Class 7 : Maths – Lesson 3. A Peek Beyond the Point

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On December 11, 2025

EXPLANATION AND ANALYSIS

🔵 Introduction: Moving Beyond Whole Numbers

🧠 In earlier classes, we mostly worked with whole numbers and integers. However, many situations in daily life involve numbers that are not whole. For example, the length of a ribbon may be 2.5 metres, the weight of a packet may be 1.75 kilograms, or the time taken to complete a race may be 3.2 seconds.

🌿 Such numbers help us measure quantities more accurately. These numbers are called decimal numbers. This chapter introduces us to the idea of numbers that go beyond the point, that is, numbers written using a decimal point.

🟢 Meaning of Decimal Numbers

🧠 A decimal number is a number that has a decimal point and digits after it.

🔹 The part before the decimal point shows whole units
🔹 The part after the decimal point shows parts of a whole

📌 Example
In the number 4.7
🔹 4 represents whole units
🔹 7 represents parts of a unit

💡 Concept:
Decimals help us represent quantities that lie between two whole numbers.

🔵 Place Value in Decimal Numbers

🧠 Just like whole numbers, digits in decimal numbers also have place values.

🔹 Ones
🔹 Tenths
🔹 Hundredths
🔹 Thousandths

📌 Example
In the number 3.456
🔹 4 is in the tenths place
🔹 5 is in the hundredths place
🔹 6 is in the thousandths place

💡 Concept:
Each place to the right of the decimal point is one-tenth of the previous place.

🟢 Reading and Writing Decimal Numbers

🧠 Decimal numbers are read by reading the whole number part first, then saying “point”, followed by each digit after the point.

📌 Example
2.35 is read as
Two point three five

✏️ Note:
Digits after the decimal point are read individually, not as a whole number.

🔵 Writing Decimals from Words

🧠 To write decimal numbers given in words, identify the place value of each part.

📌 Example
Three and five tenths

🔹 Three = 3
🔹 Five tenths = 0.5
🔹 Decimal number = 3.5

💡 Concept:
The word “tenths” shows one digit after the decimal point, while “hundredths” shows two digits.

🟡 Comparing Decimal Numbers

🧠 Decimal numbers can be compared just like whole numbers, but with special care.

🔹 First compare the whole number part
🔹 If equal, compare digits after the decimal point

📌 Example
Compare 4.25 and 4.3

🔹 Whole number part is same
🔹 Compare tenths: 2 < 3
🔹 So 4.3 is greater

✏️ Note:
Write the decimals with the same number of decimal places to compare easily.

🟢 Ordering Decimal Numbers

🧠 Ordering means arranging numbers from smallest to greatest or vice versa.

🔹 Ascending order: smallest to greatest
🔹 Descending order: greatest to smallest

📌 Example
Arrange 2.5, 2.35, 2.8

Ascending order
2.35 < 2.5 < 2.8

🔵 Using Zeros in Decimal Numbers

🧠 Adding zeros after the decimal point does not change the value of a decimal number.

📌 Example
2.5 = 2.50 = 2.500

💡 Concept:
Zeros are often added to make decimals easier to compare or calculate.

🟡 Decimal Numbers on the Number Line

🧠 Decimal numbers can be shown clearly on a number line.

🔹 Divide the space between two whole numbers into equal parts
🔹 Each part represents tenths or hundredths

📌 Example
The number 3.4 lies between 3 and 4, closer to 3 than to 4.

✏️ Note:
The number line helps us visualise the position of decimal numbers.

🟢 Decimals in Daily Life

🧠 Decimal numbers are used widely in everyday life.

🔹 Money such as 12.50 rupees
🔹 Length like 1.75 metres
🔹 Weight like 2.3 kilograms
🔹 Time like 4.5 seconds

💡 Concept:
Decimals make measurements more precise and meaningful.

🔴 Common Mistakes to Avoid

🔴 Ignoring place value after the decimal point
🔴 Comparing decimals without aligning decimal points
🔴 Thinking that 2.5 is smaller than 2.35
🔴 Misreading decimal numbers

✏️ Note:
Always compare decimals by looking at place values step by step.

