# GRE Math : Decimals

## Example Questions

### Example Question #382 : Arithmetic

Write  in scientific notation.

Explanation:

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 * 105.

### Example Question #1 : How To Convert Decimals To Scientific Notation

is equal to which of the following?

Explanation:

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:

### Example Question #2 : How To Convert Decimals To Scientific Notation

is equal to which of the following?

Explanation:

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:

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.)

### Example Question #1 : How To Add Decimals

Solve for :

Explanation:

To add decimals, simply treat them like you would any other number.  Any time two of the digits in a particular place (i.e. tenths, hundredths, thousandths) add up to more than ten, you have to carry the one to the next greatest column.  Therefore:

So .

### Example Question #1 : Decimals

Solve for :

Explanation:

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.

### Example Question #3 : Decimals

Solve for :

Explanation:

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

### Example Question #4 : Decimals

Solve for :

Explanation:

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 .

### Example Question #5 : Decimals

Solve for :

Explanation:

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

### Example Question #1 : Decimals

Solve for :

Explanation:

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

### Example Question #1 : Decimals

Quantity A:

Quantity B:

The two quantities are equal.

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.