Let's actually simplify the top of the fraction.  divides into .

We should have: 

.

Then move the decimal two spots to the right and add two zeroes to the denominator.

Let's actually multiply top and bottom by  to get:  .

Now we want to eliminate those zeroes. By dividing, the decimal point in the numerator moves to the left three places to get an answer of  or .

Since each decimal has two digits, we can convert easily to integers.

Then multiply top and bottom by  to get: 

 is reduced to  and  is reduced to  

Then  and  can be divided by  to get  and  respectively.

Let  be . Let's multiply that value by . The reason is when we subtract it, we will get us an integer instead and the repeating decimals will disappear. 

If we subtract, we get .

Divide both sides by  and we get .

If you divide by  on top and bottom, you should get the answer. Otherwise, just divide top and bottom by  three times based on the divisibility rules for . If the sum is divisible by , then the number is divisible by .

To compare these two quantities, we'll want to simplify Quantity A.

The fraction

may be a bit daunting; let's convert it to scientific notation:

Now multiply the non-ten terms, and the ten terms (add the exponents together):

Now cancel like factors in the numerator and denominator:

The two quantities are equal.

To begin, it can be useful to convert the values in the fraction

into a modified scientific notationnotation:

Now multiply the ten terms (adding exponents together) and the non-ten terms:

From here, reduce the terms, subtracting the bottom tens exponent from the top tens exponent:

For this problem, realize that the store cannot buy part of a crate of socks. If they only have enough to pay for part of a crate, they might as well not have any money at all.

For the amount of money listed, figure out how many crates can be purchased:

Quantity A

So six crates can be purchased.

Quantity B:

Not quite enough for seven; only six crates can be purchased.

The two quantities are equal.

.45 is equivalent to 45 out of 100, or .

Divide both the numerator and denominator by 5 to simplify the fraction: 

To convert from a decimal to a fraction, simply put the digits over  followed by a number of zeroes equal to the number of digits:

Then, you can reduce:

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

 is prime, so there's no way to reduce.  You're done!

To convert from a decimal to a fraction, simply put the digits over one followed by a number of zeroes equal to the number of digits:

The zero in front of the  can be removed, leaving: , which can be reducted to: