Rounding Off Decimal Numbers.

ROUNDING OFF DECIMAL NUMBERS:

Rounding means making a number simplier but keeping its value close to what it was. The result is less accurate, but easier to use.

Rounding off of Decimal number is same as Rounding-off Whole numbers.

While Rounding off a decimal number ,we need to follow the steps same as in Rounding off  whole number .They are:

Step-1 : Underline the  digit in the given place to be rounded in the decimal number.

Step-2 : Circle the digit right to the underlined digit .

Step-3 : Comparision: The circled digit in the  decimal number is compared with number ‘ 5 ‘ always.

(i) Rounded Down : If the circled digit in the decimal number is smaller than

 ( < ) number ‘5’,then the decimal number is Rounded down.i.e; the underline digit in the given place remains the same.

(ii)  Rounded Up: If the circled digit in the decimal number is greater than or equals to ( ≥) number ‘5’,then the decimal number is Rounded up.i.e; the underlined digit in the given place is increased to number ‘1’.

i.e; we need to add number ‘1’ to the underlined digit.

Step-4: After Rounded-down or Rounded-up  , replace all the digits to the right of the given place with Zeros.

Note: If Round off to nearest place is not given, then we need to round off that decimal number to its greatest place value by following the above steps.

 

1) Round off : 249.267 to its nearest Hundredths place ?

Answer:

Step-1: Underline the digit in the given place (Hundredth) to be rounded in the given decimal number: 249.267 .

Step-2:Circle the digit right to the digit to be rounded. We need to circle the digit in the Thousandths place i.e: digit ‘7’ .

Step-3: Comparing the circled digit ‘7’  with number ‘5’.  7 > 5,  i.e; Rounded-Up case.Therefore, we add number’1’ to the underlined digit. i.e; 6 + 1 =7.

Step-4: Replace all the digits right of the Hundredth place  with Zero.

Thus the decimal number formed after rounded off to its nearest Hundredths place is : 249.270 = 249.27 .

 

2)  Round off : 17.95 nearest to its Tenths place?

Answer:

Step-1: Underline the digit in the given place (Tenths) to be rounded in the given decimal number: 17.95 = 17.95 .

Step-2:Circle the digit right to the digit to be rounded. We need to circle the digit in the Hundredths place i.e: digit ‘5’ .

Step-3: Comparing the circled digit ‘5’  with number ‘5’.  5 = 5,  i.e; Rounded-Up case.Therefore, we add number’1’ to the underlined digit. i.e; 9 + 1 =10.

Here, it’s a two digit number. Tens place digit : ‘1 ‘ is carry forward to whole number place Ones place.Digit ‘0’ is written in Tenths place.

Step-4: Replace all the digits right of the Tenth place  with Zero.

Thus the decimal number formed after rounded off to its nearest Tenths place is

= 18.00 = 18 , a whole number.

 

3) Round off : 3.3541 to its nearest Thousandths place.

Answer:

Step-1: Underline the digit in the given place (Hundredth) to be rounded in the given decimal number: 3.3541 .

Step-2:Circle the digit right to the digit to be rounded. We need to circle the digit in the TenThousandths place i.e: digit ‘1’ .

Step-3: Comparing the circled digit ‘1’  with number ‘5’.  1 < 5  i.e; Rounded-down  case. Therefore, we keep the digit to be rounded as it is.

Step-4: Replace all the digits right of the Thousandth place  with Zero.

Thus the decimal number formed after rounded off to its nearest Thousandths place is : 3.3540 = 3.354 .

 

The below table shows the Round-Off  decimal numbers to its nearest     

Tenths( 1/10), Hundredths( 1/100), Thousandths( 1/1000).

S.NO	NUMBER	ROUND OFF TO NEAREST PLACE
		1/ 10	1/ 100	1/ 1000
1	7.3485	7.3000    =  7.3	7.3500     = 7.35	7.3490  = 7.349
2	2.9868	3.0000   = 3	2.9900    =  2.99	2.9870   = 2.987
3	5.09187	5.10000    = 5.1	5.09000   = 5.09	5.09200  = 5.092
4	23.1381	23.1000  = 23.1	23.1400  = 23.14	23.1380 = 23.138
5	43.91441	43.90000 = 43.9	43.91000  = 43.91	43.91400 = 43.914