Chapter 10 of 14
Chapter 10: Tenths and Hundredths
दसवाँ और सौवाँ भाग (दशमलव, मिलीमीटर-सेंटीमीटर एवं मुद्रा गणना) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Understanding Decimals: Tenths (1/10 = 0.1) and Hundredths (1/100 = 0.01).
- Length measurement: 1 cm = 10 mm ⇒ 1 mm = 0.1 cm.
- Currency notation: 1 Rupee = 100 paise ⇒ 1 paisa = ₹0.01; 75 paise = ₹0.75.
- Temperature reading and comparing decimal values across different Indian cities.
- (a) 4 cm 8 mm: Since $1\text{ mm} = 0.1\text{ cm}$, $8\text{ mm} = 0.8\text{ cm}$. Total = $4 + 0.8 = \mathbf{4.8\text{ cm}}$.
- (b) 75 paise: Since $100\text{ paise} = ₹1$, $75\text{ paise} = \frac{75}{100} = \mathbf{₹0.75}$.
- (c) 3 m 45 cm: Since $100\text{ cm} = 1\text{ m}$, $45\text{ cm} = 0.45\text{ m}$. Total = $3 + 0.45 = \mathbf{3.45\text{ m}}$.
- (d) 5 mm: $\frac{5}{10} = \mathbf{0.5\text{ cm}}$.
All Textbook Exercises & In-Text Tasks (24 Questions)
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Q1
Textbook Exercise • Pencil Measurement in Millimetres
Look at a ruler: (a) How many millimetres are there in 1 centimetre? (b) What fraction of a centimetre is 1 mm? (c) A small pencil measures 3 cm and 6 mm. Write its length in centimetres using decimals.
[3 Marks]
✅ Step-by-Step Solution & Working
Metric Conversions:
• (a) Millimetres in 1 cm: 10 millimetres (10 mm).
• (b) Fraction: 1 mm = 1/10 of a cm.
• (c) Decimal notation: 3 cm + 6/10 cm = 3.6 cm.
• (a) Millimetres in 1 cm: 10 millimetres (10 mm).
• (b) Fraction: 1 mm = 1/10 of a cm.
• (c) Decimal notation: 3 cm + 6/10 cm = 3.6 cm.
CBSE Step-by-Step Marking Scheme
Part (a): 10 mm
1 M
Part (b): 1/10 cm
1 M
Part (c): 3.6 cm
1 M
Q2
Textbook Exercise • Frog Jump Lengths
Two species of frogs are found in India: A Gold Frog is 0.9 cm long. A Bull Frog is 30.5 cm long. (a) How many millimetres long is the Gold Frog? (b) About how many Gold Frogs can sit on the body of one Bull Frog?
[3 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• (a) Gold Frog in mm: 0.9 cm = 0.9 × 10 = 9 mm.
• (b) Number of Gold Frogs: 30.5 cm ÷ 0.9 cm ≈ 305 ÷ 9 = 33.88 (about 33 or 34 frogs).
• (a) Gold Frog in mm: 0.9 cm = 0.9 × 10 = 9 mm.
• (b) Number of Gold Frogs: 30.5 cm ÷ 0.9 cm ≈ 305 ÷ 9 = 33.88 (about 33 or 34 frogs).
CBSE Step-by-Step Marking Scheme
Part (a): 9 mm
1.5 M
Part (b): About 33-34 frogs
1.5 M
Q3
Textbook Exercise • Money in Decimals (Paise to Rupee)
Convert the following paise amounts into rupees using decimals:
(a) 50 paise
(b) 75 paise
(c) 5 paise
(d) 250 paise
[4 Marks]
(a) 50 paise
(b) 75 paise
(c) 5 paise
(d) 250 paise
✅ Step-by-Step Solution & Working
Rupee Conversions (1 Rupee = 100 paise; divide by 100):
• (a) 50 paise = 50 ÷ 100 = ₹0.50.
• (b) 75 paise = 75 ÷ 100 = ₹0.75.
