Rounding Off Significant Figures

Rounding off is a type of estimation. Estimation is used in everyday life and also in subjects like Mathematics and Physics. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.

What is Rounding Off?

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc. Rounding off numbers is done to preserve the significant figures. The number of significant figures in a result is simply the number of figures that are known with some degree of reliability.

The number 13.2 is said to have 3 significant figures. Non-zero digits are always significant. 3.14159 has six significant digits (all the numbers give you useful information). Thus, 67 has two significant digits, and 67.3 has three significant digits.

Rounding off

Rounding Rules for Whole Numbers

Rounding rules for whole numbers is as follows:

  • To get an accurate final result, always choose the smaller place value.
  • Look for the next smaller place which is towards the right of the number that is being rounded off to. For example, if you are rounding off a digit from tens place, look for a digit in the ones place.
  • If the digit in the smallest place is less than 5, then the digit is left untouched. Any number of digits after that number becomes zero and this is known as rounding down.
  • If the digit in the smallest place is greater than or equal to 5, then the digit is added with +1. Any digits after that number become zero and this is known as rounding up.

Rounding Rules for Decimal Numbers

Rounding rules for decimal numbers are as follows:

  • Determine the rounding digit and look at its righthand side.
  • If the digits at the righthand side are less than 5, consider them as equal to zero.
  • If the digits at the righthand side are greater than or equal to 5, then add +1 to that digit and consider all other digits as zero.

Learn more about errors in arithmetic operation here.

Example of How to Round Off

Round to Nearest Hundred

Let’s consider the number 3350. To round off to the nearest significant number, consider hundreds place and follow the steps as given below:

  • Identify the digit present in the hundreds place: 3
  • Identify the next smallest place in the number: 5
  • If the smallest place digit is greater than or equal to 5, then round up the digit.
  • Now add +1 to the digit in the hundreds place. 3+1=4. Therefore, the other digits become zero.
  • So the final number is 3400.

Round to Nearest Ten

Let’s consider the number 313.5. To round off to the nearest significant number, consider tens place and follow the steps as given below:

  • Identify the digit present in the tens place: 1
  • Identify the next smallest place in the number: 3
  • If the smallest place digit is greater than or equal to 5, then round up the digit.
  • Since the digit in the smallest place is less than 5, round down has to be done and also the digit remains unchanged.
  • Every other digit becomes zero.
  • So the final number is 310.

Round to Nearest Ten

Let’s consider the number 499. To round off to the nearest significant number, consider tens place and follow the steps as given below:

  • Identify the digit present in the tens place: 9
  • Identify the next smallest place in the number: 9
  • If the smallest place digit is greater than or equal to 5, then round up the digit.
  • As the digit in the ones place is greater than 5, +1 has to be added.
  • Therefore, 9+1=10 and the 1 is carried to the next place.
  • So the final number is 500.

Round to Nearest Tenth

Let’s consider the number 0.73. To round off to the nearest significant number, consider tenths place and follow the steps as given below:

  • Identify the digit present in the tenth place: 7
  • Identify the next smallest place in the number: 3
  • If the smallest place digit is greater than or equal to 5 then round up the digit.
  • As the digit in the smallest digit is less than 5, the digit gets round down.
  • So the final number is 0.7

Stay tuned with BYJU’S to learn more about other Physics related concepts.

 

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