No mathematician likes to work with a long and awkward string of decimals, so they often use a technique called "rounding" (or sometimes "rounding") to make these numbers easier to work with. Rounding a decimal is like rounding a whole number; just find the value you need to round and look at the digit to the right. Yes it is five or higher, round it up. Yes it is less than five, round down.
Steps
Part 1 of 2: Instructions for Rounding
Step 1. Understand the idea of decimal places
In any number, the different digits represent different quantities. For example: in the number 1872, "1" represents thousands, "8" represents hundreds, "7" represents tens, and "2" represents ones. When there is a decimal point in a number, the numbers to the right of the comma represent the fractions of one.
 The positions to the right of the decimal point have names that reflect the names of the positions of the whole numbers. The first number to the right of the decimal point represents the tenths, the second represents the hundredths, the third represents the thousandths and so on for the ten thousandths, etc.
 For example: in the number 2, 37589, the "2" is the number of the units, the "3" is the number of the tenths, the "7" is the number of the hundredths, the "5" is the number of the thousandths, the "8" is the number of the ten thousandths and the "9" is the number of the hundred thousandths.
Step 2. Find the decimal you need to round
The first step in rounding a decimal is determining which decimal you are rounding it to. If it's school work, they usually give you this information; Often times, the problem will say something like "round your answer to the nearest tenth, hundredth, or thousandth."

For example: if you are asked to round the number 12, 9889 to the nearest thousandth, you will start by looking for the thousandth. Counting from the decimal point, the spaces to the right represent tenths, hundredths, thousandths and ten thousandths, so the second "8" (12, 98
Step 8.9) is the one you are looking for.
 Sometimes the instructions will tell you exactly which decimal to round to (for example: "round to the third decimal place" means the same as "round to the thousandth").
Step 3. Look at the number in the space to the right
Now, find the decimal to the right of which you are going to round. Based on that number, you can round up or down.

In the example number (12, 9889), you will round to the thousandth (12, 98
Step 8.9), so now look at the number to the right of this, which is the final "9" (12, 98
Step 9.).
Step 4. If this number is greater than or equal to five, round it up
To be clear: if the decimal you are rounding is followed by a 5, 6, 7, 8, or 9, round it up. In other words, convert that decimal to a larger value and remove subsequent digits.
 In the example number (12, 9889), since the final 9 is greater than 5, round the thousandth upwards. The rounded value becomes 12, 989. Note that you must remove the digits that are after the rounded decimal.
Step 5. If this number is less than five, round it down
On the other hand, if the decimal you are rounding is followed by a 4, 3, 2, 1, or 0, round it down. This means that you should leave the digit as is and remove the subsequent digits.

You are not going to round 12,9889 down because the final 9 is not 4 or less. However, if you were working with the number 12, 988
Step 4., you could round it down to 12, 988.
 Does this process look familiar to you? If so, it is because basically it is like rounding whole numbers; the decimal point does not change things.
Step 6. Use the same technique to round a whole number
A common rounding task is to round a number to the nearest whole number (sometimes this will be explained as "rounding the number to units"). In this case, use the same rounding technique as before.
 In other words, start in units and then look at the number to the right. If this number is 5 or greater, round it up. If it is 4 or less, round it down. The decimal point in the middle does not change anything.

For example: if you need to round the number in the previous example (12, 9889) to the nearest whole number, you would start by looking at the ones place: 1
Step 2., 9889. Since the "9" on the right is greater than 5, you will round it
Step 13.. Because you have a whole number for your answer, you no longer need the decimal point.
Step 7. Look for the special instructions
The rounding instructions above will work fine in general. However, when you are given special instructions for rounding decimals, be sure to follow them before using the normal rules for rounding.
 For example: if you receive the instructions: "Round 4, 59 down to the nearest tenth ", you should round the 5 of the tenths down, even though the 9 on the right means that you would normally round it up. This will give you 4, 5.
 In the same way, if they tell you that you must "round 180, 1 upwards to the nearest whole number ", you should round it to 181, even though you would normally round it down.
Part 2 of 2: Sample Problems
Step 1. Round 45,783 to the nearest hundredth
You will find the solution below.

First, find the hundredths place, that is, two spaces to the right of the decimal point or 45,7
Step 8.3.

Then look at the number on the right: 45, 78
Step 3.
 Since 3 is less than 5, round it down. The answer is 45, 78.
Step 2. Round 6.2979 to the third decimal place
Remember that "third decimal" means to count three spaces to the right of the decimal point. It is the same as saying the "thousandth". Here is the solution:

Find the third decimal, that is 6, 29
Step 7.9.

Look at the number on the right, that is 6, 297
Step 9..
 Since 9 is greater than 5, round it up. The answer is 6, 298.
Step 3. Round 11.90 to the nearest tenth
The "0" here makes it a bit difficult, but remember that zeros count as numbers less than four. Here is the solution:

Find the tenth. In this case it is 11,
Step 9.0.
 Look at the number on the right, that is 11, 9 0.
 Since 0 is less than 5, round it down. The answer is 11, 9.
Step 4. Round 8.7 to the nearest whole number
Don't be intimidated by the negative sign; Rounding negative numbers is exactly the same as rounding positive numbers.
 Find the units. In this case '¬ 8 ', 7.

Look at the number on the right 8,
Step 7..

Since 7 is greater than 5, round it up. The answer is 
Step 9.. Leave the negative sign as it is.
Advice
 If you're having trouble controlling some of the higher decimals, take a look at this handy guide.
 Another useful tool is this automatic rounding calculator, which can help you when working with large numbers.