Question

What is 10 divided by (1 divided by 0.1)?

Answer 1

Hint: This question can be solved by just converting from the word to equation format. By doing so, we get the equation as $10\div \left( 1\div 0.1 \right).$ We use the method of BODMAS to solve this equation. We first solve what is inside the brackets and the divided 10 by the resulting answer from inside the brackets.

Complete step by step solution:
In order to solve this problem, we need to convert this problem given in words to an equation format. This equation is given as:
$\Rightarrow 10\div \left( 1\div 0.1 \right)$
We apply the method of BODMAS which shows the priority order for the equation to be solved. BODMAS stands for Bracket Of Division Multiplication Addition Subtraction. We need to solve the equation in this order. Since brackets should be solved first, we solve what is given in brackets first.
We know that 0.1 can be written as $\dfrac{1}{10}$ in fraction format. Writing this in the equation,
$\Rightarrow 10\div \left( 1\div \dfrac{1}{10} \right)$
We all know that $a\div \dfrac{1}{b}=a\times b.$
Therefore, we can change the division sign inside the brackets to the multiplication sign by reciprocating the $\dfrac{1}{10}$ term. Implementing this in the equation,
$\Rightarrow 10\div \left( 1\times 10 \right)$
Simplifying the term inside the bracket by multiplying 1 and 10,
$\Rightarrow 10\div 10$
Since we have only one operation to be performed, we do not need to refer to BODMAS. We next carry out this division. This can be represented as,
$\Rightarrow \dfrac{10}{10}$
Since we can cancel the numerator and denominator, we get the resultant answer as,
$\Rightarrow \dfrac{10}{10}=1$
Hence the answer to the given problem 10 divided by (1 divided by 0.1) is 1.

Note: To answer this question, students are required to know about the BODMAS rule while simplifying equations. We can also solve by directly dividing 1 by 0.1 if we know division by decimal, which will simplify to 10 inside the brackets. Then the remaining steps remain the same.