Rounding off by S. Manna, Department of Geography, Narajole Raj College GEOGRAPHY (U.G), SEM-I I, Paper –C4T: Rounding off

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Rounding off by S. Manna, Department of Geography, Narajole Raj College

GEOGRAPHY (U.G), SEM-I I, Paper –C4T: Rounding off Source;https://byjus.com/physics/error-significant-figures-rounding-off/, http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/roundoff.html

Rounding off

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 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.

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Rounding off by S. Manna, Department of Geography, Narajole Raj College

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

• 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.

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

• 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.

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:

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Rounding off by S. Manna, Department of Geography, Narajole Raj College

• Identify the digit present in the tenth place: 7

• 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

GET THESE RULES FOR ROUNDING OFF NUMBERS CASE A:

In rounding off numbers, the last figure kept should be unchanged if the first figure dropped is less than 5.

For example, if only one decimal is to be kept, then 6.422 becomes 6.4.

CASE B:

In rounding off numbers, the last figure kept should be increased by 1 if the first figure dropped is greater than 5.

For example, if only two decimals are to be kept, then 6.4872 becomes 6.49. Similarly, 6.997 becomes 7.00.

CASE C:

In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should

be unchanged if that last figure is even.

For example, if only one decimal is to be kept, then 6.6500 becomes 6.6.

For example, if only two decimals are to be kept, then 7.485 becomes 7.48.

CASE D:

In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be increased by 1 if that last figure is odd.

For example, if only two decimals are to be kept, 8.995 becomes 9.00.

CASE E:

In rounding off numbers, if the first figure dropped is 5, and there are any figures following the five that are not zero, then the last figure kept should be increased by 1.

or example, if only one decimal is to be kept, then 6.6501 becomes 6.7.