Question

Express 63.63 repeating as a fraction. Show your work.

Answer 1

To express 63.63 repeating as a fraction, you can use the concept of repeating decimals. Start by multiplying x by 100 to eliminate the decimal. Then, subtract x from 100x to eliminate the repeating part. Finally, write the equation as a fraction and simplify if possible.

Step-by-step explanation:

To express 63.63 repeating as a fraction, we can use the concept of repeating decimals. Let's call the repeating decimal 63.63 as x.

Step 1: Multiply x by 100 to move the decimal point two places to the right. This gives us 100x.

Step 2: Subtract x from 100x to eliminate the repeating part. This gives us 100x - x = 99x.

Step 3: Subtract the original x from 99x to eliminate the non-repeating part. This gives us 99x - x = 98x.

Step 4: Write the equation as a fraction by putting 98x over 99. This gives us the fraction 98x/99.

Step 5: Simplify the fraction if possible.

Since the numerator and denominator have a common factor of 2, we can divide both by 2 to simplify the fraction. This gives us the final simplified fraction of 49x/49.

Answer 2

The repeated decimal 63.63 is expressed as a fraction by defining the repeating decimal as x, multiplying by 100 to create a solvable equation, and then simplifying the resulting fraction. The final fraction for 63.63 repeating is 70/1.

Step-by-step explanation:

To express 63.63 repeating as a fraction, we will use algebraic methods. Let's define x as the repeating decimal:

x = 63.6363...

Since the '63' is the repeating part, we can multiply x by 100 to shift the decimal two places to the right:

100x = 6363.6363...

Now we subtract the original equation from this new one to eliminate the repeating decimal:

100x - x = 6363.6363... - 63.6363...

99x = 6300

Divide both sides by 99 to solve for x:

x = 6300 / 99

Finally, simplify the fraction:

x = 70 / 1

Now we have expressed the repeating decimal 63.63 as a fraction, which is 70/1.