Solution :
Repeating or recurring decimals :
Repeating or recurring decimals are those decimal expansions that do not terminate or end after a specific number of digits. Such numbers have an infinite number of digits after the decimal point. And there is a repetitive pattern in those digits.
Decimal numbers can be converted to fractions by dividing the number with a power of 10 which is equal to the number of decimal places. For example, 1.5 = 15/10 = 3/2. But with repeating decimals, it is impossible to count the number of decimal places as it is infinite. So, there are some specific steps to be followed to convert repeating decimals to fractions.
The repeating decimal to fraction steps of conversion are given below:
Step 1: Identify the repeating digits in the given decimal number.
Step 2: Equate the decimal number with x or any other variable.
Step 3: Place the repeating digits to the left of the decimal point by multiplying the equation obtained in step 2 by a power of 10 equal to the number of repeating digits. This way you will get another equation.
Step 4: Subtract the equation obtained in step 2 from the equation obtained in step 3.
Step 5: Simplify to get the answer.
Let us take an example to understand the conversion of repeating decimals to fractions in a better way. Convert 0.77777... to a fraction.
Step 1: We can observe that 7 is repetitive in the given decimal number.
Step 2: Let x = 0.7777...
Step 3: There is only 1 repetitive digit, so multiply this equation by 10. We get, 10x = 7.7777...
Step 4: Subtract x = 0.7777... from 10x = 7.7777... We will get 9x = 7.
Step 5: x = 7/9. Therefore, 0.7777... = 7/9.
Hence,
you multiply 10 by the repeating decimal to make a fraction
For more information: brainly.com/question/27871485
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