NCERT Solutions for Class 7 Mathematics Chapter 3 A Peek Beyond the Point

This worksheet introduces students to Class 7 Mathematics Chapter A Peek Beyond the Point in a simple and engaging way. It focuses on understanding decimals, measurement, number patterns, and real-life applications of numbers. Students learn how to read, write, compare, and perform operations with decimals, which are essential skills for everyday calculations. This chapter is important because it builds a strong foundation for advanced mathematical concepts and helps students develop accuracy and logical thinking. This worksheet provides complete and accurate NCERT Solutions that help students check their work and understand the correct approach to solving each question.

Chapter summary: stories, poems & themes

This chapter is activity-based and focuses on numerical understanding rather than stories or poems. It includes picture-based questions, number line activities, and measurement-based exercises. Students observe patterns, identify decimal values, and solve real-life problems involving lengths, weights, and money. The main focus of the chapter is to build a clear understanding of decimals and their applications through practical examples and visual learning.

What this NCERT chapter covers?

• Understanding decimal numbers using tenths and hundredths 
• Reading and writing decimals correctly 
• Representing decimals on number lines 
• Comparing and arranging decimal numbers 
• Converting fractions into decimals 
• Performing addition and subtraction of decimals 
• Identifying patterns in number sequences 
• Converting units of measurement like mm, cm, m, g, and kg 
• Solving real-life problems involving money and measurement 
• Developing observation and logical reasoning skills 

How to use these NCERT solutions?

• First, students should attempt all questions on their own to test their understanding 
• After attempting, they can refer to the solutions to check their answers 
• Parents and teachers can guide students by explaining difficult steps 
• Solutions follow the same order as the worksheet, making it easy to track progress 
• Students should revise incorrect answers and practice similar questions 
• These solutions can be used for quick revision before tests and exams 

Student tips & learning tricks

• Always align decimal points correctly while performing operations 
• Pay attention to place value when comparing numbers 
• Practice number line questions to improve understanding 
• Be careful while converting units like cm to m or grams to kilograms 
• Read each question carefully before solving 
• Do not skip steps in calculations 
• Practice regularly to improve speed and accuracy 
• Focus on understanding patterns in sequences 
• For activity-based questions, think logically and observe carefully 

Why NCERT solutions are important?

NCERT Solutions help students understand concepts clearly and provide the correct way to solve problems. They build a strong foundation in Mathematics and improve accuracy in calculations. These solutions also help students prepare better for exams and boost their confidence by giving them clarity in concepts and problem-solving methods.

Complete answer key – NCERT solutions

Write the measurements of the objects shown in the picture.
1. Eraser → 2 4/10 cm 
2. Pencil → 4 5/10 cm → 4 1/2 cm 
3. Chalk → 1 4/10 cm 

Arrange the lengths in increasing order:
1. 4/10, 9/10, 1 7/10, 7 6/10, 10 5/10, 130/10, 13 1/10 

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

The lengths of the body parts of a honeybee are given. Find its total length.
1. 15 2/10 units 

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?
1. 1 5/10 cm 

Observe the given sequences of numbers. Identify the change after each term and extend the pattern:
1. 4, 4 3/10, 4 6/10, 4 9/10, 5 2/10, 5 5/10, 5 8/10 → increment of 3/10 each time 
2. 8 2/10, 8 7/10, 9 2/10, 9 7/10, 10 2/10, 10 7/10, 11 2/10 → increment of 5/10 each time 
3. 7 6/10, 8 7/10, 9 8/10, 10 9/10, 12, 13 1/10 → increment of 1 + 1/10 
4. 5 7/10, 5 3/10, 4 9/10, 4 5/10, 4 1/10, 3 7/10 → subtracting: 4/10 each time 
5. 13 5/10, 13, 12 5/10, 12, 11 5/10, 11, 10 5/10 → decreasing by 5/10 
6. 11 5/10, 10 4/10, 9 3/10, 8 2/10, 7 1/10, 6 → decreasing by 1 1/10 

How many one-hundredths make one-tenth? Can we also say that the length is 4 units and 45 one-hundredths?
1. 1/10 = 10/100 
2. So, 10 one-hundredths make one-tenth. 
3. Yes, we can write it 4 + 45/100 = 4 units and 45 one-hundredths 

Observe the figure below. Notice the markings and the corresponding lengths written in the boxes when measured from 0. Fill the lengths in the empty boxes.
1. student-generated activity 

For the lengths shown below write the measurements and read out the measures in words.
1. Measurement − 5 37/100 
In words: Five and thirty seven-hundredths. 
2. Measurement − 15 3/100 
In words: Fifteen and three-hundredths. 
3. Measurement − 7 52/100 
In words: Seven and fifty two-hundredths. 
4. Measurement − 9 80/100 
In words: Nine and eighty-hundredths. 

