Question

Which of the following are arranged from smallest unit to largest unit?
(A) cm, m, mm, km
(B) km, m, mm, cm
(C) cm, mm, m, km
(D) mm, m, cm, km
(E) mm, cm, m, km

Answer 1

Hint: All the given units are of length and the m at the end of the unit stands for meter. There are various prefixes which are used for describing certain values like centi, mili, kilo, etc.


Complete step by step solution:
All the units given here are of length. Let’s see what they mean in order to arrange them from smaller to larger ones.
mm: - mm stands for millimeters. The prefix milli stands for ${{10}^{-3}}$. Thus we can say that one millimeter is equal to $1\times {{10}^{-3}}$ m.
cm: - cm stands for centimeters. The prefix centi is used for ${{10}^{-2}}$. So, we can say that one centimeter is equal to $1\times {{10}^{-2}}$ m. Here, m is meter.
m: - Here, we can see that there is no prefix before m (meter), so it is the original unit, meter.
km: - km stands for kilometers. Here, the prefix used is kilo. Kilo stands for ${{10}^{3}}$. So, we can say that 1 km is equal to $1\times {{10}^{3}}$m.
Now, we have got the values of the units in terms of meter units. So, we can easily arrange them in increasing order and find out the order of the units.
The increasing order of the values obtained is:
\[1\times {{10}^{-3}}<1\times {{10}^{-2}}<1<1\times {{10}^{3}}\]
Thus, we can conclude that as we arrange the units given in the options starting from smaller to bigger units, we get the order as:
mm < cm < m < km

So, correct answer is (E).


Note: All the units given here differ from each other from the power of 10. Do not forget the sign of the power of 10. Such as kilo stands for ${{10}^{3}}$ while milli stands for ${{10}^{-3}}$. So, do not get confused between them and remember all the common prefixes used in units.