🟢 Importance of Learning Decimals

🧠 Learning decimal numbers helps us:

🔹 Measure quantities accurately
🔹 Understand money calculations
🔹 Read scientific data
🔹 Prepare for higher mathematics

This chapter builds a strong foundation for fractions, percentages, and algebra.

📘 Summary

🔵 Decimal numbers represent parts of a whole
🟢 They contain a decimal point
🟡 Place value extends beyond the decimal point
🔴 Tenths, hundredths, and thousandths show precision
🔵 Decimals can be compared and ordered
🟢 Zeros after the decimal do not change value
🟡 Decimals are widely used in daily life

📝 Quick Recap

📝 Quick Recap
🔵 Decimal numbers go beyond whole numbers
🟢 Decimal point separates whole and fractional parts
🟡 Place value continues after the point
🔴 Decimals help in accurate measurement
🔵 Decimals are essential in daily life

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TEXTBOOK QUESTIONS

🔵 A TENTH PART

🔒 ❓ Arrange these lengths in increasing order:

(a) 9/10
(b) 1 7/10
(c) 130/10
(d) 13 1/10
(e) 10 5/10
(f) 7 6/10
(g) 6 7/10
(h) 4/10

📌 ✅ Answer:

🔹 Convert all to tenths for easy comparison.
🔸 9/10 = 9/10
🔸 1 7/10 = 17/10
🔸 130/10 = 130/10
🔸 13 1/10 = 131/10
🔸 10 5/10 = 105/10
🔸 7 6/10 = 76/10
🔸 6 7/10 = 67/10
🔸 4/10 = 4/10

🔹 Arrange from smallest to largest (by numerators).

✔️ Final:
4/10, 9/10, 1 7/10, 6 7/10, 7 6/10, 10 5/10, 130/10, 13 1/10

🔒 ❓ Arrange the following lengths in increasing order:
4 1/10, 4/10, 41/10, 1/10.

📌 ✅ Answer:

🔹 Write all lengths in tenths.
🔸 4 1/10 = 41/10
🔸 4/10 = 4/10
🔸 41/10 = 41/10
🔸 1/10 = 1/10

🔹 Compare numerators.

✔️ Final:
1/10, 4/10, 4 1/10, 41/10

🔒 ❓ Sonu is measuring some of his body parts. The length of Sonu’s lower arm is 2 7/10 units, and that of his upper arm is 3 6/10 units. What is the total length of his arm?

📌 ✅ Answer:

🔹 Add whole-number parts.
🔸 2 + 3 = 5

🔹 Add fractional parts.
🔸 7/10 + 6/10 = 13/10

🔹 Combine whole and fractional parts.
🔸 5 + 13/10

🔹 Convert improper fraction.
🔸 13/10 = 1 + 3/10

🔹 Add again.
🔸 5 + 1 + 3/10 = 6 3/10

✔️ Final:
The total length of Sonu’s arm is 6 3/10 units.

🔒 ❓ The lengths of the body parts of a honeybee are given. Find its total length.

Head: 2 3/10 units
Thorax: 5 4/10 units
Abdomen: 7 5/10 units

📌 ✅ Answer (Teacher-like explanation):

🔹 We are given three lengths written as mixed numbers.
🔹 To add them easily, we first add whole parts and tenths parts separately.

🔹 Step 1: Add the whole-number parts
🔸 Head = 2 units
🔸 Thorax = 5 units
🔸 Abdomen = 7 units
🔸 Total whole units = 2 + 5 + 7 = 14

🔹 Step 2: Add the tenths
🔸 3/10 + 4/10 + 5/10
🔸 = 12/10

🔹 Step 3: Convert extra tenths into units
🔸 12/10 means 1 whole unit and 2/10
🔸 So, 12/10 = 1 + 2/10

🔹 Step 4: Add everything together
🔸 14 + 1 + 2/10 = 15 2/10

✔️ Final:
The total length of the honeybee is 15 2/10 units.

