Question

Divide \[0.57\] by \[10\]

Answer 1

Hint:
Here, we will follow the rules while converting a decimal number into a fraction. First, we will rewrite the decimal as a fraction by writing the decimal number as the numerator and the number 1 as the denominator. Then we will multiply the numerator and the denominator by the number 10 raised to the power of \[n\] where \[n\] is the number of digits after the decimal point. Now, we will express into a fraction which can be reduced into its simplest form.

Complete step by step solution:
We are given a decimal number \[0.57\].
Let \[x\] be the given decimal number.
\[x = \dfrac{{0.57}}{1}\]
Now, the given decimal number will be converted into a fraction.
Multiplying both the numerator and the denominator by 100, we get
Thus, we get
\[ \Rightarrow x = \dfrac{{0.57}}{1} \times \dfrac{{100}}{{100}}\]
\[ \Rightarrow x = \dfrac{{57}}{{100}}\]
Now, we will divide both sides by 10. Therefore, we get
\[ \Rightarrow \dfrac{x}{{10}} = \dfrac{{\dfrac{{57}}{{100}}}}{{10}}\]
Thus, the denominator has to be reciprocally written and we get
 \[ \Rightarrow \dfrac{x}{{10}} = \dfrac{{57}}{{100}} \times \dfrac{1}{{10}}\]
Thus, the numerator of both the fractions has to be multiplied and denominators in the fraction has to be multiplied.
\[ \Rightarrow \dfrac{x}{{10}} = \dfrac{{57}}{{1000}} = 0.057\]

Therefore, when \[0.57\] is divided by \[10\] , then the solution is \[0.057\].

Note:
We know that the number which can be expressed as the ratio of two integers, then the number is said to be a rational number. Therefore the given number is a rational number. A decimal point is said to be a terminating decimal if it has no repeating digits. We should know that if a decimal number is multiplied by the powers of 10, then the decimal moves towards the right and if a decimal number is divided by the powers of 10, then the decimal moves towards the left. The number of digits moved is according to the powers of 10.