Decimals with Fractions - GRE Quantitative Reasoning

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:

Both decimals and fractions represent part of a whole. To convert this decimal number to a mixed number fraction, use the following steps:

(because the decimal number has a in the ones place value and an in the hundredths place value).

Then simplify .

Thus, the correct answer is

Both decimals and fractions represent part of a whole. Since this decimal number has a value of in the tenths place and a value of in the hundredths place, it can be re-written as:

.

Then, simplify the fraction by dividing both the numerator and denominator by a divisor of

Thus, the solution is:

This problem requires several conversions. First, convert into a mixed number fraction. This means, the new fraction will have a whole number of and a fraction that represents thousandths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.

Thus, the solution is:

This problem requires two conversions. First convert to a mixed number fraction. This must equal a whole number of and a fraction that represents a value of tenths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.

Thus, the solution is:

To solve this problem, make a mixed number fraction with a whole number of and a fraction that represents hundredths. Then simplify the fraction portion of the mixed number by dividing the numerator and denominator by their largest common divisor.

To convert this fraction to a decimal number, divide the numerator by the denominator. Since this fraction has a larger numerator than denominator, the fraction is classified as an improper fraction. This means that the fraction represents a value greater than one whole. Thus, the solution must be greater than one.

Note that fits into evenly times, and has a remainder for of

This problem requires you to first convert the decimal number to a mixed number fraction that has a whole number of and a fraction that represents thousandths. Then reduce the numerator and denominator by common divisors until you can no longer simplify the fraction.

Both fractions and decimals represent part of a whole. The value of this decimal number reaches the ten-thousandths place value. Thus, the fraction must represent ten-thousandths. Then reduce the numerator and denominator by the common divisor of .

Fractions and decimals both represent part of a whole. To solve this problem you may divide by , or you can reduce the fraction by dividing the numerator and denominator by the common factor of This will equal a fraction of hundredths, which can be written as the decimal number "zero and hundredths."

Note: both and equal

First convert this decimal number to a mixed number fraction, then covert the mixed number to an improper fraction. The mixed number fraction must have a whole number of and a fraction that represents tenths. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number, and then add that product to the numerator.

Decimal numbers and fractions both represent part of a whole. This decimal number has a value of in the tenths and thousandths place values. Since the decimal number reaches the thousandths place, the correct answer is over --which represents thousandths.

Since the starting number is a mixed number fraction, the decimal number must also have a value in the ones place. Since the denominator in the fraction has a value that is a factor of , both the numerator and denominator can be multiplied by a factor of to form tenths. (Note, the first decimal place value is the tenths place).

The key to this problem is to realize that the store cannot buy partial crates of wristbands--it's all or nothing. Calculate how many crates can be bought with each sum of money by dividing the sum by the price of a crate.

Quantity A:

Although oh so close, only eight crates can be bought with this sum of money. Don't round up!

Quantity B:

There's just enough to buy nine crates.

Quantity B is greater.

Whenever there are decimals in fractions, we remove them by shifting the decimal place over however many it takes to make number an integer.

In this case we have to move the decimal in the numerator to the right one place.

Then, we add just one zero to the denominator.

Final answer becomes:

.

With the numerator having more decimal spots than the denominator, we need to move the decimal point in the numerator two places to the right.

Then in the denominator, we move the decimal point also two to the right. Since there's only one decimal place we just add one more zero.

Then we can reduce by dividing top and bottom by .

Since there are four decimal places, we shift the decimal point in the numerator four places to the right.

For the denominator, since there is no decimal point, we just add four more zeroes.

Then reduce by dividing top and bottom by .

We need to convert the sentence into a math expression. Anytime there is "of" means we need to multiply. Let's first convert the decimal to a fraction. We need to move the decimal point two places to the right.

Since is the same as we can add two more zeroes to the denominator.

We can reduce the to a and the to a .

Then reduce the to and the to .

.

Then dividing into and we get .

We need to convert this sentence into a math expression. Anytime there is "of" in a sentence it means we need to multiply. Let's convert into a decimal which is .

Thus our mathematical expression becomes:

.

Divide both sides by .

Move decimal point two places to the right. The numerator will become . Then simplify by dividing top and bottom by .