Class 7 Maths Chapter 3 NCERT Solutions – A Peek Beyond the Point

NCERT Solutions for Class 7 Maths Chapter 3 A Peek Beyond the Point (2025-26) – Exercise Solutions

3.1 The Need for Smaller Units – In-text Questions

Q1. Which scale helped you measure the length of the screws accurately? Why?

Answer: The scale with smaller divisions (such as millimeters or tenths of a centimeter) helped measure the screws accurately because it allows us to see small differences in length that a coarser scale cannot show.

Q2. What is the meaning of 2 ⁷⁄₁₀ cm (the length of the first screw)?

Answer: 2 ⁷⁄₁₀ cm means 2 whole centimeters and 7 tenths of a centimeter. That is, it is 2 cm plus 0.7 cm, i.e., 2.7 cm in decimal notation.

Q3. Can you explain why the unit was divided into smaller parts to measure the screws?

Answer: The unit was divided into smaller parts so that we could measure very small differences that are not visible with only whole number divisions. This gives greater accuracy in measurement.

Q4. Write the measurements of these objects (between 2 cm and 3 cm, more than 2¹⁄₂ cm but less than 3 cm: 2 ⁷⁄₁₀ cm).

Answer: Objects between 2 cm and 3 cm can have lengths like 2.1 cm, 2.7 cm, 2.9 cm (as per what is shown in the picture). “More than 2¹⁄₂ cm but less than 3 cm” indicates measurements such as 2.6 cm, 2.8 cm, etc. The given value is 2 ⁷⁄₁₀ cm, i.e., 2.7 cm.

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3.2 A Tenth Part – In-text Questions

Q5. Arrange these lengths in increasing order:
(a) 9⁄10, (b) 1⁷⁄₁₀, (c) 130⁄10, (d) 13¹⁄₁₀, (e) 10⁵⁄₁₀, (f) 7⁶⁄₁₀, (g) 6⁷⁄₁₀, (h) 4⁄10.

Answer: Arranged in increasing order:

• 4⁄10
• 9⁄10
• 6⁷⁄₁₀
• 7⁶⁄₁₀
• 1⁷⁄₁₀
• 10⁵⁄₁₀
• 13¹⁄₁₀
• 130⁄10

Q6. Arrange the following lengths in increasing order: 4¹⁄₁₀, 4⁄10, 41⁄10, 41¹⁄₁₀.

Answer: Increasing order:

• 4⁄10
• 4¹⁄₁₀
• 41⁄10
• 41¹⁄₁₀

Q7. Sonu is measuring some of his body parts. The length of Sonu’s lower arm is 2⁷⁄₁₀ units, and that of his upper arm is 3⁶⁄₁₀ units. What is the total length of his arm?

Answer: 2⁷⁄₁₀ + 3⁶⁄₁₀ = (2 + 3) + (7 + 6)⁄10 = 5 + 13⁄10 = 6³⁄₁₀ units (since 13 tenths is 1 unit and 3 tenths).

Q8. The lengths of the body parts of a honeybee are given. Find its total length.
Head: 2³⁄₁₀ units, Thorax: 5⁴⁄₁₀ units, Abdomen: 7⁵⁄₁₀ units.

Answer: Add their lengths: 2³⁄₁₀ + 5⁴⁄₁₀ + 7⁵⁄₁₀ = (2+5+7) + (3+4+5)/10 = 14 + 12/10 = 15²⁄₁₀ units.

Q9. The length of Shylaja’s hand is 12⁴⁄₁₀ units, and her palm is 6⁷⁄₁₀ units. What is the length of the longest (middle) finger?

Answer: Finger length = 12⁴⁄₁₀ − 6⁷⁄₁₀ = (12−6) + (4−7)⁄10 = 6 − 3⁄10 = 5⁷⁄₁₀ units.

Q10. A Celestial Pearl Danio’s length is 2⁴⁄₁₀ cm, and the length of a Philippine Goby is 9⁄10 cm. What is the difference in their lengths?

