Question

Find the product of the following \[6\,\text{km}\,5\,\text{hm}\,3\,\text{dam}\,4\,\text{m}\] by 12.

Answer 1

Hint: First convert all the terms into the same units and then do the multiplication. The standard unit of measuring length is , which can be converted into other prefixes units. Each step is ten times or one-tenth of the standard unit.

Complete step-by-step answer:
Given expression is \[6\,\text{km}\,5\,\text{hm}\,3\,\text{dam}\,4\,\text{m}\].
The other unit prefixes of the unit are \[\text{kilo}\], \[\text{hecta}\], \[\text{deca}\], \[\text{deci}\], \[\text{centi}\], and \[\text{milli}\].
Now, \[1\,\text{km} = 1000\,\text{m}\]
\[1\,\text{hm} = 100\,\text{m}\]
\[1\,\text{dam} = 10\,\text{m}\]
Using the above conversion, the expression is simplified as,
\[\begin{align*}6\,\text{km}\,5\,\text{hm}\,3\,\text{dam}\,4\,\text{m} &= (6\times 1000)\,\text{m}+(5\times 100)\,\text{m}+(3\times 10)\,\text{m}+4\,\text{m}\\ &= (6000+500+30+4)\,\text{m}\\ &= 6534\,\text{m}\end{align*}\]
So, \[6534\,\text{m}\] when multiplied by 12 gives,
\[6534\,\text{m}\times 12 = 78,408\,\text{m}\]

Note: The given expression can be also simplified by converting them into any of the given prefixes Kilo ,hecto and deca using the above conversion.
Km- Kilometer hm- hectometer dec- decameter