• (c) 5 paise = 5 ÷ 100 = ₹0.05 (note the zero in tenths place!).
• (d) 250 paise = 250 ÷ 100 = ₹2.50.
• (a) 50 paise = 50 ÷ 100 = ₹0.50.
• (b) 75 paise = 75 ÷ 100 = ₹0.75.
• (c) 5 paise = 5 ÷ 100 = ₹0.05 (note the zero in tenths place!).
• (d) 250 paise = 250 ÷ 100 = ₹2.50.
CBSE Step-by-Step Marking Scheme
₹0.50
1 M
₹0.75
1 M
₹0.05 (vital zero check)
1 M
₹2.50
1 M
Q4
Textbook Exercise • City Temperature Readings
The temperature recorded at 3:00 PM in different cities on 16 January were:
• Chennai: 29.9°C
• Mumbai: 35.1°C
• Srinagar: 8.1°C
• Jaipur: 37.9°C
(a) Which place was the hottest at 3 PM? (b) Which place was the coolest? (c) How much higher was Mumbai's temperature than Srinagar's?
[3 Marks]
• Chennai: 29.9°C
• Mumbai: 35.1°C
• Srinagar: 8.1°C
• Jaipur: 37.9°C
(a) Which place was the hottest at 3 PM? (b) Which place was the coolest? (c) How much higher was Mumbai's temperature than Srinagar's?
✅ Step-by-Step Solution & Working
Temperature Analysis:
• (a) Hottest place: Jaipur (37.9°C).
• (b) Coolest place: Srinagar (8.1°C).
• (c) Difference between Mumbai and Srinagar: 35.1°C - 8.1°C = 27.0°C higher.
• (a) Hottest place: Jaipur (37.9°C).
• (b) Coolest place: Srinagar (8.1°C).
• (c) Difference between Mumbai and Srinagar: 35.1°C - 8.1°C = 27.0°C higher.
CBSE Step-by-Step Marking Scheme
Hottest: Jaipur (37.9°C)
1 M
Coolest: Srinagar (8.1°C)
1 M
Difference: 27.0°C
1 M
Q5
Textbook Exercise • Sports Day Long Jump
In the School Sports Day long jump event: Teena jumped 3.50 m, Meena jumped 4.05 m, and Rehana jumped 4.50 m. (a) Who jumped the longest distance? (b) By how many metres did Rehana beat Teena? Express your answer in metres and centimetres.
[3 Marks]
✅ Step-by-Step Solution & Working
Jump Comparisons:
• (a) Longest jump: Rehana (4.50 m).
• (b) Difference: 4.50 m - 3.50 m = 1.00 m = 1 metre (or 100 cm).
• (a) Longest jump: Rehana (4.50 m).
• (b) Difference: 4.50 m - 3.50 m = 1.00 m = 1 metre (or 100 cm).
CBSE Step-by-Step Marking Scheme
Longest: Rehana (4.50 m)
1.5 M
Difference: 1 metre (100 cm)
1.5 M
Q6
Textbook Exercise • Foreign Currency Exchange
Look at the exchange rates against Indian Rupee (₹):
• 1 US Dollar ($) = ₹75.00
• 1 Euro (€) = ₹85.00
• 1 Kuwaiti Dinar = ₹250.00
(a) Arun's aunt sent him $10 from USA. How much money is that in Indian Rupees? (b) Majid's father works in Kuwait and gets 100 Dinars as salary. How much is his salary in Indian Rupees?
[3 Marks]
• 1 US Dollar ($) = ₹75.00
• 1 Euro (€) = ₹85.00
• 1 Kuwaiti Dinar = ₹250.00
(a) Arun's aunt sent him $10 from USA. How much money is that in Indian Rupees? (b) Majid's father works in Kuwait and gets 100 Dinars as salary. How much is his salary in Indian Rupees?
✅ Step-by-Step Solution & Working
Currency Conversions:
• (a) $10 in Rupees: 10 × ₹75 = ₹750.
• (b) 100 Kuwaiti Dinars in Rupees: 100 × ₹250 = ₹25,000.
