Question

Write the following number in the form of ${\text{k }} \times {\text{ 1}}{{\text{0}}^{\text{n}}}$where 1 ≤ k ≤ 10 and n is an integer.
0.00729

Answer 1

Hint: In order to find the value of the integer ‘n’, we express the number as a multiple of a decimal number up to one digit and ten raised to the power of a number. The power of the number ten must be taken such that it is an integer.

Complete step by step answer:
Given number is 0.00729
We know any decimal number can be expressed as a multiple of ten raised to a power.
Here we are given that the power of ten must be an integer.
Therefore it consists of both positive and negative values.
Now we can express this number 0.00729 as
$
   \Rightarrow 0.00729 \\
   \Rightarrow \dfrac{{729}}{{100000}} \\
   \Rightarrow \dfrac{{7.29}}{{1000}} \\
   \Rightarrow 7.29{\text{ }} \times {\text{ }}\dfrac{1}{{1000}} \\
   \Rightarrow 7.29{\text{ }} \times {\text{ 1}}{{\text{0}}^{ - 3}} \\
$
Here k = 7.29 and ${10^{\text{n}}} = {10^{ - 3}}$, therefore n = -3, which is an integer.

Note: In order to solve this type of problems we have to know how to express a decimal in terms of multiple of ten raised to a power and the definition of an integer.
An integer is defined as the number which can be written without having a fractional component in it.
It takes both positive and negative values.
For example, numbers like 8.88, $\dfrac{1}{2}$, $\sqrt 7 $are not integers.