🔒 ❓ The length of Shylaja’s hand is 12 4/10 units, and her palm is 6 7/10 units, as shown in the picture. What is the length of the longest (middle) finger?

📌 ✅ Answer (Teacher-like explanation):

🔹 The hand length includes the palm and the finger.
🔹 To find only the finger length, we subtract the palm length from the total hand length.

🔹 Step 1: Write the subtraction clearly
🔸 (12 4/10) − (6 7/10)

🔹 Step 2: Separate whole numbers and tenths
🔸 (12 − 6) + (4/10 − 7/10)

🔹 Step 3: Subtract the whole numbers
🔸 12 − 6 = 6

🔹 Step 4: Observe the tenths carefully
🔸 We cannot subtract 7/10 from 4/10
🔸 So, we regroup 1 unit from 6

🔹 Step 5: Regroup 1 unit as tenths
🔸 1 unit = 10/10
🔸 6 becomes 5 + 10/10

🔹 Step 6: Subtract the tenths
🔸 10/10 − 3/10 = 7/10

🔹 Step 7: Combine the result
🔸 5 + 7/10 = 5 7/10

💡 Concept:
Regrouping helps when the fractional part of the minuend is smaller than the fractional part of the subtrahend.

✔️ Final:
The length of the longest (middle) finger is 5 7/10 units.

🔒 ❓ Try computing the difference by converting both lengths to tenths.
A Celestial Pearl Danio’s length is 2 4/10 cm, and the length of a Philippine Goby is 9/10 cm. What is the difference in their lengths?

📌 ✅ Answer (Teacher-like explanation):

🔹 To find the difference, both lengths should be written in the same form.
🔹 We convert both lengths into tenths.

🔹 Step 1: Convert mixed number to tenths
🔸 2 4/10 = 24/10

🔹 Step 2: Write the second length in tenths
🔸 9/10 = 9/10

🔹 Step 3: Subtract the lengths
🔸 24/10 − 9/10 = 15/10

🔹 Step 4: Convert back to mixed number
🔸 15/10 = 1 5/10

✔️ Final:
The difference in their lengths is 1 5/10 cm.

🔒 ❓ How big are these fish compared to your finger?

📌 ✅ Answer (Teacher-like explanation):

🔹 The lengths of both fish are less than 3 cm.
🔹 A finger of a student is usually longer than 5 cm.

🔹 Therefore, both fish are shorter than a finger.

✔️ Final:
Both fish are shorter than a finger.

🔒 ❓ Observe the given sequences of numbers. Identify the change after each term and extend the pattern:

🔒 ❓ (a) 4, 4 3/10, 4 6/10, ___, ___, ___

📌 ✅ Answer (Teacher-like explanation):

🔹 Write the numbers in tenths.
🔸 4 = 4 0/10

🔹 Find the change between terms.
🔸 4 0/10 → 4 3/10 = +3/10
🔸 4 3/10 → 4 6/10 = +3/10

🔹 The pattern increases by 3/10 each time.

✔️ Final:
4 9/10, 5 2/10, 5 5/10

🔒 ❓ (b) 8 2/10, 8 7/10, 9 2/10, ___, ___, ___

📌 ✅ Answer (Teacher-like explanation):

🔹 Find the difference between terms.
🔸 8 2/10 → 8 7/10 = +5/10
🔸 8 7/10 → 9 2/10 = +5/10

🔹 The pattern increases by 5/10.

✔️ Final:
9 7/10, 10 2/10, 10 7/10

🔒 ❓ (c) 7 6/10, 8 7/10, ___, ___, ___

📌 ✅ Answer (Teacher-like explanation):

🔹 Convert to tenths.
🔸 7 6/10 = 76/10
🔸 8 7/10 = 87/10

🔹 Find the change.
🔸 87/10 − 76/10 = 11/10 = 1 1/10

🔹 The pattern increases by 1 1/10.

