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State Board · Class 5 · Mathematics

Lesson 9: Decimal Fractions

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

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Tenths and hundredths as decimals

From daily life

A 1-metre ribbon is cut into 10 equal pieces and 3 pieces are used. The used part is 310 of a metre, which we write as 0.3 m. The dot in 0.3 is a decimal point.

Simple definition

A fraction with denominator 10 or 100 can be written as a decimal (दशांश). The decimal point separates the whole number (left) from the parts of one (right). 9100 = 0.09 and 4310 = 4.3.

A strip cut into 10 equal parts with 3 shaded: 3/10 is written 0.3.One whole cut into 10 equal parts3/10 = 0.3three tenths1/10 = 0.110/10 = 1.0

In the figure : A strip cut into 10 equal parts with 3 shaded: 310 is written 0.3.

Rule 1: Tenths and hundredths — Denominator 10 → one digit after the point. Denominator 100 → two digits after the point.

  • Easy : 710 = 0.7 and 23100 = 0.23.
  • Medium : 5100 = 0.05 (the zero holds the tenths place).
  • Exam-type : 6110 = 6.1 and 1245100 = 12.45.
Live figure

Tenths and hundredths as decimals

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Rule 2: Fractions to decimals — Change the fraction to an equal fraction with denominator 10 or 100.

  • Easy : 12 = 510 = 0.5.
  • Medium : 14 = 25100 = 0.25 and 34 = 75100 = 0.75.
  • Exam-type : A zero at the end does not change the value: 0.3 = 0.30 = 0.300.
Remember

The number of digits after the point equals the number of zeros in the denominator (10 → 1, 100 → 2).

Common mistake

Writing 5100 as 0.5. It is 0.05, because there are no tenths.

Shortcut

Memory clue: As many zeros, as many decimal places.

Spot the difference

FractionDecimal
1100.1
140.25
120.5
340.75

Practice questions

Easy
  1. 1Write 710 as a decimal.
  2. 2Write 23100 as a decimal.
  3. 3Write 5100 as a decimal.
Medium
  1. 4Write 0.9 as a fraction.
  2. 5Write 15 as a decimal using 10ths.
  3. 6Write 6110 and 1245100 as decimals.
Challenging
  1. 7Is 0.5 equal to 0.50? Why?
  2. 8A shopkeeper sells 34 kg of sugar. Write the weight as a decimal in kg.
Show answers (try them yourself first)
  1. 10.7
  2. 20.23
  3. 30.05
  4. 4910
  5. 5210 = 0.2
  6. 66.1 and 12.45
  7. 7Yes, a zero at the end does not change the value.
  8. 834 = 75100 = 0.75 kg

Place value of decimals

From daily life

A school bag costs ₹ 345.67 in a shop. Here 345 are rupees and .67 shows paise. Each digit has a place: the digits to the right of the point are tenths and hundredths.

Simple definition

To the right of the point the places are tenths (दशांश, first place) and hundredths (शतांश, second place). Each place to the right is 10 times smaller. A zero holds a place.

The number 345.67 in a place value chart: 3 hundreds, 4 tens, 5 ones, point, 6 tenths and 7 hundredths.3100hundreds410tens51ones.61⁄10tenths71⁄100hundredths

In the figure : The number 345.67 in a place value chart, with tenths and hundredths to the right of the point.

Rule 1: Place value — Digit × value of its place.

  • Easy : In 345.67, the 6 means 6 tenths = 0.6 and the 7 means 7 hundredths = 0.07.
  • Medium : 52.38 = 50 + 2 + 0.3 + 0.08.
  • Exam-type : In 8.07 there are no tenths; the 7 is worth 0.07, not 0.7.

Rule 2: Expanded form — Write each digit with its place value and add.

  • Easy : 6.84 = 6 + 0.8 + 0.04.
  • Medium : 7.09 = 7 + 0.09 (zero in the tenths place).
  • Exam-type : 30.5 + 0.25 = 30.75, so 30.75 = 30 + 0.7 + 0.05.
Remember

Each place is 10 times the place on its right and 10 times smaller than the place on its left.

Common mistake

Reading 0.07 as "seven tenths". It is seven hundredths.

Shortcut

Memory clue: First place after the point = tenths; second = hundredths.

