## Rounding Numbers

This chapter will teach us how to round off numbers. Rounding off is a method used in mathematics to decrease the quantity of numbers while keeping its value. The resulting number after rounding off is less precise however it is not difficult to use.

Here are the steps in rounding off numbers:

1. First, determine the last digit to retain. For example; tens, hundreds, tenths, hundredths, decimal places,
significant numbers among others.
2. Do not change the number if the value of the next digit or number is less than 5. This method is called rounding down.

Example:

Round 43 to the nearest 10

Since 4 is in the tens position that is the digit we keep. 3 is less than 5 so we round it down to 0. Therefore, 43 is rounded to the nearest 10 is 40.

3. However, if the value of the next digit or number is equal to or more than 5, then increase it by 1. This method is called rounding up since we increase the value of the number.
4. Example:

Round 75 to the nearest 10

As we can see, the digit in the tens position is 7 so we keep it. The next number is equal to 5 and as
mentioned above, we add 1 to the number we retain making 7 to 8. Thereby, 75 is rounded up to 80.

#### How to round off decimals?

In rounding off decimals, we determine how many numbers we retain by counting the decimal places. For example; tenths, hundredths, thousandths, and so on.

Example:

1.     1.235 rounded to tenths
= 1.2
Since the next digit is 3 which is less than 5 so we retain the number 2
2.     4.768 rounded to hundredths
= 4.77
3.     3.9030 rounded to thousandths
= 3.903
4.     2.65 rounded to tenths
= 2.7
5.     765.89091 rounded to ten thousandths
= 765.8909

#### Rounding off whole numbers

Rounding off whole numbers is easier. We will still follow the same procedure above. However, when the number is less than 5 we need to change the next digit to 0.

Example:

1.     56 rounded to tens
= 60
The number on the tens place is 5 so we keep it. But the number that follows it is greater than 5. According
to the procedure above, when the digit that follows the number we retain is equal to or greater than the
number 5, we add 1 to the number we keep. And so, we add 1 to 5 making it 6.
2.     943 rounded to hundreds
= 900
3.     45902 rounded to thousands
= 46000
4.     3456 rounded to tens
= 3460
5.     3459 rounded to thousands
= 3000

#### Rounding off to significant digits

Significant digits or numbers are numbers bearing a value. This includes all numbers except leading zeros.

Example:

0.009 (This number only has 1 significant digit which is 9)

The principle in rounding off is still the same as above. In rounding off significant figures, we just have to be
careful with counting the significant digits.

Example:

1.    1.908 rounded to 3 significant digits
= 1.91
2.    2.984 rounded to 2 significant digits
= 3.0
As you can see 0 here is a significant digit because it is a trailing zero
3.     0.000532 rounded to 1 significant digit
= 0.0005
4.     39.045 rounded to 1 significant figure
= 30
5.     456.0043 rounded to 5 significant digits
= 456.00