✔️ Final:
9 8/10, 10 9/10, 12 0/10

🔒 ❓ (d) 5 7/10, 5 3/10, ___, ___, ___

📌 ✅ Answer (Teacher-like explanation):

🔹 Observe the change.
🔸 5 7/10 → 5 3/10 = −4/10

🔹 The pattern decreases by 4/10.

✔️ Final:
4 9/10, 4 5/10, 4 1/10

🔒 ❓ (e) 13 5/10, 13, 12 5/10, ___, ___, ___

📌 ✅ Answer (Teacher-like explanation):

🔹 Write all terms in tenths.
🔸 13 5/10 → 13 0/10 → 12 5/10

🔹 Each step decreases by 5/10.

✔️ Final:
12 0/10, 11 5/10, 11 0/10

🔒 ❓ (f) 11 5/10, 10 4/10, 9 3/10, ___, ___, ___

📌 ✅ Answer (Teacher-like explanation):

🔹 Find the difference.
🔸 11 5/10 → 10 4/10 = −1 1/10
🔸 10 4/10 → 9 3/10 = −1 1/10

🔹 The pattern decreases by 1 1/10 each time.

✔️ Final:
8 2/10, 7 1/10, 6 0/10

🔵 A HUNDREDTH PART

🔒 ❓ Figure it Out – Find the sums and differences

🔒 ❓ (a) 3/10 + 3 4/100

📌 ✅ Answer (Teacher-like explanation):

🔹 First, both numbers should be written with the same denominator.
🔹 3/10 can be written in hundredths.

🔹 Step 1: Convert 3/10 into hundredths
🔸 3/10 = 30/100

🔹 Step 2: Write both numbers clearly
🔸 30/100 + 3 4/100

🔹 Step 3: Add fractional parts
🔸 30/100 + 4/100 = 34/100

🔹 Step 4: Add the whole number
🔸 3 + 34/100

✔️ Final:
3 34/100

🔒 ❓ (b) 9 5/10 7/100 + 2 1/10 3/100

📌 ✅ Answer (Teacher-like explanation):

🔹 Add whole parts, tenths, and hundredths separately.

🔹 Step 1: Add whole numbers
🔸 9 + 2 = 11

🔹 Step 2: Add tenths
🔸 5/10 + 1/10 = 6/10

🔹 Step 3: Add hundredths
🔸 7/100 + 3/100 = 10/100

🔹 Step 4: Convert 10/100 into tenths
🔸 10/100 = 1/10

🔹 Step 5: Add tenths again
🔸 6/10 + 1/10 = 7/10

🔹 Step 6: Combine all parts
🔸 11 7/10

✔️ Final:
11 7/10

🔒 ❓ (c) 15 6/10 4/100 + 14 3/10 6/100

📌 ✅ Answer (Teacher-like explanation):

🔹 Add each part carefully.

🔹 Step 1: Add whole numbers
🔸 15 + 14 = 29

🔹 Step 2: Add tenths
🔸 6/10 + 3/10 = 9/10

🔹 Step 3: Add hundredths
🔸 4/100 + 6/100 = 10/100

🔹 Step 4: Convert 10/100
🔸 10/100 = 1/10

🔹 Step 5: Add tenths again
🔸 9/10 + 1/10 = 10/10 = 1

🔹 Step 6: Add to whole number
🔸 29 + 1 = 30

✔️ Final:
30

🔒 ❓ (d) 7 7/100 − 4 4/100

📌 ✅ Answer (Teacher-like explanation):

🔹 Subtract whole numbers and hundredths separately.

🔹 Step 1: Subtract whole numbers
🔸 7 − 4 = 3

🔹 Step 2: Subtract hundredths
🔸 7/100 − 4/100 = 3/100

🔹 Step 3: Combine
🔸 3 3/100

✔️ Final:
3 3/100

🔒 ❓ (e) 8 6/100 − 5 3/100

📌 ✅ Answer (Teacher-like explanation):

🔹 Step 1: Subtract whole numbers
🔸 8 − 5 = 3

🔹 Step 2: Subtract hundredths
🔸 6/100 − 3/100 = 3/100

🔹 Step 3: Combine
🔸 3 3/100

✔️ Final:
3 3/100

🔒 ❓ (f) 12 6/100 2/100 − 9/10 9/100

📌 ✅ Answer (Teacher-like explanation):

🔹 Convert everything into hundredths to avoid confusion.

