LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

ROUNDING OFF DECIMAL FRACTION

__APPROXIMATION (Rounding Off) __

**Suppose we want
to round off 104, then we have to judge whether it near to 100 or 110. Here 104
is nearest to 100 than 110, so we have to round it off to 100, the rule for
rounding off a whole number to the nearest ten is as follows –**

**If the digit in the
one place is less than 5, then we should write zero ‘0’ in the unit place and
keep the digits in other places as they are **

**But, if the digit in
the one place is 5 or more than that, then we should write zero ‘0’ in the one
place and add 1 to the digit in the tens place.**

**For better
understanding, as per the example –**

**1) 145 is rounding
off to 150 as a digit in the one place is 5 = 5**

**2) 258 is rounding
off to 260 as a digit in the one place is 8 > 5**

**3) 332 is rounding
off to 330 as a digit in the one place is 2 < 5**

__Rounding off decimal fraction –__

**Decimal fraction can
be rounded off to the nearest one, tenth, hundredth, thousandth, etc. so, to
round off a decimal to the nearest unit, remember the following – if the digit
in the tenths is less than 5 then we should have write zero ‘0’ in the tenths
place and the following decimal places. Keep the other digits as they are. **

**If the digit in the ****tenths**** place is 5 or more than 5, write zeros in the decimal places and
increase the digit in the units place by one. **

**To round off a
decimal to the first decimal places, or to the nearest tenths and we should
keep in mind, if the digit in the second decimal places is less than 5, we
have to write zero ‘0’ in the second and the following decimal places. leave
the other digits as they are.**

**If the digit in the
second decimal places is 5 or more than 5, then we should write zero ‘0’ in the
second and the following decimal places and add 1 to the digit in the first
decimal places.**

__Example –__

**1) 2.8 is
rounded off to the nearest unit is 3 because 8 > 5**

**2) 3.2 is
rounded off to the nearest unit is 3 because 2 < 5**

**3) 4.5 is rounded off
to the nearest unit is 5 because 5 = 5**

**4) 12.78 is rounded
off to the nearest unit is 13 because 7 > 5**

**5) 10.31 is rounded
off to the nearest unit is 10 because 3 < 5**

__Significant Figures –__

**The significant
figures of a decimal number are those which must be retained for any position
of the decimal point. All non zero digits are significant and so are the zeros
between them. We have to start counting from the first nonzero number to the
left. **

__Example –__

**1) 5.125 kg =
5125 gm**

**2) 2.25 liter =
225 cl (****Centiliter****) **

**3) 4.512 miter
= 4512 mm (****Millimeter****) **