• (a) $10 in Rupees: 10 × ₹75 = ₹750.
• (b) 100 Kuwaiti Dinars in Rupees: 100 × ₹250 = ₹25,000.
CBSE Step-by-Step Marking Scheme
Part (a): ₹750
1.5 M
Part (b): ₹25,000
1.5 M
Q7
Textbook Exercise • Fractions to Decimals
Convert each fraction into decimal form:
(a) 7/10
(b) 45/100
(c) 3/100
(d) 1 4/10
[4 Marks]
(a) 7/10
(b) 45/100
(c) 3/100
(d) 1 4/10
✅ Step-by-Step Solution & Working
Decimals Conversion:
• (a) 7/10 = 0.7.
• (b) 45/100 = 0.45.
• (c) 3/100 = 0.03.
• (d) 1 4/10 = 1 + 0.4 = 1.4.
• (a) 7/10 = 0.7.
• (b) 45/100 = 0.45.
• (c) 3/100 = 0.03.
• (d) 1 4/10 = 1 + 0.4 = 1.4.
CBSE Step-by-Step Marking Scheme
0.7
1 M
0.45
1 M
0.03
1 M
1.4
1 M
Q8
Textbook Exercise • Decimals to Fractions in Lowest Terms
Convert each decimal to a fraction and reduce to lowest terms:
(a) 0.6
(b) 0.25
(c) 0.08
[3 Marks]
(a) 0.6
(b) 0.25
(c) 0.08
✅ Step-by-Step Solution & Working
Fractions in Lowest Terms:
• (a) 0.6 = 6/10 = 3/5 (dividing by 2).
• (b) 0.25 = 25/100 = 1/4 (dividing by 25).
• (c) 0.08 = 8/100 = 2/25 (dividing by 4).
• (a) 0.6 = 6/10 = 3/5 (dividing by 2).
• (b) 0.25 = 25/100 = 1/4 (dividing by 25).
• (c) 0.08 = 8/100 = 2/25 (dividing by 4).
CBSE Step-by-Step Marking Scheme
3/5
1 M
1/4
1 M
2/25
1 M
Q9
Textbook Exercise • Comparing Decimals
Put >, < or = between the decimal numbers:
(a) 0.5 and 0.05
(b) 3.45 and 3.54
(c) 1.20 and 1.2
(d) 0.89 and 0.9
[4 Marks]
(a) 0.5 and 0.05
(b) 3.45 and 3.54
(c) 1.20 and 1.2
(d) 0.89 and 0.9
✅ Step-by-Step Solution & Working
Decimal Comparisons:
• (a) 0.5 & 0.05: 5 tenths > 0 tenths. 0.5 > 0.05.
• (b) 3.45 & 3.54: 4 tenths < 5 tenths. 3.45 < 3.54.
• (c) 1.20 & 1.2: Trailing zeros do not change value. 1.20 = 1.2.
• (d) 0.89 & 0.9: 0.89 < 0.90 (8 tenths < 9 tenths). 0.89 < 0.9.
• (a) 0.5 & 0.05: 5 tenths > 0 tenths. 0.5 > 0.05.
• (b) 3.45 & 3.54: 4 tenths < 5 tenths. 3.45 < 3.54.
• (c) 1.20 & 1.2: Trailing zeros do not change value. 1.20 = 1.2.
• (d) 0.89 & 0.9: 0.89 < 0.90 (8 tenths < 9 tenths). 0.89 < 0.9.
CBSE Step-by-Step Marking Scheme
0.5 > 0.05
1 M
3.45 < 3.54
1 M
1.20 = 1.2
1 M
0.89 < 0.9
1 M
Q10
Textbook Exercise • Place Value in Decimals
In the number 45.68:
(a) What is the place value of digit 6?
(b) What is the place value of digit 8?
(c) Write 45.68 in expanded form.
[3 Marks]
(a) What is the place value of digit 6?
(b) What is the place value of digit 8?
(c) Write 45.68 in expanded form.
