Informative line

Estimation Of Decimals And Fractions

Rounding

  • Rounding a number means to change its value slightly.
  • It is not as exact as the original value but it is approximately close to the original value.
  • Numbers can be rounded to a certain place values like tens, hundreds, thousands etc.

Rounding off decimal to whole numbers

  • To round off a decimal number to a whole number, first analyze the first digit after the decimal point i.e. at the tenths place.

  • If the digit at the tenths place is \(5\) or greater than \(5\), then the digit at ones place increases by \(1\) and the digits after the decimal point become zero.

  • If the digit at the tenths place is less than \(5\), the digit at ones place remains same and the digits after the decimal point become zero.

Let's take an example.

Example: Round off \(125.25\) to the nearest whole number.

  • Analyze the first digit after the decimal point i.e. at the tenths place which is \(2\) and \(2\) is less than \(5\).
  • Thus, the digit at ones place i.e. \(5\) remains same and the digits after the decimal point become zero.
  • So, the nearest whole number of \(125.25\) is \(125\).

Illustration Questions

Round off \(25.700\) to the nearest whole number.

A \(25\)

B \(26\)

C \(27\)

D \(30\)

×

Analyze \(25.700\) 

Here, digit at the tenths place is \(7\) which is greater than \(5\).

Thus, the digit at ones place i.e. \(5\) is increased by \(1\) ( i.e. \(5+1=6\)) and the digits after the decimal point become zero.

So, the nearest whole number of \(25.700\) is \(26\)

Hence, option (B) is correct.

Round off \(25.700\) to the nearest whole number.

A

\(25\)

.

B

\(26\)

C

\(27\)

D

\(30\)

Option B is Correct

Rounding Rules for Decimal Number (Hundredths Place)

  • To round off the decimal to the nearest tenth's place, analyze the digit after decimal point i.e. at the hundredths place.
  • If the hundredths place value is \(5\) or greater than \(5\) then digit of tenths place increases by \(1\) and the digit at hundredths place and thereafter become zero.
  • If the hundredths place value is less than \(5\) then digit of tenths place remains same and the digit at hundredths place and thereafter becomes zero.

Rounding off decimal (hundredths place):

  • Let's take an example to understand it.

Example (1): \(49.38\)

  • Let's use place value chart.
Tens Ones   Tenths Hundredths
4 9  .  3 8
  • In place value chart analyze the hundredths place.
  • Here, the digit at the hundredths place is \(8\) and \(8\) is greater than \(5\).
  • Thus, the digit of tenths place increases by \(1\) and the digit at the hundredths place become zero.
  • So, the nearest tenths to \(49.38\) after round-off is \(49.4\).

Example (2): \(33.42\)

  • Let's use place value chart.
Tens Ones   Tenths Hundredths
3 3  .  4 2
  • In place value chart analyze the hundredths place.
  • Here, the digit at the hundredths place is \(2\) and \(2\) is less than \(5\).
  • Thus, the digit at tenths place remains same and the digit at the hundredths place become zero.
  • So, the nearest tenths to \(33.42\) after round-off is \(33.4\).

Illustration Questions

What is the round off value of \(56.37\) up to the tenths place?

A \(56.4\)

B \(57.0\)

C \(56.3\)

D \(56.0\)

×

Place value chart for given decimal number is 

Tens Ones   Tenths Hundredths
5 6  .  3 7

Here, the digit at the hundredths place is \(7\) which is greater than \(5\).

So, the digit at the tenths place is increased by \(1\).

The digit at the hundredths place becomes zero.

So, the nearest tenths to \(56.37\) after round off is \(56.4\).

Hence, option (A) is correct.

What is the round off value of \(56.37\) up to the tenths place?

A

\(56.4\)

.

B

\(57.0\)

C

\(56.3\)

D

\(56.0\)

Option A is Correct

Rounding Rule for Decimal Number (Thousandths Place)

  • To round off a decimal to the nearest hundredth place, analyze the digit at the thousandths place.
  • If the digit at the thousandths place is \(5\) or greater than \(5\) , then the digit at the hundredth place increases by \(1\) and the digits at the thousandth place and thereafter become zero.
  • If the digit at the thousandths place is less than \(5\) , then the digit at hundredth place remains same and the digits at the thousandth place and thereafter become zero.

Rounding off Decimal Number (Thousandths place):

Rounding up to hundredths place or thousandths place is similar to tenth place. Let's look at an example to understand it.

Example: \(23.759\)

Let's use the place value chart.

Tens Ones   Tenths Hundredths Thousandths
2 3  .  7 5 9
  • Analyze the digit at the thousandths place in the given decimal number.
  • Here the digit at the thousandths place is greater than \(5\)
  • Thus, the digit at the hundredths place increases by \(1\) and the digit at the thousandth place becomes zero.
  • So, the nearest hundredths to \(23.759\) after round off is \(23.76\).

