times\) \(10^{-3}\) \(m ^2\)


Hence, the volume of the book is 3.41 \(\times\) \(10 ^5\) \(m^{-5}\) and the area os each sheet is 3.41\(\times\) \(10^{-3}\) \(m^2\).

given,
Length = 50cm
Radius = 4cm

We know,
Volume of Cylinder = π(radius)\(^2\) \(\times\) (length)
= 3.14 x 4\(^2\)\(\times\) 50
= 2512

Solution ;
512mm = 51.2 cm

= \(\frac{51.2}{100}\) m = 0.512m = 5.12 \(\times\) \(10^{-2}\)m

Thus 512m = 5.12 \( \times \;10^{-2} \)m

Solution ;

1hour = 60min
\(\therefore\) 1 hour = 3600 sec

Now,
3600 \(\times\) 4.6
= 16560s

\(\therefore\) 4.6 hours =16560s

Solution;
12kg = 12 \(\times\) 1000g
= 12000g
= 1.2 \(\times\) \(10^{4}\) g [\(\therefore\)1000gm = 1kg]

Hence, 12kg equals 1.2 \(\times\) \(10^{4}\) g

Solution:

Now,
1kg = 1000000mg

So,
= \(\frac{120}{1000000}\)
= 1.2 \(\times\) \(10^{-5}\)kg

\(\therefore\) 120 milligrams equals 1.2 \(\times\) \(10^{-5}\)kg

Solution:
1min= 60 seconds
1hr = 60 minutes
So,
50 hours = 50 \(\times\) 60 (\times\) 60

= 180000S

\(\therefore\) 50 hours equals 180000Seconds.

Solution:

1kg = 1000g
6.2 x 1 kg = 6.2 x 1000 g {Multiplying both sides by 6.2}
6.2 kg = 6200g

Solution:
1 \(\times\) \(10^{16}\)
= \(10^{16}\)

Solution :

1 \(\times\) 1. \(10^{10}\) = 1. \(10^{10}\)

Solution:
= 2.3 \(\times\)5 \(\times\) 10 \(^7\) \(\times\) \(10^{-2}\)

= 1.15 \(\times\) \(10^{6}\)

Solution:

Here,
Area of room = 36\(m^{2}\)
Length of room = 6m

We know that,
Area of rectangular room = L \(\times\) B

or, 36 = 6 \(\times\) b
or, b = \(\frac{36}{6}\)
or, b = 36m

Hence, Its breadth is 36m.