✅ Step-by-Step Solution & Working
Decimal Place Value:
• (a) Digit 6: In tenths place = 6/10 = 0.6.
• (b) Digit 8: In hundredths place = 8/100 = 0.08.
• (c) Expanded form: 40 + 5 + 6/10 + 8/100 (or 40 + 5 + 0.6 + 0.08).
• (a) Digit 6: In tenths place = 6/10 = 0.6.
• (b) Digit 8: In hundredths place = 8/100 = 0.08.
• (c) Expanded form: 40 + 5 + 6/10 + 8/100 (or 40 + 5 + 0.6 + 0.08).
CBSE Step-by-Step Marking Scheme
Tenths / 0.6
1 M
Hundredths / 0.08
1 M
Expanded notation
1 M
Q11
Textbook Exercise • Adding Decimals (Shopping Bill)
Rohan bought a notebook for ₹25.75, a pen for ₹12.50, and an eraser for ₹4.25. (a) What is his total bill? (b) If he gave a ₹50 note to the shopkeeper, how much change did he receive?
[3 Marks]
✅ Step-by-Step Solution & Working
Bill & Change Calculation:
• (a) Total Bill:
25.75
+ 12.50
+ 4.25
= ₹42.50.
• (b) Change received: ₹50.00 - ₹42.50 = ₹7.50.
• (a) Total Bill:
25.75
+ 12.50
+ 4.25
= ₹42.50.
• (b) Change received: ₹50.00 - ₹42.50 = ₹7.50.
CBSE Step-by-Step Marking Scheme
Total bill: ₹42.50
1.5 M
Change: ₹7.50
1.5 M
Q12
Textbook Exercise • Subtracting Decimals
Solve: (a) 15.4 - 8.75 (b) 100.00 - 45.65.
[2 Marks]
✅ Step-by-Step Solution & Working
Decimal Subtractions:
• (a) 15.40 - 8.75:
15.40 - 8.75 = 6.65.
• (b) 100.00 - 45.65:
100.00 - 45.65 = 54.35.
• (a) 15.40 - 8.75:
15.40 - 8.75 = 6.65.
• (b) 100.00 - 45.65:
100.00 - 45.65 = 54.35.
CBSE Step-by-Step Marking Scheme
Part (a): 6.65
1 M
Part (b): 54.35
1 M
Q13
Textbook Exercise • Metres and Centimetres in Decimals
Express in metres using decimals:
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7 cm
[4 Marks]
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7 cm
✅ Step-by-Step Solution & Working
Metre Conversions (1 m = 100 cm; divide cm by 100):
• (a) 15 cm = 15 ÷ 100 = 0.15 m.
• (b) 6 cm = 6 ÷ 100 = 0.06 m.
• (c) 2 m 45 cm = 2 + 0.45 = 2.45 m.
• (d) 9 m 7 cm = 9 + 0.07 = 9.07 m.
• (a) 15 cm = 15 ÷ 100 = 0.15 m.
• (b) 6 cm = 6 ÷ 100 = 0.06 m.
• (c) 2 m 45 cm = 2 + 0.45 = 2.45 m.
• (d) 9 m 7 cm = 9 + 0.07 = 9.07 m.
CBSE Step-by-Step Marking Scheme
0.15 m
1 M
0.06 m
1 M
2.45 m
1 M
9.07 m
1 M
Q14
Textbook Exercise • Kilograms and Grams in Decimals
Express in kilograms using decimals:
(a) 500 g
(b) 250 g
(c) 50 g
(d) 4 kg 75 g
[4 Marks]
(a) 500 g
(b) 250 g
(c) 50 g
(d) 4 kg 75 g
✅ Step-by-Step Solution & Working
Kilogram Conversions (1 kg = 1,000 g; divide g by 1,000):
• (a) 500 g = 500 ÷ 1000 = 0.5 kg.
• (b) 250 g = 250 ÷ 1000 = 0.25 kg.
• (c) 50 g = 50 ÷ 1000 = 0.05 kg.
• (d) 4 kg 75 g = 4 + 75/1000 = 4.075 kg.
