Question

Complete the following table. [Ratio is comparison of quantities expressed in same units]
Fill this first
1 rupee = _____ paisa
1000 g = ______ kg
1 hour = ______ min
100 cm = ______ m
1 minute = ______ sec
10 mm = ________ cm

Answer 1

Hint- Here, we will be using the formulas for unit conversion in order to represent the ratio of two quantities given in different units in terms of the ratio of two quantities which are in the same units so that we can cancel these units with each other.

Complete step by step answer:
1 rupee = 100 paise
1000 g = 1 kg
1 hour = 60 min
100 cm = 1 m
1 minute = 60 sec
10 mm = 1 cm
In the below evaluation, the second last term represents the ratio and the last term represents the simplified ratio.
As we know that for two quantities a and b, the ratio between them is expressed as $\dfrac{a}{b}$ = a:b
For the first row of the table, \[\dfrac{{20{\text{ paisa}}}}{{\operatorname{Re} {\text{ 1}}}} = \dfrac{{20{\text{ paise}}}}{{1 \times 100{\text{ paise}}}} = \dfrac{{20{\text{ paise}}}}{{100{\text{ paise}}}} = \dfrac{{20}}{{100}} = \dfrac{1}{5}\]
For the second row of the table, \[\dfrac{{800{\text{ g}}}}{{{\text{1 kg}}}} = \dfrac{{800{\text{ g}}}}{{1 \times 1000{\text{ g}}}} = \dfrac{{800{\text{ g}}}}{{1000{\text{ g}}}} = \dfrac{{800}}{{1000}} = \dfrac{4}{5}\]
For the third row of the table, \[\dfrac{{{\text{1 hr}}}}{{{\text{30 min}}}} = \dfrac{{{\text{1}} \times {\text{60 min}}}}{{{\text{30 min}}}} = \dfrac{{60{\text{ min}}}}{{{\text{30 min}}}} = \dfrac{{60}}{{30}} = 2\]
For the fourth row of the table, \[\dfrac{{{\text{2 m}}}}{{{\text{125 cm}}}} = \dfrac{{2 \times 100{\text{ cm}}}}{{{\text{125 cm}}}} = \dfrac{{200{\text{ cm}}}}{{{\text{125 cm}}}} = \dfrac{{200}}{{125}} = \dfrac{8}{5}\]
For the fifth row of the table, \[\dfrac{{{\text{3 min}}}}{{{\text{45 sec}}}} = \dfrac{{3 \times 60{\text{ sec}}}}{{{\text{45 sec}}}} = \dfrac{{180{\text{ cm}}}}{{{\text{45 cm}}}} = \dfrac{{180}}{{45}} = \dfrac{4}{1}\]
For the sixth row of the table, \[\dfrac{{{\text{30 mm}}}}{{{\text{1 cm}}}} = \dfrac{{{\text{30 mm}}}}{{{\text{1}} \times {\text{10 mm}}}} = \dfrac{{{\text{30 mm}}}}{{{\text{10 mm}}}} = \dfrac{{30}}{{10}} = \dfrac{3}{1}\]

Note- In this particular problem, we will get the same results if we would have converted both the units in Re given in the first row, kg in the second row, hr in the third row, m in the fourth row, min in the fifth row and cm in the sixth row. This will complicate the calculation a little bit in order to avoid this division, we have proceeded in a way shown in the solution.