Question

How can $ - 1$ divided by $ - 2.5$ equal to $0.4$?

Answer 1

Hint:This question is from the topic of division by decimal number. In this question we need to explain why dividing $ - 1$ by $ - 2.5$ we get our result equals $0.4$. To explain it we need to know the definition of decimal numbers and its operations. To explain it we also need the knowledge of exponents and conversion of decimal numbers into scientific notation.

Complete step by step answer:
Let us try to explain this question in which we are asked why we get $0.4$ when divide $ - 1$ divided by $ - 2.5$? To explain this we are required to have the knowledge of scientific notation, laws of exponents and decimal numbers. Scientific notation is a way of writing very big or small decimal numbers in powers of $10$. Decimal numbers are a type of number system whose base is 10. In this question we have to explain why $\dfrac{{ - 1}}{{ - 2.5}} = 0.4$? We can write above equation as follows
$\dfrac{{ - 1}}{{ - 2.5}} = \dfrac{{ - 1 \times 1}}{{ - 1 \times 2.5}}$ $(1)$
After cancellation of $ - 1$, we get
$\dfrac{{ - 1}}{{ - 2.5}} = \dfrac{1}{{2.5}}$
Now $2.5$can be written as $2.5 = 25 \times {10^{ - 1}}$. So we have
$\dfrac{{ - 1}}{{ - 2.5}} = \dfrac{1}{{25 \times {{10}^{ - 1}}}}$
Now using this result from exponents ${a^b} = \dfrac{1}{{{a^{ - b}}}}$, we get
$\dfrac{{ - 1}}{{ - 2.5}} = \dfrac{{10}}{{25}}$
As we know that $10$ can be written as $10 = 100 \times {10^{ - 1}}$. So we have
$\dfrac{{ - 1}}{{ - 2.5}} = \dfrac{{100 \times {{10}^{ - 1}}}}{{25}}$
As we that $100 = 4 \times 25$.So we have
$\dfrac{{ - 1}}{{ - 2.5}} = \dfrac{{4 \times 25 \times {{10}^{ - 1}}}}{{25}}$
Now, we can cancel $25$ because it is in both numerator and denominator. So we get
$\dfrac{{ - 1}}{{ - 2.5}} = 4 \times {10^{ - 1}}$
Now as we know that $4 \times {10^{ - 1}}$can be written as $4 \times {10^{ - 1}} = 0.4$, we get,
$\dfrac{{ - 1}}{{ - 2.5}} = 0.4$

Hence this is the reason for getting $0.4$ when divided $ - 1$ by $ - 2.5$.

Note:To solve these types of questions in which we have to perform mathematical operations on decimal numbers. We need to know the definition of decimal numbers and writing decimal numbers in powers of $10$ and laws of exponents such as ${a^b} = \dfrac{1}{{{a^{ - b}}}}$.