🔹 Step 1: Convert tenths to hundredths
🔸 9/10 = 90/100

🔹 Step 2: Write numbers clearly
🔸 12 8/100 − 9 90/100

🔹 Step 3: Regroup 1 whole unit
🔸 12 = 11 + 100/100

🔹 Step 4: Subtract hundredths
🔸 108/100 − 90/100 = 18/100

🔹 Step 5: Subtract whole numbers
🔸 11 − 9 = 2

🔹 Step 6: Combine
🔸 2 18/100

✔️ Final:
2 18/100

🔵 ADDITION AND SUBTRACTION OF DECIMALS

🔒 ❓ 1. Find the sums

🔒 ❓ (a) 5.3 + 2.6

📌 ✅ Answer (Teacher-like explanation):

🔹 Write decimals one below the other, aligning the decimal points.
🔸 5.3
🔸 2.6

🔹 Add tenths first.
🔸 3 + 6 = 9

🔹 Add whole numbers.
🔸 5 + 2 = 7

✔️ Final:
7.9

🔒 ❓ (b) 18 + 8.8

📌 ✅ Answer:

🔹 Write 18 as 18.0 to match decimal places.
🔸 18.0
🔸 8.8

🔹 Add tenths and whole numbers.

✔️ Final:
26.8

🔒 ❓ (c) 2.15 + 5.26

📌 ✅ Answer:

🔹 Align decimal points carefully.
🔹 Add hundredths, then tenths, then whole numbers.

🔸 0.15 + 0.26 = 0.41
🔸 2 + 5 = 7

✔️ Final:
7.41

🔒 ❓ (d) 9.01 + 9.10

📌 ✅ Answer:

🔹 Align decimals.
🔹 Add hundredths and tenths first.

🔸 0.01 + 0.10 = 0.11
🔸 9 + 9 = 18

✔️ Final:
18.11

🔒 ❓ (e) 29.19 + 9.91

📌 ✅ Answer:

🔹 Add hundredths.
🔸 0.19 + 0.91 = 1.10

🔹 Regroup 1 whole.

🔸 29 + 9 + 1 = 39

✔️ Final:
39.10

🔒 ❓ (f) 0.934 + 0.6

📌 ✅ Answer:

🔹 Write 0.6 as 0.600.
🔹 Add thousandths, hundredths, tenths.

✔️ Final:
1.534

🔒 ❓ (g) 0.75 + 0.03

📌 ✅ Answer:

🔹 Add hundredths.

✔️ Final:
0.78

🔒 ❓ (h) 6.236 + 0.487

📌 ✅ Answer:

🔹 Add thousandths carefully.
🔹 Regroup where needed.

✔️ Final:
6.723

🔒 ❓ 2. Find the differences

🔒 ❓ (a) 5.6 − 2.3

📌 ✅ Answer:

🔹 Subtract tenths, then whole numbers.

✔️ Final:
3.3

🔒 ❓ (b) 18 − 8.8

📌 ✅ Answer:

🔹 Write 18 as 18.0.
🔹 Subtract tenths carefully.

✔️ Final:
9.2

🔒 ❓ (c) 10.4 − 4.5

📌 ✅ Answer:

🔹 Regroup 1 unit if needed.

✔️ Final:
5.9

🔒 ❓ (d) 17 − 16.198

📌 ✅ Answer:

🔹 Write 17 as 17.000.
🔹 Regroup across decimal places.

✔️ Final:
0.802

🔒 ❓ (e) 17 − 0.05

📌 ✅ Answer:

🔹 Write 17 as 17.00.

✔️ Final:
16.95

🔒 ❓ (f) 34.505 − 18.1

📌 ✅ Answer:

🔹 Write 18.1 as 18.100.
🔹 Subtract step-by-step.