Answer: 2⁴⁄₁₀ − 9⁄10 = (2−0) + (4−9)/10 = 2 − 5/10 = 1⁵⁄₁₀ cm.

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3.3 A Hundredth Part – In-text Questions

Q11. What is the length of one smaller part if each one-tenth is divided into 10?

Answer: Each smaller part is 1⁄100 (one-hundredth) of a unit.

Q12. How many such smaller parts make a unit length?

Answer: 100 such smaller parts (one-hundredths) make a unit length.

Q13. What is the length of the folded paper (original length 8⁹⁄₁₀ units)?

Answer: The folded paper’s length is 4⁴⁄₁₀⁵⁄₁₀₀ units, i.e., 4 units, 4 one-tenths, and 5 one-hundredths, or 4.45 units.

Q14. How many one-hundredths make one-tenth?

Answer: 10 one-hundredths make one-tenth.

Q15. Is it correct to say that the length is 4 units and 45 one-hundredths?

Answer: Yes, since 4 one-tenths and 5 one-hundredths is 40 one-hundredths + 5 one-hundredths = 45 one-hundredths; hence, 4 units and 45 one-hundredths.

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3.4 Decimal Place Value – In-text Questions

Q16. Why do we split a unit into 10 parts every time?

Answer: We split a unit into 10 parts because 10 has a special role in our place value system; each place value is 10 times the preceding one, and this helps to extend the system beyond whole numbers for measurements.

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3.5 Units of Measurement – Summary (Conversion-based Questions)

Q17. Convert the following as mentioned:

• 65 mm to cm
• 420 g to kg
• Rs 25.75 to paise

Answer:

• 65 mm ÷ 10 = 6.5 cm
• 420 g ÷ 1000 = 0.420 kg
• Rs 25.75 × 100 = 2575 paise

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3.6 Locating and Comparing Decimals – In-text Questions

Q18. Mark 0.5, 0.7, and 0.3 on a number line between 0 and 1.

Answer: On a number line from 0 to 1 divided into ten equal parts, 0.3 is at the 3^rd mark, 0.5 at the 5^th, and 0.7 at the 7^th mark.

Q19. Which is greater: 0.36 or 0.4?

Answer: 0.4 is greater because 0.40 > 0.36 when compared to two decimal places.

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3.7 Addition and Subtraction of Decimals – In-text Questions

Q20. Add: 15.34 + 2.68

Answer: 15.34 + 2.68 = 18.02

Q21. Subtract: 25.9 − 6.47

Answer: 25.90 − 6.47 = 19.43

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3.8 More on the Decimal System – In-text Questions

Q22. What comes next in the sequence: 0.8, 1.0, 1.2, __?, __?

Answer: 1.4, 1.6 (adding 0.2 each time)

Q23. Are 2.5 and 2.50 equal in value?

Answer: Yes, both represent the same value.

Q24. If Rs 1 = 100 paise, how much is Rs 5.60 in paise?

Answer: 5.60 × 100 = 560 paise

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Summary

• A unit can be split into smaller parts to measure more exactly: tenths, hundredths, thousandths, etc.
• The Indian place value system uses 10 as the base for each place.
• A decimal point separates the whole and fractional parts.
• Decimals make comparing, adding, and subtracting measurements easier.

Understanding Decimals in Class 7 Maths Chapter 3

Mastering NCERT Solutions for Class 7 Maths Chapter 3 A Peek Beyond the Point is crucial for developing strong decimal concepts. With well-structured solutions, students learn to measure, compare, and perform calculations with decimals confidently.

The chapter explains units, tenths, and hundredths—an essential part of the syllabus for 2025-26. Practicing all exercise-based questions will boost both problem-solving skills and concept clarity for Class 7 exams and beyond.

To score higher, students should review decimal place value and attempt different question types. Regular practice and revision are key strategies for building confidence and ensuring success in mathematics.