Decimals - GRE Quantitative Reasoning

To solve this problem, subtract from both sides of the eqution,

Therefore, .

If you're having trouble subtracting the decimal, mutliply both numbers by followed by a number of zeroes equal to the number of decimal places. Then subtract, then divide both numbers by the number you multiplied them by.

To solve, you need to do some algebra:

Isolate x by adding the 4.150 to both sides of the equation.

Then add the decimals. If you have trouble adding decimals, an effective method is to place one decimal over the other, and add the digits one at a time. Remember to carry every time the digits in a given place add up to more than .

To solve for , first add to both sides of the equation, so that you isolate the variable:

Then, add your decimals, and remember that .

To solve, first add to both sides of your equation, so you isolate the variable:

Then add the decimals together:

To solve, first add to both sides of the equation:

Then add the decimals together:

We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative. If the decimal had moved left, we would have had a positive exponent.

In this case we get 6.009 * 10–5.

We need to convert into a number of the form .

The trick is, however, figuring out what should be. When you have to move your decimal point to the right, you need to make the decimal negative. (Note, though, when you multiply by a negative decimal, you move to the left. We are thinking in "reverse" because we are converting.)

Therefore, for our value, . So, our value is:

The easiest way to do this is to convert each of your answer choices into scientific notion and compare it to .

For each of the answer choices, this would give us:

(Which is, thus, the answer.)

When you convert, you add for each place that you move to the left and subtract for each place you move to the right. (Note that this is opposite of what you do when you multiply out the answer. We are thinking in "reverse" because we are converting.)

To solve, first divide both sides of the equation by , leaving you with:

Then simply divide the decimals, which will yield your answer:

.

If you have trouble dividing the decimals, you can multiply both of the numbers by one followed by a number of zeroes equal to the number of digits beyond the decimal point (one hundred, in this case), then divide, then divide your result by the same number (one hundred again).

To solve, first divide both sides of the equation by :

To do this division, you can divide as normal, or if you are having trouble, you can multiply both numbers by 10 to eliminate the decimal:

To solve, first divide both sides of the equation by so you isolate the variable:

Then, divide the decimal--if you have trouble doing so, remember that you can multiply both numbers by to eliminate the decimal, and then divide as normal:

To solve, first divide both sides of the equation by so you can isolate the variable:

Now divide. If you have trouble dividing decimals, you may multiply both dividend and divisor by to eliminate the decimal and divide normally:

To solve, first divide both sides of the equation by so you isolate your variable:

Then, divide the decimals. If you have trouble with this, you can multiply both numbers by to eliminate the decimals and then divide normally:

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