• (a) 500 g = 500 ÷ 1000 = 0.5 kg.
• (b) 250 g = 250 ÷ 1000 = 0.25 kg.
• (c) 50 g = 50 ÷ 1000 = 0.05 kg.
• (d) 4 kg 75 g = 4 + 75/1000 = 4.075 kg.
CBSE Step-by-Step Marking Scheme
0.5 kg
1 M
0.25 kg
1 M
0.05 kg
1 M
4.075 kg
1 M
Q15
Textbook Exercise • Temperature Fall Calculation
At 3:00 PM, the temperature in Kolkata was 28.5°C. By 3:00 AM next morning, the temperature had fallen to 19.8°C. How many degrees did the temperature fall?
[2 Marks]
✅ Step-by-Step Solution & Working
Temperature Drop:
• Temperature fall = 28.5°C - 19.8°C = 8.7°C.
• Temperature fall = 28.5°C - 19.8°C = 8.7°C.
CBSE Step-by-Step Marking Scheme
Subtraction statement
1 M
Answer: 8.7°C
1 M
Q16
Textbook Exercise • Height Growth in Decimals
Dinesh was 1.42 metres tall in Class 4. By Class 5, his height increased by 0.08 metres. How tall is Dinesh now?
[2 Marks]
✅ Step-by-Step Solution & Working
Height Addition:
• New height = 1.42 m + 0.08 m = 1.50 metres (or 1.5 m).
• New height = 1.42 m + 0.08 m = 1.50 metres (or 1.5 m).
CBSE Step-by-Step Marking Scheme
Addition 1.42 + 0.08
1 M
Answer: 1.50 m
1 M
Q17
Textbook Exercise • Hundredths Grid Model
A large square is divided into 100 small equal squares. (a) What fraction and what decimal does 1 small square represent? (b) If 38 squares are shaded green, what decimal does the shaded region represent? (c) What decimal represents the unshaded region?
[3 Marks]
✅ Step-by-Step Solution & Working
Hundredths Grid:
• (a) 1 small square: Fraction = 1/100, Decimal = 0.01.
• (b) 38 shaded squares: 38/100 = 0.38.
• (c) Unshaded region: 100 - 38 = 62 squares. Decimal = 62/100 = 0.62.
• (a) 1 small square: Fraction = 1/100, Decimal = 0.01.
• (b) 38 shaded squares: 38/100 = 0.38.
• (c) Unshaded region: 100 - 38 = 62 squares. Decimal = 62/100 = 0.62.
CBSE Step-by-Step Marking Scheme
1/100 & 0.01
1 M
Shaded: 0.38
1 M
Unshaded: 0.62
1 M
Q18
Textbook Exercise • Matchstick Length Measurement
A matchstick placed against a ruler starts at mark 2.4 cm and ends at mark 6.7 cm. What is the actual length of the matchstick?
[2 Marks]
✅ Step-by-Step Solution & Working
Length Difference:
• Length = End mark - Start mark = 6.7 cm - 2.4 cm = 4.3 cm (or 43 mm).
• Length = End mark - Start mark = 6.7 cm - 2.4 cm = 4.3 cm (or 43 mm).
CBSE Step-by-Step Marking Scheme
Subtraction shown
1 M
Length: 4.3 cm
1 M
Q19
Textbook Exercise • Multiplying Decimals by 10, 100
Evaluate without long multiplication:
(a) 4.56 × 10
(b) 0.07 × 100
(c) 3.8 ÷ 10
[3 Marks]
(a) 4.56 × 10
(b) 0.07 × 100
(c) 3.8 ÷ 10
✅ Step-by-Step Solution & Working
Decimal Shift Rules:
• (a) 4.56 × 10: Move decimal 1 place right = 45.6.
• (b) 0.07 × 100: Move decimal 2 places right = 7.
• (c) 3.8 ÷ 10: Move decimal 1 place left = 0.38.
• (a) 4.56 × 10: Move decimal 1 place right = 45.6.
• (b) 0.07 × 100: Move decimal 2 places right = 7.
