i don't get how to do this problem mrs. sue please help

how would you convert the repating nonterminating decimal to a fraction? explain the process as you solve the problem/0.1515... remember to show all of the steps that you use to solve the problem

how would you convince a fellow student that the number 0.57 is a rational number?

http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/conv_rep_decimals/v/coverting-repeating-decimals-to-fractions-1

for the second part i don't get how to convince that the number 0.57 is a rational number please help me

What Sal is basically showing you in the video is this:

look at the repeating decimal places , there are 2 digits in the repeating loop
so, let
x = .151515...
because we have 2 digits repeating, let's multiply the equation by 100
100x = 15,151515...
notice the decimal part of 100x looks the same as the decimal part of x
so if we subtract the two equations we get
100x = 15.151515...
x = .1515151...
----------------
99x = 15
divide by 99
x = 15/99 which reduces to 5/33

Use your calculator to divide 5 by 33 and see what you get

In the above method , if there had been 3 digits repeating, then I would have multiplied by 1000 etc

For .57 , since there are no repeating decimals (well, I guess we can say .5700000.... )
the result is simply 57/100 by definition
and 57/100 is surely a fraction, thus rational

thanks

To convert a repeating non-terminating decimal to a fraction, follow these steps. Let's take the example of converting the decimal 0.1515...

Step 1: Identify the repeating pattern
In this case, the decimal pattern that repeats is "15".

Step 2: Write the decimal as a rational expression
Let x be the repeating decimal "0.1515..."
Multiply both sides of the equation by 100, so that when we subtract, the repeating part will cancel:
100x = 15.1515...

Step 3: Subtract the original equation from the modified equation
100x - x = 15.1515... - 0.1515...
99x = 15

Step 4: Solve for x
Divide both sides of the equation by 99:
x = 15/99

Step 5: Simplify the fraction, if possible
In this case, both 15 and 99 can be divided by 3:
x = 5/33

So, the repeating decimal 0.1515... can be represented as the fraction 5/33.

Now, let's move on to convincing a fellow student that the number 0.57 is a rational number.

A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. In order to show that 0.57 is a rational number, we need to demonstrate that it can be written as a fraction.

Step 1: Write the decimal as a fraction
The decimal 0.57 can be written as 57/100 because the decimal point is two places to the right of the decimal digit.

Step 2: Simplify the fraction, if possible
In this case, both 57 and 100 can be divided by 1:
57/100

So, 0.57 is a rational number because it can be expressed as the fraction 57/100, where both the numerator and denominator are integers.