Question

How to convert 3.248 repeating decimal with 48 repeating into a simplified fraction

Answer 1

Answer:

$x=\frac{536}{165}$

Step-by-step explanation:

Let X be the value of 3.2484848.... infinite times

Multiply by 100

$x=3.24848....\\100x = 324.8484.....$

Subtract to get

$100x-x = 324.8484...-3.248484....\\99x = 321.60\\x=\frac{321.6}{99} \\x=\frac{1072}{330} \\x=\frac{536}{165}$

Thus the number 3.248 repeating decimal with 48 repeating in fraction form is

$\frac{536}{165}$

Answer 2

Answer:

$\frac{536}{165}$

Step-by-step explanation:

Step 1: let's call $x$ the repeating decimal.

So, $x=32.2484848484848...$

Step 2: identify the number of digits that repeats.

We see that two digits repeat 4 and 8.

Step 3: multiply 100 at each side of the equation, two digits, two zeros, that's why is 100.

$100x=324.84848484848...$

Step 4: we subtract the repeating decimal the last expression:

$100x-x=(324.8484848...)-(3.2484848...)\\99x=321.6$

Step 5: solve for $x$.

$x=\frac{321.6}{99}$

In this case, we have to multiply each part of the fraction by 10 to get rid of the decimal number.

$x=\frac{321.6(10)}{99(10)}=\frac{3216}{990}=\frac{536}{165}$

Therefore, the repeating decimal is equal to $\frac{536}{165}$