Question

Convert 100 millimeters to meter.

Answer 1

Hint:We know that one of the basic relationship in mathematical units is:\[1{\text{m}} = 1000{\text{mm}}\]
So using this basic knowledge we can solve this question. We first have to find the general relation of 1mm and 1m and then we have to apply that for the given value.

Complete step by step answer:
Given, \[100{\text{mm}}................................\left( i \right)\]
We know that the unit millimeter is a unit of length in the metric system and its equivalent to one thousandth of a meter. Such that \[1{\text{m}} = 1000{\text{mm}}\].Now we have to convert the given value \[100{\text{mm}}\] into meters.For that we first have to find the general relation of 1mm and 1m. Then we have to use that relation and thus find the value 100 millimeters in meters.Now let’s try to find the general relation of 1mm and 1m.We know that:
\[1{\text{m}} = 1000{\text{mm}}......................\left( {ii} \right)\]
Let’s divide LHS and RHS with 1000 such that we can find the value of $1{\text{mm}}$.
Such that:
\[1{\text{m}} = 1000{\text{mm}} \\
\Rightarrow \dfrac{1}{{1000}}{\text{m}} = \dfrac{{1000}}{{1000}}{\text{mm}} \\
\Rightarrow {\text{1}}{{\text{0}}^{ - 3}}{\text{m}} = 1{\text{mm}} \\
\Rightarrow 1{\text{mm}} = {\text{1}}{{\text{0}}^{ - 3}}{\text{m}}.....................\left( {iii} \right) \\ \]
Now from (iii) we have got the general value of $1{\text{mm}}$.Such that we can find the value of \[100{\text{mm}}\] in meters by using the relation in (iii). We have \[1{\text{mm}} = {\text{1}}{{\text{0}}^{ - 3}}{\text{m}}\] so for finding the value of \[100{\text{mm}}\] we just have to multiply the LHS and RHS in (iii) with $100$.So we can write:
\[\Rightarrow 1{\text{mm}} = {\text{1}}{{\text{0}}^{ - 3}}{\text{m}} \\
\Rightarrow {\text{100mm}} = {\text{100}} \times {\text{1}}{{\text{0}}^{ - 3}}{\text{m}} \\
\Rightarrow {\text{100mm}} = {\text{1}}{{\text{0}}^{ - 1}}{\text{m}} \\
\therefore {\text{100mm}} = 0.1{\text{m}}..........................\left( {iv} \right) \\ \]
Therefore on converting \[100{\text{ millimeters}}\] to meter we get \[0.1{\text{m}}\].

Note:While approaching similar conversion questions the above method is widely preferred.Also meter is the unit of length in the metric system and it is also the basic unit of length in the International System of Units (SI). Millimeter is a unit of length in the metric system and its equivalent to one thousandth of a meter.