### All GRE Math Resources

## Example Questions

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

Write in scientific notation.

**Possible Answers:**

**Correct answer:**

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}.

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

is equal to which of the following?

**Possible Answers:**

**Correct answer:**

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 #1 : How To Convert Decimals To Scientific Notation

is equal to which of the following?

**Possible Answers:**

**Correct answer:**

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.)

### Example Question #1 : Decimals

Solve for :

**Possible Answers:**

**Correct answer:**

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 : How To Add Decimals

Solve for :

**Possible Answers:**

**Correct answer:**

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 :

**Possible Answers:**

**Correct answer:**

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

Then add the decimals together:

### Example Question #4 : Decimals

Solve for :

**Possible Answers:**

**Correct answer:**

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 #1 : How To Add Decimals

Solve for :

**Possible Answers:**

**Correct answer:**

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

Then, add your decimals, and remember that .

### Example Question #1 : Decimals

Solve for :

**Possible Answers:**

**Correct answer:**

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

Then add the decimals together:

### Example Question #1 : Decimal Operations

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

**Correct answer:**

The relationship cannot be determined.

Use the values of .5 and 2 as possible x values. If x = 2, Quantity A is positive and greater, but if x = .5, Quantity A is negative and therefore smaller. As such, the relationship cannot be determined.