# Error Significant Figures Rounding Off

## What is Rounding Off Numbers?

Often people fail to understand the meaning of the question “What is rounding off?” or “What is to round off?” Rounding off is a technique which helps a number in becoming simpler without losing its original value. Through this technique, the number converts into its closest whole number. It is practised on whole numbers as well as various decimal places like tens or hundreds. The main purpose of rounding off is to keep the significant figures intact. Most physics problems require the knowledge of significant digits for properly expressing the answers. Significant digits are a measure of the accuracy of knowing the values.

For example, if an answer comes out to be 1.538756839, it has 10 significant digits. However, it is good enough to work with two significant figures, and one can round it off to 1.5.

In other words, rounding off is a method of estimation which is quite common in the fields of Physics and Mathematics. The estimation has become a regular part of our lives while measuring various quantities like weight, distance covered, length, etc. In most cases, we round off the actual number to their nearest whole number for convenience.

### What are the Rules for Rounding Off Numbers?

There are several rules which are required to be followed to round off numbers. Different numbers like whole numbers and decimal numbers do not follow the same rule while rounding off and hence they should be kept in mind to avoid mistakes.

### Rules for Rounding Whole Numbers

There are a number of rules in rounding off whole numbers that one needs to follow:

• To obtain accurate results, one must opt for the smaller place value.

• Next, one has to choose the following smaller place to the right of the number it is rounded off to. Suppose if someone rounds off a digit from tens place, he/she needs to next look for the digit in the unit place.

• If the digit present in the smallest place is smaller than 5, then the number must be kept unchanged. Any number of digits following that number is considered as zero. This process is termed as rounding down.

• If the digit is greater than or equal to 5, then one must add 1 to the digit. Any digits that follow that number become zero. This process is termed as rounding up.

This is what is rounding to the nearest whole number stands for.

### Rounding Rules for Decimal Numbers

There are a few rules which need to be kept in mind while rounding off for decimal numbers:

• The first thing that one needs to do is to determine the rounding digit. Then one needs to look to the right of the digit.

• If the digits located to the right of the rounding digit are less than 5, then they should be considered as equal to zero.

• If the digits placed to the right are more than or equal to 5, then 1 should be added to them while the rest of the digits should be considered as zero.

### Examples

1. Rounding Off to Nearest Ten: Suppose the number 560.5.

The following steps need to be followed for rounding off:

• The digit at tens place is identified, which is 6.

• Next, the smallest place is identified, which is 0.

• Since the number is less than 5, every other digit must be 0.

• Hence the number is rounded off to 560.

1. Rounding Off to Nearest Tenth: Suppose the number is 0.84.

One needs to follow the following steps to round it off:

• The digit at the tenth place is identified to be 8.

• Next, the smallest place is identified as 4.

• The smallest place digit is less than 5. Hence the digit gets round down.

• The final number after rounding off is obtained as 0.8.

### Did You Know?

Zeroes which are used to fill the values up to the decimal point are not accepted as significant digits.

For example, 3600 has only two significant digits. However, in the case of 3600._, the number of significant figures increases to four. Thus, the place of decimal has an important role in the number of significant figures.

Non-zero digits are always considered significant.

Q1. What is the Meaning of Rounding to the Nearest Whole Number?

Ans: Rounding off is a process by which a number is made simpler by approximation without changing the original value. However, while carrying out the process, one needs to keep in mind the rounding rules for whole numbers to obtain accurate results after applying.

Suppose there is a number 9.63 which one wants to round off to the nearest whole number. In the beginning, one has to look at the digit in the tenths place, which is 6. As 6 is greater than 5, the number must be rounded off to the next whole number, which is 10.

Again if another number 6.32 is considered, one needs to have a look at the digit in the tenths place. Here the number is 3 and is less than 5. Hence the number is rounded off to the nearest whole number 6.

Q2. What are the Rules for Measuring Significant Figures?

Ans: Significant figures refer to the number of important single digits in a certain number which has a contribution towards the accuracy level of the value. To measure the significant figures, one needs to keep in mind a few rules:

• All the non-zero digits, i.e. 1-9 are significant digits.

• Zeroes, when situated between non-zero digits, are considered as significant.

• Only a trailing zero is considered as significant in the decimal portion.

Some examples are listed below:

The number 5609 has 4 significant figures.

The number 30.08 also has 4 significant figures.

The number 36000 only has 2 significant figures.

On the other hand, 7.00 has 3 significant figures.