Spot the difference

PlaceValue in 345.67
tenths (6)0.6
hundredths (7)0.07
ones (5)5

Practice questions

Easy
  1. 1In 2.74, what is the place value of 7?
  2. 2In 2.74, what is the place value of 4?
  3. 3Write 3 + 0.5 + 0.02 as a decimal.
Medium
  1. 4Write 52.38 in expanded form.
  2. 5What is the place value of 0 in 8.07?
  3. 6Write 7 + 0.09 as a decimal.
Challenging
  1. 7A bill shows ₹ 126.45. Name the place value of each digit.
  2. 8Ravi writes 4 tenths + 5 hundredths as 4.5. What is wrong?
Show answers (try them yourself first)
  1. 10.7 (7 tenths)
  2. 20.04 (4 hundredths)
  3. 33.52
  4. 450 + 2 + 0.3 + 0.08
  5. 50 (it holds the tenths place)
  6. 67.09
  7. 71 hundred, 2 tens, 6 ones, 4 tenths, 5 hundredths.
  8. 8It should be 0.45. 4.5 would mean 4 ones and 5 tenths.

Comparing and ordering decimals

From daily life

Two plants grow: one is 3.6 m tall and the other is 3.06 m. Which is taller? We compare digits from the left.

Simple definition

To compare decimals: compare the whole parts first; if they are equal compare the tenths, then the hundredths. Add zeros at the end to make the number of decimal places equal.

A number line from 2 to 3 split into tenths with 2.3 and 2.8 marked.2.02.53.02.32.8further right = bigger: 2.3 < 2.8

In the figure : On the number line 2.3 is to the left of 2.8, so 2.3 < 2.8.

Rule 1: Compare place by place — Whole, then tenths, then hundredths.

  • Easy : 7.9 > 7.19 because 9 tenths > 1 tenth.
  • Medium : 3.6 > 3.06: 3.60 against 3.06, 6 tenths > 0 tenths.
  • Exam-type : 2.5 = 2.50, which is bigger than 2.05.

Rule 2: Order decimals — Make the places equal, then arrange.

  • Easy : Ascending 0.45, 4.05, 4.5, 4.55 (smallest to biggest).
  • Medium : Descending 4.55, 4.5, 4.05, 0.45.
  • Exam-type : On a number line the number further to the right is bigger.
Remember

Longer does not mean bigger. 0.5 is bigger than 0.45.

Common mistake

Thinking 0.45 > 0.5 because 45 > 5. Write 0.5 = 0.50 and compare 50 > 45.

Shortcut

Memory clue: Add zeros, then compare like whole numbers.

Spot the difference

CompareResult
3.6 and 3.063.6 > 3.06
0.5 and 0.450.5 > 0.45
2.30 and 2.3equal

Practice questions

Easy
  1. 1Which is bigger: 7.9 or 7.19?
  2. 2Which is bigger: 3.6 or 3.06?
  3. 3Put < or >: 0.5 __ 0.45.
Medium
  1. 4Put < or >: 2.30 __ 2.3.
  2. 5Arrange from smallest: 4.55, 4.5, 4.05, 0.45.
  3. 6Arrange from biggest: 1.2, 1.02, 1.21, 0.12.
Challenging
  1. 7Two plants are 3.6 m and 3.06 m tall. Which is taller and by how much?
  2. 8Sita says 0.45 is bigger than 0.5 because 45 is more than 5. Correct her.
Show answers (try them yourself first)
  1. 17.9
  2. 23.6
  3. 3>
  4. 4They are equal (=).
  5. 50.45, 4.05, 4.5, 4.55
  6. 61.21, 1.2, 1.02, 0.12
  7. 73.6 m is taller by 3.60 − 3.06 = 0.54 m.
  8. 80.5 = 0.50 and 50 > 45, so 0.5 is bigger.

Adding and subtracting decimals

From daily life

A tailor has a 3.45 m piece of cloth and buys 2.70 m more. To know the total length, he adds the two decimals.

Simple definition

To add or subtract decimals, write them with the decimal points one below the other, add zeros to fill gaps and work from the right as for whole numbers. Put the point in the answer straight below the points.

Column addition of 3.45 and 2.70 with the decimal points lined up gives 6.15.Line up the decimal points3 . 4 5+ 2 . 7 06 . 1 5write 2.7 as 2.70add from the right

In the figure : Lining up the decimal points: 3.45 + 2.70 = 6.15.

Rule 1: Add decimals — Align the points, add from the right, carry over as usual.

  • Easy : 2.35 + 4.50 = 6.85.
  • Medium : 12.4 + 7.85 = 20.25 (write 12.40).
  • Exam-type : 15.3 + 0.75 = 16.05; the sum of the hundredths is 5 and the carry makes the tenths 3 + 7 = 10.

