Question

what is \\(\frac{9}{25}\\) written as a decimal?
0.36 \\(0.3\overline{6}\\) \\(0.\overline{36}\\)
what is \\(\frac{4}{11}\\) written as a decimal?
0.36 \\(0.3\overline{6}\\) \\(0.\overline{36}\\)
what is \\(\frac{11}{30}\\) written as a decimal?
0.36 \\(0.3\overline{6}\\) \\(0.\overline{36}\\)

Explanation:

First Sub - Question: What is $\frac{9}{25}$ written as a decimal?

Step 1: Multiply numerator and denominator to get denominator as 100

To convert a fraction to a decimal, we can make the denominator a power of 10. We know that $25\times4 = 100$. So we multiply both the numerator and the denominator of $\frac{9}{25}$ by 4.
$\frac{9\times4}{25\times4}=\frac{36}{100}$

Step 2: Convert the fraction with denominator 100 to decimal

A fraction with denominator 100 can be written as a decimal by moving the decimal point two places to the left in the numerator. So $\frac{36}{100}=0.36$

Step 1: Perform long division

We divide 4 by 11. $4\div11 = 0.363636\cdots$

Step 2: Identify the repeating pattern

We can see that the digits 36 repeat indefinitely. So we write it as $0.\overline{36}$

Step 1: Perform long division

Divide 11 by 30. $11\div30 = 0.36666\cdots$

Step 2: Identify the repeating pattern

We can see that the digit 6 repeats indefinitely after the first two decimal places. So we write it as $0.3\overline{6}$

Answer:

0.36

Second Sub - Question: What is $\frac{4}{11}$ written as a decimal?