Question

Thickness of a thick paper is $ 0.07 $ mm or $ 7 \times {10^{ - m}} $ mm. What is the value of m ?

Answer 1

Hint: Here this question belongs to the conversion topic that is we have to represent the unit in scientific notation. Here we have to convert the unit millimetres to the unit metres. In the question, we have to find what number of metres correspond to the given number of metres or to represent the given number of millimetres in scientific notation.

Complete step by step solution:
The metres and millimetres are the units to measure the length of physical commodities or items. A metre is abbreviated as m and millimetre is abbreviated as mm. A millimetre is a metric unit of length and it is used for measuring small lengths.
We know that each metre of length consists of $ 1000 $ millimetres. So,
 $ 1m = 1000mm $ .
Hence, we are given the thickness of the paper as $ 0.07 $ mm.
We have to represent the thickness of the paper in scientific notation and then find the power of ten that is given to us as m in the question.
So, thickness of the paper
 $ = 0.07 $ mm $ = 7 \times {10^{ - 2}}\;mm - - - - - - \left( 1 \right) $
So, According to the question,
Thickness of the paper $ = 7 \times {10^{ - m}}mm - - - - - - \left( 2 \right) $
Hence, equating equations $ \left( 1 \right) $ and $ \left( 2 \right) $ , we get,
 $ m = 2 $
Hence, the value of m is $ 2 $ .
So, the correct answer is “2”.

Note: We have different units for solid quantity, liquid quantity and gaseous quantity. Every quantity has a measurement unit from the low quantity to the high quantity. While converting the unit of a quantity from one form to another form we have standard value. By multiplying or dividing we can convert the unit of the quantity. We have a different system of measurement of a quantity.