Question

Convert $4cm$ $38m$ into decimeters.
A.$384dm$
B.$380.4dm$
C.$420dm$
D.$38.04dm$

Answer 1

Hint: We know that meter and deci - meters are the units of length. But why do we need different units for the same quantity? The answer is simple, for Longer distances, the bigger unit is better suited and for shorter distances, smaller unit is suited. All we need to know is the conversion from one unit to the other.

Complete step-by-step answer:
Length is one of the most widely used fundamental quantities. The SI unit of length is meters. Meter is defined as the path travelled by light in vacuum during a time interval of ${{\left( \dfrac{1}{299792458} \right)}^{th}}$ part of a seconds.
Deci meter is a much smaller quantity to measure length. There are units to measure the length, for example: miles, foot, inch, etc.
Over here, we need to convert $4cm$ $38m$ to deci - meter.
The conversion scale is the most important factor to answer this question.
For this conversion, we need a scale to convert meter to deci - meter. So, by the definition of deci:
$deci=0.1$ .
Hence, $1dm=0.1m$ . - (1)
Therefore, $1m=10dm$ - (2)
Multiplying – (2) with $38$ :
$38\left( 1m=10cm \right)$
$\Rightarrow 38m=380dm$
Therefore, $38m\And 4cm=380.4dm$
Hence, option B. $380.4dm$, is the correct option.

Note: We must always remember the correct conversion scale in the conversion from one unit to the other. We must be very careful in writing the conversion scale, and not to confuse conversion scale with some other scale. Different units are used to measure different amounts of quantities. For length, two very different units are Kilometers and Miles. We can only compare or convert things of the same quantities.