K2KARAKORAM
मराठीEnglish
Open the app

State Board · Class 6 · Mathematics

Lesson 11: Decimal Fractions

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी

Decimal fractions and place values

From daily life

A bottle of water costs ₹ 18.50, a pencil is 15.5 cm long and a mobile weighs 0.185 kg. Prices and measurements are full of numbers with a dot. These are decimal numbers.

Simple definition

A fraction whose denominator is 10, 100, 1000 … is a decimal fraction (दशांश अपूर्णांक). It is written with a decimal point.

Rule 1: Decimal point and place values — 710 = 0.7, 16100 = 0.16, 151000 = 0.015. Digits before the point are the integer part; digits after it are tenths (दशमांश), hundredths (शतांश) and thousandths (सहस्रांश). In 34.76 the 7 is in the tenths place (value 710) and the 6 in the hundredths place (value 6100).

Place values of 54.632.5Tens104Ones1.6Tenths1/103Hundredths1/1002Thousandths1/100054.63254.632 = 50 + 4 + 6/10 + 3/100 + 2/1000Each place is 10 times smaller than the one on its left

In the figure : In the figure the place values of 54.632.

Live figure

Decimal fractions and place values

In the app you can move this figure with your finger.

Open in the app
  • Easy : Easy: 910 = 0.9, 43100 = 0.43, 81000 = 0.008.
  • Medium : Medium: In 71.95 the 9 is in the tenths place with value 910 and the 5 is in the hundredths place with value 5100.
  • Exam-type : Exam: A zero at the end after the point changes nothing: 0.40 = 0.4. A hundred-square makes it easy: 34 shaded squares out of 100 is 0.34.
Remember

Decimal fraction: denominator 10, 100, 1000. After the point: tenths, hundredths, thousandths.

Common mistake

Reading 0.05 as five tenths. It is five hundredths.

Shortcut

Memory clue: "One digit → tenths; two → hundredths; three → thousandths".

Spot the difference

DecimalFraction
0.7710
0.1616100
0.015151000

Practice questions

Easy
  1. 1Write 310 as a decimal.
  2. 2Write 27100 as a decimal.
  3. 3Write 91000 as a decimal.
Medium
  1. 4In 52.84, what is the place of 8?
  2. 5In 52.84, what is the value of 4?
  3. 6Is 0.60 equal to 0.6?
Challenging
  1. 7Write 'six hundredths' in figures.
  2. 8In 0.35, 35 squares are shaded in a hundred-square. How many are not?
Show answers (try them yourself first)
  1. 10.3.
  2. 20.27.
  3. 30.009.
  4. 4Tenths.
  5. 54100.
  6. 6Yes, a zero at the end does not change the value.
  7. 70.06.
  8. 865, which is 0.65.

Reading, writing and expanded form

From daily life

The cashier says "twenty-five rupees and fifty paise". On a bill it is written ₹ 25.50. Reading and writing decimals is something we do every time we shop.

Simple definition

The expanded form (विस्तारित रूप) of a decimal writes the value of each digit separately and adds them.

Rule 1: Reading and expanded form — Read the integer part, say "point", then read each digit after the point one by one: 5.3 is "five point three" and 0.05 is "zero point zero five". Expanded form: 54.632 = 50 + 4 + 610 + 3100 + 21000. Each place is 10 times smaller than the place on its left.

  • Easy : Easy: 7.28 is read "seven point two eight".
  • Medium : Medium: 38.405 = 30 + 8 + 410 + 0100 + 51000 = 30 + 8 + 410 + 51000.
  • Exam-type : Exam: Why is 0.05 read "zero point zero five" and not "point five"? The 0 in the tenths place must be read, or the value changes.

Rule 2: Going back from the expanded form — Add the parts and write 0 in the empty places: 26 + 410 + 9100 = 26.49 and 8 + 51000 = 8.005.

A hundred-square showing 0.34.34 of 100 squares34/100 = 0.343 tenths + 4 hundredths0.3 + 0.04 = 0.34Whole = 1 = 100 squares

In the figure : In the figure a hundred-square showing 0.34.

  • Easy : Easy: 12 + 310 + 7100 = 12.37.
  • Medium : Medium: 40 + 2100 = 40.02 (a 0 goes in the tenths place).
  • Exam-type : Exam: Write 9 + 110 + 61000 as a decimal: 9.106.
Remember

Read digits after the point one by one. Write 0 in empty places.

Common mistake

Reading 3.14 as "three point fourteen". It is "three point one four".

Shortcut

Memory clue: "Before the point — as a number; after the point — digit by digit".