✔️ Final:
16.405

🔒 ❓ (g) 9.9 − 9.09

📌 ✅ Answer:

🔹 Write 9.9 as 9.90.
🔹 Subtract hundredths.

✔️ Final:
0.81

🔒 ❓ (h) 6.236 − 0.487

📌 ✅ Answer:

🔹 Subtract thousandths with regrouping.

✔️ Final:
5.749

🔵 FIGURE IT OUT ?

🔒 ❓ 1. Convert the following fractions into decimals:

🔒 ❓ (a) 5/100

📌 ✅ Answer (Teacher-like explanation):

🔹 The denominator is 100, so the fraction represents hundredths.
🔹 Move the decimal point two places to the left.

🔸 5/100 = 0.05

✔️ Final:
0.05

🔒 ❓ (b) 16/1000

📌 ✅ Answer:

🔹 The denominator is 1000, so the fraction represents thousandths.
🔹 Move the decimal point three places to the left.

🔸 16/1000 = 0.016

✔️ Final:
0.016

🔒 ❓ (c) 12/10

📌 ✅ Answer:

🔹 The denominator is 10, so the fraction represents tenths.
🔹 Move the decimal point one place to the left.

🔸 12/10 = 1.2

✔️ Final:
1.2

🔒 ❓ (d) 254/1000

📌 ✅ Answer:

🔹 Denominator 1000 means thousandths.
🔹 Move the decimal point three places to the left.

🔸 254/1000 = 0.254

✔️ Final:
0.254

🔒 ❓ 2. Convert the following decimals into a sum of tenths, hundredths and thousandths:

🔒 ❓ (a) 0.34

📌 ✅ Answer:

🔹 The digit 3 is in the tenths place.
🔹 The digit 4 is in the hundredths place.

🔸 0.34 = 3/10 + 4/100

✔️ Final:
3/10 + 4/100

🔒 ❓ (b) 1.02

📌 ✅ Answer:

🔹 1 is the whole number.
🔹 0 tenths and 2 hundredths.

🔸 1.02 = 1 + 2/100

✔️ Final:
1 + 2/100

🔒 ❓ (c) 0.8

📌 ✅ Answer:

🔹 8 is in the tenths place.

🔸 0.8 = 8/10

✔️ Final:
8/10

🔒 ❓ (d) 0.362

📌 ✅ Answer:

🔹 3 tenths, 6 hundredths, 2 thousandths.

🔸 0.362 = 3/10 + 6/100 + 2/1000

✔️ Final:
3/10 + 6/100 + 2/1000

🔒 ❓ 3. What decimal number does each letter represent in the number line below?

📌 ✅ Answer (Teacher-like explanation):
🔹 The arrow a is on the tick just after 6.44, so
🔸 a = 6.46

🔹 The arrows c and b are the first two ticks to the right of 6.5, so
🔸 c = 6.52
🔸 b = 6.54

✔️ Final (Correct):
📌 ✅ a = 6.46, c = 6.52, b = 6.54

🔒 ❓ 4. Arrange the following quantities in descending order:

🔒 ❓ (a) 11.01, 1.011, 1.101, 11.10, 1.01

📌 ✅ Answer:

🔹 Compare whole numbers first.

✔️ Final:
11.10, 11.01, 1.101, 1.011, 1.01

🔒 ❓ (b) 2.567, 2.675, 2.768, 2.499, 2.698

📌 ✅ Answer:

✔️ Final:
2.768, 2.698, 2.675, 2.567, 2.499

🔒 ❓ (c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g

📌 ✅ Answer:

✔️ Final:
4.678 g, 4.666 g, 4.656 g, 4.600 g, 4.595 g

🔒 ❓ (d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m

📌 ✅ Answer:

✔️ Final:
33.331 m, 33.313 m, 33.31 m, 33.133 m, 33.13 m

🔒 ❓ 5. Using the digits 1, 4, 0, 8, and 6 make:

🔒 ❓ (a) the decimal number closest to 30

📌 ✅ Answer:

🔹 We must use only digits 1,4,0,8,6 exactly once.
🔹 To be closest to 30, the nearest possible whole-part using these digits is 40 (because we cannot form 29 or 30 without digit 2 or 3).
🔹 To make it closest, keep the decimal part as small as possible while using remaining digits.

