Question

How many meters are there in 1,865 cm? \[\]

Answer 1

Hint: We recall that 1 metre is 100 cm or 100 cm is 1 m. We apply a unitary method for direct variation and find how many meters are there in 1 cm by dividing 1 by 100. We then multiply 1,865 to the result to get the answer. \[\]

Complete step by step answer:
We know that the unitary method when one quality $a$ increases with another quantity $b$ and also $a$ decreases with $b$ then we say the quantities $a$ and $b$ are in direct variation. Here the fraction $\dfrac{a}{b}$ always remains constant. We divide the increasing quantity $a$ by $b$ to obtain the value of a single unit and then multiply to find the required value.
 We also know that metre and centimetre(cm) are units to measure length. 1 metre has 100 cm which means 100 cm has 1m. Since more cm is more metres the problem is in direct variation. So we first find the value of single unit by dividing 1m by 100cm to have
\[\dfrac{1}{100}\text{m}=0.01\text{ m}\]
We are asked to find the number of metres 1,865 cm. So we multiply 1865 with single unit value to have
\[1865\times 0.01\]
We know how to multiply decimals. We forget the decimals and multiply the numbers to get $1865\times 1=1865$. We put the decimal point in as many places from right as there are in multiplying decimal numbers after the decimal point which here is 2 because $0.001$ has 2 digits after decimal point. . So the result is
\[1865\times 0.01=18.65\text{ m}\]

Note: We can directly convert by dividing the given measurement in cm to metre by 100. So we have $1865\text{ cm}=\dfrac{1865}{100}\text{ m}$. We recall how to divide by $10,100,1000$. We put decimal points as many places from right as many 0s are there in the divisor of type $10,100,1000$ of the number. Since 100 has two zeros we put decimal point 2 places from right and have
\[1865\text{ cm}=\dfrac{1865}{100}\text{ m}=18.65\text{ m}\]