Spot the difference

DecimalRead as
5.3five point three
0.05zero point zero five
12.37twelve point three seven

Practice questions

Easy
  1. 1Read 6.4.
  2. 2Read 0.08.
  3. 3Write the expanded form of 23.58.
Medium
  1. 4Write 15 + 210 + 9100 as a decimal.
  2. 5Write 7 + 41000 as a decimal.
  3. 6Write the expanded form of 306.07.
Challenging
  1. 7How many times smaller is each place than the one on its left?
  2. 8Why must we write 0 in empty places such as 8.005?
Show answers (try them yourself first)
  1. 1Six point four.
  2. 2Zero point zero eight.
  3. 320 + 3 + 510 + 8100.
  4. 415.29.
  5. 57.004.
  6. 6300 + 6 + 010 + 7100, i.e. 300 + 6 + 7100.
  7. 710 times.
  8. 8Without 0 the digits would shift and the value would change.

Comparing and ordering

From daily life

Two runners finish a race in 9.42 and 9.72 seconds. To know who won, we compare the decimals digit by digit from the left.

Simple definition

To compare (तुलना करणे) decimals, compare the integer parts first, then tenths, then hundredths.

Rule 1: Comparing decimals — Compare the integer parts first. If they are equal, compare tenths; then hundredths, and so on: 24.27 < 32.48, 9.42 < 9.72, 8.78 > 8.71. Write the numbers with the same count of digits if it helps: 0.9 = 0.90 is smaller than 0.91.

Decimals on a number line from 8 to 9.8.08.28.48.68.89.08.098.598.68.88.09 < 8.59 < 8.6 < 8.8Further right = larger

In the figure : In the figure decimals on a number line.

  • Easy : Easy: 6.8 and 6.3: integer parts are equal, tenths 8 > 3, so 6.8 > 6.3.
  • Medium : Medium: 0.7 and 0.65: write 0.70 and 0.65; 70 > 65, so 0.7 > 0.65.
  • Exam-type : Exam: The winner has the smaller time: 9.42 s is less than 9.72 s, so the first runner wins.

Rule 2: Ordering and the number line — Ascending order of 8.6, 8.59, 8.09, 8.8 is 8.09, 8.59, 8.6, 8.8. On a number line, the number further to the right is larger.

  • Easy : Easy: Ascending order of 3.2, 3.02, 3.22 is 3.02, 3.2, 3.22.
  • Medium : Medium: Descending order of 5.5, 5.05, 5.15 is 5.5, 5.15, 5.05.
  • Exam-type : Exam: Which is larger, 4.9 or 4.89? Write 4.90 and 4.89; 90 > 89, so 4.9 is larger.
Remember

Compare from the left. Use equal digits (add zeros). Right on the number line = larger.

Common mistake

Thinking 4.89 is larger than 4.9 because 89 is more than 9. Compare 4.89 with 4.90.

Shortcut

Memory clue: "Make the digits equal, then compare".

Spot the difference

PairLarger
6.8 and 6.36.8
0.7 and 0.650.7
4.9 and 4.894.9

Practice questions

Easy
  1. 1Which is greater, 7.5 or 7.05?
  2. 2Which is smaller, 2.34 or 2.4?
  3. 3Put in ascending order: 1.2, 1.02, 1.22.
Medium
  1. 4Put in descending order: 6.1, 6.01, 6.11.
  2. 5Insert > or < : 0.5 __ 0.45.
  3. 6Three students jump 2.15 m, 2.5 m and 2.05 m. Who jumped farthest?
Challenging
  1. 7Which is larger: 12.09 or 12.1?
  2. 8Why is 0.9 less than 0.91?
Show answers (try them yourself first)
  1. 17.5.
  2. 22.34 (compare with 2.40).
  3. 31.02, 1.2, 1.22.
  4. 46.11, 6.1, 6.01.
  5. 50.5 > 0.45.
  6. 6The second (2.5 m).
  7. 712.1.
  8. 80.9 = 0.90 and 90 hundredths is less than 91 hundredths.

Converting fractions and decimals

From daily life

Half a litre of milk is 0.5 L, and a quarter is 0.25 L. Shopkeepers, doctors and engineers all swap between fractions and decimals.

Simple definition

Any fraction can be converted to a decimal by making its denominator 10, 100 or 1000.

Rule 1: Fraction to decimal — If the denominator is 10, 100, 1000, write it as a decimal directly. Otherwise multiply (or divide) top and bottom to reach 10, 100 or 1000: 34 = 75100 = 0.75. More examples: 23125 = 1841000 = 0.184 and 16400 = 4100 = 0.04. Half = 0.5, quarter = 0.25, 114 = 1.25.

Converting common fractions to decimals.3/4=75/100=0.75× 25 (top and bottom)FractionDenominator 10, 100Decimal1/25/100.51/425/1000.253/475/1000.751 1/4125/1001.25

In the figure : In the figure fractions to decimals.