✔️ Final (Correct):
📌 ✅ 40.168

🔒 ❓ (b) the smallest possible decimal number between 100 and 1000

📌 ✅ Answer:

🔹 The smallest number is formed by keeping the hundreds digit as small as possible.

✔️ Final:
104.68

🔒 ❓ 6. Will a decimal number with more digits be greater than a decimal number with fewer digits?

📌 ✅ Answer:

🔹 No.
🔹 The value of a decimal depends on its place value, not the number of digits.

✔️ Final:
A decimal with more digits is not always greater.

🔒 ❓ 7. Mahi purchases 0.25 kg of beans, 0.3 kg of carrots, 0.5 kg of potatoes, 0.2 kg of capsicums, and 0.05 kg of ginger. Calculate the total weight.

📌 ✅ Answer:

🔹 Add all weights.

🔸 0.25 + 0.30 + 0.50 + 0.20 + 0.05
🔸 = 1.30

✔️ Final:
1.3 kg

🔒 ❓ 8. Pinto supplies 3.79 L, 4.2 L, and 4.25 L of milk in the first three days. In 6 days, he supplies 25 L of milk. Find the quantity supplied in the last three days.

📌 ✅ Answer:

🔹 Milk supplied in first three days:

🔸 3.79 + 4.20 + 4.25 = 12.24

🔹 Milk supplied in last three days:

🔸 25 − 12.24 = 12.76

✔️ Final:
12.76 L

🔒 ❓ 9. Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?

📌 ✅ Answer (Teacher-like explanation):

🔹 January weight = 35.75 kg
🔹 February weight = 34.50 kg

🔹 To find the change, subtract February weight from January weight.

🔸 35.75 − 34.50 = 1.25

🔹 Since the weight has decreased, Tinku has lost weight.

✔️ Final:
Tinku has lost 1.25 kg.

🔒 ❓ Q10. Extend the pattern:
5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, ___, ___

📌 ✅ Answer (Teacher-like, step-by-step explanation):

🔹 First, observe that the numbers come in pairs.

🔹 Write the numbers pair-wise to see the pattern clearly:

🔸 (6.4, 6.39)
🔸 (7.29, 7.28)
🔸 (6.18, 6.17)

🔹 In each pair, the second number is 0.01 less than the first.

🔹 Now focus only on the first numbers of each pair:

🔸 6.4
🔸 7.29
🔸 6.18

🔹 Notice the change:

6.4 → 7.29 (+0.89)
7.29 → 6.18 (−1.11)

🔹 This increase and decrease happens alternately.

🔹 Since the last first-number was 6.18, the next first-number will be:

🔸 6.18 − 1.11 = 5.07

🔹 Following the pair rule, the next number will be:

🔸 5.07 − 0.01 = 5.06

✔️ Final:
📌 ✅ 5.07, 5.06

🔒 ❓ 11. How many millimeters make 1 kilometer?

📌 ✅ Answer (Teacher-like explanation):

🔹 1 kilometer = 1000 meters
🔹 1 meter = 1000 millimeters

🔹 Multiply:

🔸 1000 × 1000 = 1,000,000

✔️ Final:
1 kilometer = 1,000,000 millimeters

🔒 ❓ 12. Indian Railways offers optional travel insurance costing 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?

📌 ✅ Answer (Teacher-like explanation):

🔹 Cost per passenger = 45 paise
🔹 1 lakh people = 100,000 people

🔹 Total cost in paise:

🔸 100,000 × 45 = 4,500,000 paise

🔹 Convert paise to rupees
🔸 100 paise = 1 rupee

🔸 4,500,000 ÷ 100 = 45,000

✔️ Final:
The total insurance fee paid is ₹45,000.

