Question

Express the following into International 
System of Units (S.I.) : 

(i) 90 million miles (Distance between Earth and Sun) 

(ii) 90 miles/hour (Speed of Rajdhani Express Train) 

(iii) 5 Feet 6 inches (Average length of Indian males) 

Answer 1

(i) 90 millon miles - S.I. unit of distance is metre. 

So, 

1 mile = 1.60 km 

= 1.60 × 10³ metre 

= 1.60 × 10³ m 

Conversion coefficient 

\( = \frac{1.60\times10^3\ m}{1mile}\)

For 90 million miles = 90 x 10⁶ miles 

= 90 x 10⁶ miles × conversion coefficient 

\(= \frac{90\times 10^6\ miles\times 1.6\times 10^3\ m}{1 mile }\) 

= 90 × 1.6 × 10⁶ m 

= 1.44 × 10¹¹ metre 

(ii) 90 miles per hour 

1 mile = 1.6 km = 1.6 × 10³ 

Conversion coefficient = \(\frac{1.6\times10^3\ m}{1mile}\)

1 Hour = 60 × 60 s = 3.6 × 10³s 

Conversion coefficient = 

= 40 m/s

(iii) 5 Feet 6 inches = 5 × 12 + 6 = 66 inches 
1 inch = 2.54 × 10^-2 m 

Conversion coefficient = \(\frac{10^{-2}\ m}{inches}\) 

66 inches = 66 inches × conversion coefficient 
= 66 × 2.54 × 10^-2 m 

= 167.64 × 10^-2 m 

= 1.68 m