find rational numbers between 2/5 and 3/8 by converting them into decimals
Answers
Answer:
Rational numbers are the numbers in form of fractions. They can also be converted in the decimal number form by dividing the numerator of the fraction by its denominator. Let us assume ‘xy’ to be a rational number. Here, ‘x’ is the numerator of the fraction and ‘y’ is the denominator of the fraction. Hence, the given fraction is converted to the decimal number by dividing ‘x’ by ‘y’.
To check whether a given rational fraction is terminating or non- terminating, we can use the following formula:
x2m×5n, where x ∈ Z is the numerator of the given rational fraction and ‘y’ (denominator) can be written in the powers of 2 and 5 and m ∈ W; n ∈ W.
If a rational number can be written in the above form then the given rational fraction can be written in terminating decimal form otherwise it can’t be written in that form.
The concept can be easily understood by having a look at the below given solved example:
1. Check whether 14 is a terminating or non- terminating decimal. Also, convert it into decimal number.
Solution:
To check the given rational number for terminating and non- terminating decimal number we will convert it into the form of x2m×5n. So,
14 = 122×50
Since, the given rational fraction can be converted into above form, so the given rational fraction is a terminating decimal number. Now, to convert it into decimal number the numerator of the fraction will be divided by denominator of the fraction. Hence, 14 = 0.25. So, the required decimal conversion of given rational fraction is 0.25.
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Answer:
rational number between 0.4 and 0.3
are -- 0.31 , 0.32 , 0.35 , 0.37 , 0.39