🔒 ❓ 13. Which is greater?

🔒 ❓ (a) 10/1000 or 1/10 ?

📌 ✅ Answer:

🔹 Convert both to decimals.

🔸 10/1000 = 0.01
🔸 1/10 = 0.1

✔️ Final:
1/10 is greater.

🔒 ❓ (b) One-hundredth or 90 thousandths?

📌 ✅ Answer:

🔹 One-hundredth = 1/100 = 0.01
🔹 90 thousandths = 90/1000 = 0.09

✔️ Final:
90 thousandths is greater.

🔒 ❓ (c) One-thousandth or 90 hundredths?

📌 ✅ Answer:

🔹 One-thousandth = 1/1000 = 0.001
🔹 90 hundredths = 90/100 = 0.90

✔️ Final:
90 hundredths is greater.

🔒 ❓ 14. Write the decimal forms of the quantities mentioned:

🔒 ❓ (a) 87 ones, 5 tenths and 60 hundredths

📌 ✅ Answer:

✔️ Final:
88.10

🔒 ❓ (b) 12 tens and 12 tenths

📌 ✅ Answer (Teacher-like explanation):

🔹 12 tens = 120
🔹 12 tenths = 1.2

✔️ Final:
121.2

🔒 ❓ (c) 10 tens, 10 ones, 10 tenths, and 10 hundredths

📌 ✅ Answer:

🔹 10 tens = 100
🔹 10 ones = 10
🔹 10 tenths = 1
🔹 10 hundredths = 0.10

✔️ Final:
111.10

🔒 ❓ (d) 25 tens, 25 ones, 25 tenths, and 25 hundredths

📌 ✅ Answer:

🔹 25 tens = 250
🔹 25 ones = 25
🔹 25 tenths = 2.5
🔹 25 hundredths = 0.25

✔️ Final:
277.75

🔒 ❓ 15. Using each digit 0–9 not more than once, fill the boxes so that the sum is closest to 10.5

📌 ✅ Answer (Teacher-like explanation):

🔹 One possible arrangement close to 10.5 is:

🔸 5.26
🔸 5.24

🔹 Sum = 10.50

✔️ Final:
A correct arrangement gives a sum of 10.5.

🔒 ❓ 16. Write the following fractions in decimal form:

🔒 ❓ (a) 1/2

📌 ✅ Answer:
0.5

🔒 ❓ (b) 3/2

📌 ✅ Answer:
1.5

🔒 ❓ (c) 1/4

📌 ✅ Answer:
0.25

🔒 ❓ (d) 3/4

📌 ✅ Answer:
0.75

🔒 ❓ (e) 1/5

📌 ✅ Answer:
0.2

🔒 ❓ (f) 4/5

📌 ✅ Answer:
0.8

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Important Notice : The lessons and study materials up to July–August 2025 have been sent. Soon, after receiving feedback from teachers and students, we will deliver the latest and more innovative study materials for the upcoming months.

Class 7 : Maths – Lesson 3. A Peek Beyond the Point

EXPLANATION AND ANALYSIS

🔵 Introduction: Moving Beyond Whole Numbers

🟢 Meaning of Decimal Numbers

🔵 Place Value in Decimal Numbers

🟢 Reading and Writing Decimal Numbers

🔵 Writing Decimals from Words

🟡 Comparing Decimal Numbers

🟢 Ordering Decimal Numbers

🔵 Using Zeros in Decimal Numbers

🟡 Decimal Numbers on the Number Line

🟢 Decimals in Daily Life

🔴 Common Mistakes to Avoid

🟢 Importance of Learning Decimals

📘 Summary

📝 Quick Recap

TEXTBOOK QUESTIONS

OTHER IMPORTANT QUESTIONS

🔵 Section A – Very Short Answer (1 × 6 = 6 marks)

🟢 Section B – Short Answer I (2 × 6 = 12 marks)

🟡 Section C – Short Answer II (3 × 10 = 30 marks)

🔴 Section D – Long Answer (4 × 8 = 32 marks)

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