Rounding Decimals

Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate values and to limit the amount of decimal place.

We round off the numbers or approximate the value of decimal to a specified decimal place to make it easy to understand, instead of having a long string of decimal places.

In, rounding decimals we will learn how to round a decimal in different conditions.

Rounding off to the nearest whole number means, rounding off a decimal to the nearest whole number.

Rounding off to the nearest tenths means, rounding off a decimal number correct to 1 decimal place.

Rounding off to the nearest hundredths means, rounding off a decimal number correct to 2 decimal places.

Rounding off to the nearest thousandths means, rounding off a decimal number correct to 3 decimal places.

ROUNDING OFF A DECIMAL NUMBER

We round off a decimal in the same way as we round off a whole number. We can round off a decimal to the nearest one, tenth, hundredth, etc. But, while rounding off a decimal, we do not consider the zeros on the extreme right of the decimal point. Let us consider some examples.

I. Round off the following decimals to the nearest one.

(i) 2.9

(ii) 15.2


Solution:

(i) To round off 2.9 to the nearest one, we consider the digit at tenths place.

Round off to Nearest One

So, 2.9 can be rounded off to its nearest one as 3.


(ii) To round off 15.2 to the nearest one, we consider the digit at tenths place

Rounded to the Nearest One

So, 15.2 can be rounded off to its nearest one as 15.


II. Round off the following decimals to the nearest tenth.

(i) 7.58

(ii) 18.624


Solution:

(i) The digit at hundredths place in 7.58 is 8.

              8 > 5

So, 7.58 can be rounded off to its nearest tenth as 7.60 or 7.6


(ii) The digit at hundredths place of 18.624 is 2.

              2 < 5

So, 18,624 can be rounded off to its nearest tenth as 18.6.



III. Round off each of the following to the nearest hundredth.

(i) 7.346

(ii) 28.723


Solution:

(i) The digit at thousandths place in 7.346 is 6.

              6 > 5

So, 6.346 can be rounded off to its nearest hundredth as 6.35.


(ii) The digit at thousandths place of 28.723 is 3.

              3 < 5

So, 28.723 can be rounded off to its nearest hundredth as 28.72.


ROUNDING OFF RECURRING DECIMALS

Some decimals have endless digits as

                  0.7777..........,

                  0.050505..........,

                  0.924386924336.......... etc.

Such decimals are called recurring decimals.


Let us consider some examples

I. Round off 0.1666.......... to the nearest tenth

Solution:

The digit at the hundredths place is 6. 65 So, we can round off 0.1666. as 0.2 to its nearest tenth


II. Round off 0.7777 to the nearest hundredth

Solution:

The digit at the thousandths place is 7

                    7 > 5

So, 0.7777.......... can be rounded off as 0.78 to its nearest hundredth.


Note:

(a) When the rounded number is less than the number itself, it means the number is rounded down.

(b) When the rounded number is greater than the number itself, it means the number is rounded up.

You might like these

Related Concept

Decimals

Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

Rounding Decimals to the Nearest Whole Number

Rounding Decimals to the Nearest Tenths

Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

Simplify Decimals Involving Addition and Subtraction Decimals

Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number




7th Grade Math Problems

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