Decimals with Fractions - GRE Quantitative Reasoning

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 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:

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

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.

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.

The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.

1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.

√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.

Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

The GRE test now has a built-in calculator. Simply convert the fractions to decimals and compare:

Quantity A = 0.333 +0.43 + 0.2 = 0.963

Quantity B = 0.1429 + 0.5 + 0.3333 = 0.976

Thus, Quantity B is larger.

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

To solve this problem, simply divide the numerator by the denomenator. We see that when we try to divide these two numbers that 9 does not go into 2 therefore we need to add a decimal place and a zero to 2. Now we have 2.0 divided by 9 from here we can see that .2 times 9 gives us 1.8 which is close to 2. Now we subtract 1.8 from 2 and are left with .2. We repeat this process.

You are left with repeating, which can be rounded to , so that is the best answer.

To express a fraction as a decimal, simply divide the numerator by the denomenator. In this case, you divide thirty two by thirty seven. From here add a decimal place and a zero after 32. Now we are able to divide.

Thus yielding: repeating.

Round to the nearest hundredth, and you get because the value in the thousandths place is a four or lower therefore, the value in the hundredths place remains the same.

To convert, first divide the numerator (twelve), by the denomenator (eleven), and you will yield:

repeating.

Then, you may round to the nearest hundredth, which gives you .

Since the value in the thousandths place is less than four this means the the value in the hundredths place will remain the same.

To convert, first divide the numerator by the denomenator. For this problem we will need to add a decimal place and a zero to the end of 17 before we divide.

Then, you will yield repeating.

Then you can round to the nearest hundredth, which will give you your final answer of .

Since the value in the thousandths place is a seven which is greater than four, we will need to round the value in the hundredths place up to eight.

.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!