  • Easy : Easy: 12 = 510 = 0.5.
  • Medium : Medium: 720 = 35100 = 0.35 (multiply top and bottom by 5).
  • Exam-type : Exam: 9250 = 361000 = 0.036 (multiply by 4).

Rule 2: Decimal to fraction — Count the digits after the point and put that many zeros after 1 in the denominator: 0.62 = 62100 = 3150, 25.382 = 253821000.

  • Easy : Easy: 0.3 = 310.
  • Medium : Medium: 0.45 = 45100 = 920 (divide by 5).
  • Exam-type : Exam: 12.5 = 12510 = 252 = 1212.
Remember

Make the denominator 10, 100 or 1000. Decimal digits count = zeros in the denominator.

Common mistake

Writing 0.05 as 510. It is 5100.

Shortcut

Memory clue: "Two digits after the point → over 100".

Spot the difference

FractionDecimal
120.5
340.75
7200.35
92500.036

Practice questions

Easy
  1. 1Write 14 as a decimal.
  2. 2Write 35 as a decimal.
  3. 3Write 1120 as a decimal.
Medium
  1. 4Write 0.8 as a fraction.
  2. 5Write 0.125 as a fraction in the simplest form.
  3. 6Write 212 as a decimal.
Challenging
  1. 7Write 1850 as a decimal.
  2. 8Why do we multiply top and bottom by the same number?
Show answers (try them yourself first)
  1. 10.25.
  2. 2610 = 0.6.
  3. 355100 = 0.55.
  4. 4810 = 45.
  5. 51251000 = 18.
  6. 62.5.
  7. 736100 = 0.36.
  8. 8The value of the fraction does not change.

Adding and subtracting decimals

From daily life

You buy a notebook for ₹ 24.75 and a pen for ₹ 8.5. How much did you spend? Add the decimals just like whole numbers, but line up the points.

Simple definition

While adding or subtracting decimals, the decimal points must be in one vertical line.

Rule 1: Adding and subtracting decimals — Write the numbers one below the other so that the decimal point is below the decimal point. Fill empty places with zeros, then add or subtract as usual. Example: 3.64 + 5.4 = 3.64 + 5.40 = 9.04 and 20 − 11.35 = 20.00 − 11.35 = 8.65.

Adding and subtracting decimals in columns.Add: 3.64 + 5.43.64+ 5.409.04Subtract: 20 − 11.3520.00− 11.358.65Keep the decimal point under the decimal pointFill empty places with zeros

In the figure : In the figure adding and subtracting in columns.

  • Easy : Easy: 12.4 + 3.25 = 12.40 + 3.25 = 15.65.
  • Medium : Medium: 9.6 − 4.37 = 9.60 − 4.37 = 5.23.
  • Exam-type : Exam: 15 − 6.08 = 15.00 − 6.08 = 8.92.

Rule 2: Word problems — A rope is 7.5 m long and 2.75 m is cut off, so 7.50 − 2.75 = 4.75 m is left. Anita runs 3.27 km + 2.8 km = 6.07 km.

  • Easy : Easy: Notebook ₹ 24.75 + pen ₹ 8.50 = ₹ 33.25.
  • Medium : Medium: A ribbon of 5.6 m has 1.85 m used; left = 5.60 − 1.85 = 3.75 m.
  • Exam-type : Exam: Ravi paid ₹ 50 for items costing ₹ 18.40 and ₹ 22.15. Total = 40.55; change = 50.00 − 40.55 = ₹ 9.45.
Remember

Align the points. Fill zeros. Then add or subtract. Put the point in the answer straight below.

Common mistake

Writing numbers aligned to the right like whole numbers. Align the decimal points instead.

Shortcut

Memory clue: "Point under point".

Spot the difference

StepAction
1Write point under point
2Fill empty places with 0
3Add or subtract

Practice questions

Easy
  1. 1Add 4.5 + 2.37.
  2. 2Add 0.8 + 0.75.
  3. 3Subtract 8.2 − 3.45.
Medium
  1. 4Subtract 10 − 2.6.
  2. 5Add 12.05 + 7.9 + 0.35.
  3. 6A tank has 15.6 L water and 4.75 L is used. How much is left?
Challenging
  1. 7Meera runs 2.4 km, 1.85 km and 3.3 km. Find the total distance.
  2. 8Why do we write 0 to fill empty places?
Show answers (try them yourself first)
  1. 16.87.
  2. 21.55.
  3. 34.75.
  4. 47.4.
  5. 520.30 = 20.3.
  6. 615.60 − 4.75 = 10.85 L.
  7. 77.55 km.
  8. 8It makes the digits equal in number so the places match without changing the value.