  • So, the nearest hundredths to \(23.759\) after  round off is \(23.76\) .

Illustration Questions

What is the round off value of \(28.39173\) up to hundredth place?

A \(28.38\)

B \(28.391\)

C \(28.3\)

D \(28.39\)

×

Place value chart for given decimal number is

Tens Ones   Tenths Hundredths Thousandths Ten thousandths Millionths
2 8  .  3 9 1 7 3

Analyze the place value chart.

Here, the digit at the thousandths place is \(1\) which is less than \(5\).

Thus, the digit at the hundredths place i.e. \(9\) remains same and the digits at the thousandths place and thereafter are removed.

image

So, the nearest hundredth of \(28.39173\) after round off is \(28.39\).

Hence, option (D) is correct.

What is the round off value of \(28.39173\) up to hundredth place?

A

\(28.38\)

.

B

\(28.391\)

C

\(28.3\)

D

\(28.39\)

Option D is Correct

Rounding off simple Fraction

Rounding off fraction to the nearest half

  • To round off a fraction to the nearest whole number or nearest half, analyze the numerator and the denominator.
  • We have three main values to round to \(0\)\(\dfrac{1}{2}\) , \(1\), when we round a fraction to the nearest half.
  • We round the fraction to whichever half, it is closest.
  • If the numerator is almost as large as the denominator round the number up to the next whole number.
  • If the numerator is about half of the denominator round the fraction to \(\dfrac{1}{2}\).
  • If the numerator is equidistant from both the nearest half then round the fraction up.

Example: \(\dfrac{7}{8}\)

The numerator \(7\) is almost as large as the denominator \(8\), so we shall round off it up to \(1\).

Example: \(\dfrac{3}{5}\)

The numerator \(3\) is about half of the denominator \(5\), so round the fraction to \(\dfrac{1}{2}\).

Illustration Questions

What is the round off value of \(\dfrac{13}{20}\)?

A \(0\)

B \(1\)

C \(\dfrac{1}{2}\)

D \(2\)

×

Analyze the fraction \(\dfrac{13}{20}\).

The numerator \(13\) is about half of the denominator \(20\).

\(\dfrac{13}{20}\) is closest to \(\dfrac{1}{2}\).

So, \(\dfrac{13}{20}\) becomes \(\dfrac{1}{2}\).

Hence, option (C) is correct.

What is the round off value of \(\dfrac{13}{20}\)?

A

\(0\)

.

B

\(1\)

C

\(\dfrac{1}{2}\)

D

\(2\)

Option C is Correct

Rounding off Mixed Number to Nearest Whole Number

  • A mixed fraction or a mixed number lies between two nearest whole numbers.
  • A mixed fraction includes both whole numbers and a fraction.
  • To round off the mixed fraction to the nearest whole number, analyze the mixed fraction.
  • We need to figure out whether a fraction is larger than \(\dfrac{1}{2}\) or less than \(\dfrac{1}{2}\).

\(\to\) If the fraction part of mixed fraction is greater than or equal to \(\dfrac{1}{2}\), then the fraction is round-up.

\(\to\) If the fraction part of mixed fraction is less than \(\dfrac{1}{2}\) then the fraction is round-down.

Example: (i) \(1\dfrac{2}{3}\)

  • In this mixed fraction, the fraction part \(\dfrac{2}{3}\) is greater than \(\dfrac{1}{2}\) i.e. \(\dfrac{2}{3}>\dfrac{1}{2}\)
  • So, mixed fraction \(1\dfrac{2}{3}\) is round up to nearest whole number i.e. \(2.\)

(ii) \(15\dfrac{1}{4}\)

  • In this mixed fraction, the fraction part \(\dfrac{1}{4}\) is less than \(\dfrac{1}{2}\) i.e. \(\dfrac{1}{4}<\dfrac{1}{2}\)
  • So, mixed fraction \(15\dfrac{1}{4}\) is round down to nearest whole number i.e.\(15.\)

Illustration Questions

What is the round off value of \(4\dfrac{6}{7}\)?

A \(4\)

B \(5\)

C \(6\)

D \(7\)

×

Given: \(4\dfrac{6}{7}\)

Fraction \(\dfrac{6}{7}\) is greater than \(\dfrac{1}{2}\) i.e. \(\dfrac{6}{7}>\dfrac{1}{2}\)

\(\dfrac{6}{7}\) is closest to \(1\).

So, \(4\dfrac{6}{7}\) becomes \(5\).

Hence, option (B) is correct.

What is the round off value of \(4\dfrac{6}{7}\)?

A

\(4\)

.

B

\(5\)

C

\(6\)

D

\(7\)

Option B is Correct

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