# CLASS-8APPROXIMATION ( ROUNDING OFF )

APPROXIMATION ( ROUNDING OFF ) OF DECIMALS

Suppose, 35467824 people attended at playground to see a cricket match. To get a rough idea of the number of spectators, we may remember the first two digits from the left and put zeros in places of the other digits. Thus, it can be reported that approximately 3,55,00,000 people attended the match. This is called rounding off, here we have rounded off 35467824 to the nearest thousand.  Similarly, we can round off numbers to the nearest ten, hundred, ten-thousand, lakh, million, etc.

Rounding off whole numbers –

Consider the number 3264. Suppose you want to round it off to the nearest ten, you find that 3264 is nearer to 3260 than to 3270. So, 3264 rounded off to the nearest ten is 3260.

Now suppose you want to round off 6785 to the nearest hundred. 6785 is nearer to 6800 than to 6700. So, you round it off to 6800.

The general rule for rounding off a whole number to the nearest hundred is as follows.

For very serious note – If the digit in the tens place is less than 5, write 0 in the tens place as well as in the units place and keep the digits in the other places as they are.

If the digit in the tens place is 5 or more than 5, we should write 0 in the tens place as well as in the units place and add 1 to the digit in the hundreds place.

Example- 1)  5923 rounded off to the nearest  hundred is 5900 as the digit in the tens place = 2 < 5

2) 3675 rounded off to the nearest hundred is 3700 as the digit in the tens place = 7 > 5

Similarly, a whole number can be rounded off to the nearest thousand, ten thousand, etc.

1) 5769 is rounded off to 6000 ( nearest thousand )

2) 41253 is rounded off a 40000 ( nearest ten thousand )

Rounding Off Decimal Fractions –

Decimal fractions can be rounded off to the nearest one, tenth, hundredth, thousandth, etc.

The general rule for rounding off decimal is as follows -

First, we have to find the answer to one more place than you need, if the digit in the extra place is 5 or more, add 1 to the digit in the place just before it. If the digit in the extra place is less than 5, leave the digit in the place just before it as it is.

Example.1)  57.7 rounded off to the nearest unit is 58 because the digit in the first decimal place is 7 > 5.

Example.2)  67.59 rounded off to 1 decimal place is 67.6 because the digit in the second decimal place is 9 > 5.

Example.3)  46.233 rounded off to 2 decimal places is 46.23 because the digit in the third decimal places is   3 < 5.

Significant Figures –

The digits used to express a number to a specified degree of accuracy are the Significant Figures.

Finding Significant Figures Of a Number –

Ignore the decimal point and read the number from left to right. The first significant figure is considered as the first non-zero digit. All digit after that are also significant.

Example – 4.537 has four significant figures – 4, 5, 3 & 7. The number 0.0007058 also has four significant figures – 7, 0, 5 & 8. The zeros before the digit 7 are not significant but the zero after 7 is significant.

The number 243.57 has five significant figures – 2, 4, 3, 5 & 7. In the number 243.57 the digit 2 is the most significant figure as it has a place value of 200, while the digit  7 is the least significant figures it has a place value of 7/100.

Rounding Off to Significant figure –

First, find the answer to one more significant figure than you need, if the extra digit is 5 or more than 5, add 1 to the digit just before it, if the extra digit is less than 5, leave the digit just before it as it is.

Example – 763.539 correct to 5 significant figure = 763.54

As the sixth significant figure = 9 > 5, we add 1 to the fifth significant figure, that is 3

763.539 correct to 4 significant figure = 763.5

As the fifth significant figure =  3 < 5