Question

How do you write two decimals that are equivalent to 0.9?

Answer 1

Hint: To solve the question, we should know how to expand a given fraction. Expanding a given fraction simply means that multiplying and dividing a fraction by a number. We can expand the fraction by any number to get other equal fractions. If we expand them by the powers of \[10\] we get equal decimals. We will do this for the given decimal.

Complete step by step answer:
We are given the decimal number \[0.9\]. First, we need to convert the given decimal to fraction form. We can do this by multiplying and dividing the decimal by \[{{10}^{n}}\],\[n\] is the number of digits after the decimal point. Here, there is only one digit after the decimal point, so we need to multiply by \[10\]. By doing this we get
\[\begin{align}
  & \Rightarrow 0.9\times \dfrac{10}{10}=\dfrac{0.9\times 10}{10} \\
 & \Rightarrow \dfrac{9}{10} \\
\end{align}\]
We can get the equal decimals expanding the fraction by powers of 10. We will expand the fraction by \[{{10}^{1}}\And {{10}^{2}}\].
We multiply and divide the fraction \[\dfrac{9}{10}\] by \[{{10}^{1}}\], we get
\[\Rightarrow \dfrac{9}{10}\times \dfrac{10}{10}=\dfrac{90}{100}\]
Converting the above we fraction in decimal form, we get \[0.90\]
Now, we multiply and divide the fraction \[\dfrac{9}{10}\] by \[{{10}^{2}}\], by doing this we get
\[\begin{align}
  & \Rightarrow \dfrac{9}{10}\times \dfrac{{{10}^{2}}}{{{10}^{2}}}=\dfrac{9}{10}\times \dfrac{100}{100} \\
 & \Rightarrow \dfrac{900}{1000} \\
\end{align}\]
Converting the above fraction in decimal form, we get \[0.900\].

Hence, the decimals equal to the \[0.9\] are \[0.90\], and \[0.900\].

Note: Generally, if you add zeros to the right side of a decimal you get the decimals equal to the original number. Let’s take the given example, the given number is \[0.9\]. Adding a zero to the right side we get \[0.90\]. Adding one more zero to the right side, we get \[0.900\]. So, the decimals equal to the \[0.9\] are \[0.90\], and \[0.900\].