• (c) 3.8 ÷ 10: Move decimal 1 place left = 0.38.
CBSE Step-by-Step Marking Scheme
45.6
1 M
7
1 M
0.38
1 M
Q20
Textbook Exercise • Rounding Off Decimals
Round off the following decimals to the nearest whole number:
(a) 7.3
(b) 12.8
(c) 24.5
[3 Marks]
(a) 7.3
(b) 12.8
(c) 24.5
✅ Step-by-Step Solution & Working
Rounding Rules:
• (a) 7.3: Tenths digit is 3 (< 5), rounds down to 7.
• (b) 12.8: Tenths digit is 8 (≥ 5), rounds up to 13.
• (c) 24.5: Tenths digit is 5 (halfway), standard rule rounds up to 25.
• (a) 7.3: Tenths digit is 3 (< 5), rounds down to 7.
• (b) 12.8: Tenths digit is 8 (≥ 5), rounds up to 13.
• (c) 24.5: Tenths digit is 5 (halfway), standard rule rounds up to 25.
CBSE Step-by-Step Marking Scheme
7
1 M
13
1 M
25
1 M
Q21
Textbook Exercise • Petrol Price Calculation
The cost of petrol is ₹96.50 per litre. What will be the cost of 5 litres of petrol?
[2 Marks]
✅ Step-by-Step Solution & Working
Multiplication:
• Cost = 5 × ₹96.50 = ₹482.50.
• Cost = 5 × ₹96.50 = ₹482.50.
CBSE Step-by-Step Marking Scheme
Multiplication statement
1 M
Answer: ₹482.50
1 M
Q22
Textbook Exercise • Ordering Decimals Ascending
Arrange the following numbers in ascending order (smallest to greatest):
0.4, 0.04, 0.44, 4.04, 0.004.
[2 Marks]
0.4, 0.04, 0.44, 4.04, 0.004.
✅ Step-by-Step Solution & Working
Ascending Ordering:
• Converting to thousandths: 0.004, 0.040, 0.400, 0.440, 4.040.
• Ascending order: 0.004 < 0.04 < 0.4 < 0.44 < 4.04.
• Converting to thousandths: 0.004, 0.040, 0.400, 0.440, 4.040.
• Ascending order: 0.004 < 0.04 < 0.4 < 0.44 < 4.04.
CBSE Step-by-Step Marking Scheme
Equal decimal places comparison
1 M
Correct ordered sequence
1 M
Q23
Textbook Exercise • Water Jug Capacity Problem
A jug contains 2.75 litres of water. 1.25 litres are poured into a glass. How much water is left in the jug?
[2 Marks]
✅ Step-by-Step Solution & Working
Subtraction:
• Water remaining = 2.75 - 1.25 = 1.50 litres (or 1.5 litres).
• Water remaining = 2.75 - 1.25 = 1.50 litres (or 1.5 litres).
CBSE Step-by-Step Marking Scheme
Subtraction 2.75 - 1.25
1 M
Answer: 1.50 litres
1 M
Q24
Textbook Exercise • Decimal Number Line
Between which two whole numbers does 3.7 lie on a number line? Which whole number is it closer to?
[2 Marks]
✅ Step-by-Step Solution & Working
Number Line Positioning:
• 3.7 lies between whole numbers 3 and 4.
• Since the tenths digit is 7 (> 5), it is closer to 4.
• 3.7 lies between whole numbers 3 and 4.
• Since the tenths digit is 7 (> 5), it is closer to 4.
CBSE Step-by-Step Marking Scheme
Between 3 and 4
1 M
Closer to 4
1 M
🌟 NEP 2020 Competency-Based Case Study
NEP 2020 Competency Case: Tenths and Hundredths
A practical scenario involving Tenths and Hundredths in everyday life and community contexts.
Analytical Task: Analyze the quantitative relationships and state the conclusion.
Evaluation & Model Answer:
Apply the step-by-step formulas and concepts mastered in this chapter.
Rubric: 1M formula + 1M working + 1M answer