# GRE Math : Decimals

## Example Questions

### Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, and the square root of 4 is two, so the square root of 6.4 is between 3 and 2, around 2.53

### Example Question #2 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.  is a perfect square, whose square root is .

### Example Question #7 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, so the square root of 10 should be a little larger than 3, around 3.16

### Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 36 is 6, so the square root of 40 should be a little more than 6, around 6.32.

### Example Question #1 : How To Find The Square Root Of A Decimal

Solve for :

Explanation:

Just like any other equation, isolate your variable. Start by multiplying both sides by :

Now, this is the same as:

You know that  is . You can intelligently rewrite this problem as:

, which is the same as:

### Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.  is a perfect square, whose square root is .

### Example Question #1 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Put the following in order of least to greatest:

None of the other answers

None of the other answers

Explanation:

Begin by converting each fraction into a decimal:

Now we can put the decimals in order:

0.269, 0.27, 0.2788, 0.28, 0.3157

or:

No answer choice matches this order, so our answer is "None of the other answers"

### Example Question #1 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Put these decimals in order from least to greatest:

Explanation:

To put these numbers in order from least to greatest we start by looking at the number before the decimal. In this case they're all the same (7) so we move to the first number to the right of the decimal. Since 8 is greater than 3 we know that 7.8 and 7.835 must be greater than the other two options. To decide if 7.8 or 7.835 is greater we look at the next number to the right. Since 7.8 doesn't have another number to the right we know that the number to the right must be 0. Since 3 is greater than 0 we know that 7.835 is greater than 7.8. We follow the same process to find that 7.35 is less than 7.358. Then we can put the numbers in order from least to greatest: 7.35, 7.358, 7.8, 7.835.

### Example Question #2 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Order these decimals from greatest to least:

Explanation:

We first look at the whole number and see that 5 is greater than 4, so we know that the two biggest numbers are going to be 5.19 and 5.09. We then look at the number to the right of the decimal since 1 is greater than 0 we know that 5.19 is the biggest number and 5.09 is the second biggest. Then we compare the numbers that start with 4 by looking to the number to the right of the decimal. Since 9 is greater than 1 or 0 we know that 4.9 is the next biggest number. Since 1 is greater than 0 we know that 4.19 is greater than 4.09. Then we just put the numbers in order from greatest to least to get the correct answer: 5.19, 5.09, 4.9, 4.19, 4.09.

### Example Question #1 : How To Find Decimal Fractions

Convert  to an equivalent decimal number.