Rule 2: Subtract decimals — Align the points, add zeros, borrow when needed.

  • Easy : 9.40 − 4.75 = 4.65.
  • Medium : 6.2 − 2.85 = 6.20 − 2.85 = 3.35.
  • Exam-type : 10 − 3.64 = 10.00 − 3.64 = 6.36. Check: 6.36 + 3.64 = 10.00.
Remember

Always add zeros so that both numbers have the same number of decimal places.

Common mistake

Lining up the right-hand digits: 12.4 + 7.85 written with 4 under 5. Line up the points, not the last digits.

Shortcut

Memory clue: Point under point.

Spot the difference

StepWhat to do
1Line up the decimal points
2Fill with zeros
3Add or subtract; put the point below

Practice questions

Easy
  1. 1Add: 1.25 + 2.5.
  2. 2Add: 4.8 + 3.65.
  3. 3Add: 15.3 + 0.75.
Medium
  1. 4Subtract: 8 − 2.5.
  2. 5Subtract: 10.00 − 6.45.
  3. 6Subtract: 25.6 − 13.85.
Challenging
  1. 7A tailor has 3.5 m of cloth and buys 2.75 m more. How much cloth does he have?
  2. 8A can has 12.5 litres of oil. 4.75 litres are used. How much is left? Check by adding.
Show answers (try them yourself first)
  1. 13.75
  2. 28.45
  3. 316.05
  4. 45.5
  5. 53.55
  6. 611.75
  7. 73.5 + 2.75 = 6.25 m.
  8. 812.5 − 4.75 = 7.75 L. Check: 7.75 + 4.75 = 12.50.

Decimals in money and measures

From daily life

At a shop you pay ₹ 12.75. That means 12 rupees and 75 paise, because 100 paise make ₹ 1. Money and measures are everyday decimals.

Simple definition

₹ 12.75 = 12 rupees and 75 paise. Metric units are decimals: 1 cm = 0.01 m, 1 mm = 0.1 cm, 250 g = 0.25 kg. To go to a smaller unit multiply; to a bigger unit divide.

A 100 square grid with 25 squares shaded: 25 hundredths is 0.25, which equals one quarter.25 of 100 squares25/100 = 0.250.25 = 1/4

In the figure : A grid of 100 squares with 25 shaded shows 25/100 = 0.25 = 1/4. Money works the same way: 25 paise is ₹ 0.25.

Rule 1: Money — 100 paise = ₹ 1, so 50 paise = ₹ 0.50.

  • Easy : ₹ 4.60 = 4 rupees and 60 paise.
  • Medium : 250 paise = ₹ 2.50.
  • Exam-type : ₹ 15.75 + ₹ 9.50 = ₹ 25.25.

Rule 2: Units — Bigger unit to smaller: multiply. Smaller to bigger: divide.

  • Easy : 3.5 m = 3.5 × 100 = 350 cm.
  • Medium : 750 g = 750 ÷ 1000 = 0.75 kg.
  • Exam-type : Compare 1.2 m and 130 cm: 1.2 m = 120 cm, so 130 cm is longer.
Remember

Change both to the same unit before comparing.

Common mistake

Writing 5 paise as ₹ 0.5. It is ₹ 0.05.

Shortcut

Memory clue: Rupee and paise, metre and centimetre – 100 each.

Spot the difference

UnitEqual to
₹ 1100 paise
1 m100 cm
1 kg1000 g

Practice questions

Easy
  1. 1Write 250 paise in rupees.
  2. 2Write ₹ 4.60 as rupees and paise.
  3. 3Convert 3.5 m to cm.
Medium
  1. 4Convert 750 g to kg.
  2. 5Which is longer: 1.2 m or 130 cm?
  3. 6Add: ₹ 36.50 + ₹ 18.75.
Challenging
  1. 7Meena buys goods for ₹ 63.40 and pays ₹ 100. How much change should she get?
  2. 8A parcel weighs 2.4 kg and another weighs 750 g. Find the total weight in kg.
Show answers (try them yourself first)
  1. 1₹ 2.50
  2. 24 rupees 60 paise
  3. 3350 cm
  4. 40.75 kg
  5. 5130 cm (1.2 m = 120 cm).
  6. 6₹ 55.25
  7. 7100.00 − 63.40 = ₹ 36.60
  8. 8750 g = 0.75 kg; 2.4 + 0.75 = 3.15 kg.