In each group, identify the longest and the shortest lengths. Mark each length on the scale.
1. Longest = 33/100, Shortest = 3/100 
2. Longest = 3 1/10, Shortest = 1 3/10 
3. Longest = 54/100, Shortest = 4/10 
4. Longest = 3 6/10 6/100, Shortest = 3 6/100 
5. Longest = 1 8/100, Shortest = 9/100 
6. Longest = 7 5/100, Shortest = 7 3/10 5/100 
7. Longest = 65/10 15/100, Shortest = 5 7/100 

Find the sums
1. 7.9 
2. 26.8 
3. 7.41 
4. 18.11 
5. 39.10 
6. 1.534 
7. 0.78 
8. 6.723 

Find the differences
1. 3.3 
2. 9.2 
3. 5.9 
4. 0.802 
5. 16.95 
6. 16.405 
7. 0.81 
8. 5.749 

Continue this sequence and write the next 3 terms.
1. 6.4, 6.8, 7.2 

Identify the change and write the next 3 terms for each sequence.
1. 4.4, 4.45, 4.5, 4.55, 4.6, 4.65 
2. 25.75, 26.25, 26.75, 27.25, 27.75, 28.25 
3. 10.56, 10.67, 10.78, 10.89, 11.0, 11.11 
4. 13.5, 16, 18.5, 21.0, 23.5, 26.0 
5. 8.5, 9.4, 10.3, 11.2, 12.1, 13.0 
6. 5, 4.95, 4.90, 4.85, 4.80, 4.75 
7. 12.45, 11.95, 11.45, 10.95, 10.45, 9.95 
8. 36.5, 33, 29.5, 26.0, 22.5, 19.0 

Convert the following fractions into decimals:
1. 5/100 = 0/05 
2. 16/1000 = 0.016 
3. 12/10 = 1/2 
4. 254/1000 = 0/254 

Convert the following decimals into a sum of tenths, hundredths and thousandths:
1. 3/10 + 4/100 
2. 100/100 + 2/100 = 1 + 2/100 
3. 8/10 
4. 3/10 + 6/100 + 2/1000 

What decimal number does each letter represent in the number line below?
1. student-generated activity 

Arrange the following quantities in descending order:
1. 11.10, 11.01, 1.101, 1.011, 1.01 
2. 2.768, 2.698, 2.675, 2.567, 2.499 
3. 4.678, 4.666, 4.656, 4.600, 4.595 
4. 33.331, 33.313, 33.31, 33.133, 33.13 

Using the digits 1, 4, 0, 8, and 6 make:
1. 40.168 
2. 104.68 

Will a decimal number with more digits be greater than a decimal number with fewer digits?
1. No. It is not necessary. For example, 2.05 vs 2.5. 2.5 > 2.05 

Mahi purchases different vegetables. Calculate the total weight.
1. 1.3 kg 

Pinto supplies milk. Find the total quantity of milk supplied in the last three days.
1. 12.76 L 

Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?
1. He has lost weight. The change in the weight = 1.25 kg 

Extend the pattern:
1. 9.07, 9.06 

How many millimeters make 1 kilometer?
1. 1000000 mm 

Indian Railways travel insurance problem:
1. The total insurance fee paid for 1 lakh passengers is ₹45,000 

Which is greater?
1. 1/10 > 1/100 
2. 90 thousandths > One-hundredth 
3. 90 hundredths > One-thousandth 

Write the decimal forms of the quantities mentioned:
1. 88.10 
2. 121.2 
3. 111.1 
4. 277.75 

Using each digit 0 – 9 not more than once, fill the boxes so that the sum is closest to 10.5:
1. student-generated activity 

Write the following fractions in decimal form:
1. 0.5 
2. 1.5 
3. 0.25 
4. 0.75 
5. 0.2 
6. 0.8 

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