This MCQ module is based on: Chapter 3 Exercises
TOPIC 11 OF 31
Chapter 3 Exercises
🎓 Class 7
Mathematics
CBSE
Theory
Ch 3 — A Peek Beyond the Point
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Chapter 3 Exercises
Targeting Class 7 level in Decimals, with Basic difficulty.
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Chapter 3 — Exercises
Q1. Find the sums: (a) 5.3 + 2.6 (b) 18 + 8.8 (c) 2.15 + 5.26 (d) 9.01 + 9.10 (e) 29.19 + 9.91 (f) 0.934 + 0.6 (g) 0.75 + 0.03 (h) 6.236 + 0.487.
(a) 7.9 (b) 26.8 (c) 7.41 (d) 18.11 (e) 39.10 (f) 1.534 (g) 0.78 (h) 6.723.
Q2. Find the differences: (a) 5.6 − 2.3 (b) 18 − 8.8 (c) 10.4 − 4.5 (d) 17 − 16.198 (e) 17 − 0.05 (f) 34.505 − 18.1 (g) 9.9 − 9.09 (h) 6.236 − 0.487.
(a) 3.3 (b) 9.2 (c) 5.9 (d) 0.802 (e) 16.95 (f) 16.405 (g) 0.81 (h) 5.749.
Q3. Arrange in descending order: (a) 11.01, 1.011, 1.101, 11.10, 1.01 (b) 2.567, 2.675, 2.768, 2.499, 2.698 (c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g (d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.1133 m.
(a) 11.10, 11.01, 1.101, 1.011, 1.01
(b) 2.768, 2.698, 2.675, 2.567, 2.499
(c) 4.678, 4.666, 4.656, 4.600, 4.595
(d) 33.331, 33.31, 33.133, 33.13, 33.1133
(b) 2.768, 2.698, 2.675, 2.567, 2.499
(c) 4.678, 4.666, 4.656, 4.600, 4.595
(d) 33.331, 33.31, 33.133, 33.13, 33.1133
Q4. Using digits 1, 4, 0, 8, 6, make: (a) the decimal number closest to 30 (b) the smallest decimal between 100 and 1000.
(a) 40.168 (or 30.864 as an alternate close value; closest using all five digits once: 30.4+6.18… — among 5-digit decimals, 40.168 is near 30). A common accepted answer: 40.168. (b) 104.68.
Q5. Will a decimal with more digits be greater than a decimal with fewer digits? Justify.
No, not necessarily. Example: 2.05 (2 digits after decimal) vs 2.5 (1 digit). 2.5 > 2.05. Length of decimal does not determine size.
Q6. Mahi buys 0.5 kg beans, 0.3 kg carrots, 0.5 kg potatoes, 0.2 kg capsicum, and 0.05 kg ginger. Total weight of items?
0.5 + 0.3 + 0.5 + 0.2 + 0.05 = 1.55 kg.
Q7. Pinto supplies 3.79 L, 4.2 L, and 4.25 L of milk to a milk dairy in the first three days. In six days, he supplies 25 L total. Find total milk supplied to the dairy in the last three days.
First three days: 3.79 + 4.2 + 4.25 = 12.24 L. Remaining = 25 − 12.24 = 12.76 L.
Q8. Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much?
35.75 − 34.50 = 1.25 kg. Tinku has lost 1.25 kg.
Q9. Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 8.18, 8.17, ___, ___.
Alternate +0.9 then −0.01. Next: 9.07, 9.06.
Q10. How many millimetres make 1 kilometre?
1 km = 1000 m = 1000 × 1000 mm = 1 000 000 mm.
Q11. Indian Railways offers optional travel insurance at 45 paise per passenger. If one lakh people opt for insurance in a day, what is the total insurance fee paid?
₹0.45 × 1,00,000 = ₹45,000.
Q12. Which is greater: (a) \(\frac{10}{1000}\) or \(\frac{1}{10}\)? (b) one-hundredth or 90 thousandths? (c) one-thousandth or 90 hundredths?
(a) 10/1000 = 0.01; 1/10 = 0.1. So 1/10. (b) 1/100 = 0.01; 90/1000 = 0.09. 90 thousandths. (c) 1/1000 = 0.001; 90/100 = 0.9. 90 hundredths.
Q13. Write the decimal form of: (a) 87 ones, 5 tenths, 60 hundredths (b) 12 tens, 12 tenths (c) 10 tens, 10 ones, 10 tenths, 10 hundredths (d) 25 tens, 25 ones, 25 tenths, 25 hundredths.
(a) 87 + 0.5 + 0.60 = 88.10. (b) 120 + 1.2 = 121.2. (c) 100+10+1.0+0.10 = 111.10. (d) 250+25+2.5+0.25 = 277.75.
Q14. Using each digit 0–9 not more than once, fill in boxes so that the sum is closest to 10.5.
Example: 9.476 + 1.025 = 10.501 ≈ 10.5 (other near-optimal answers exist).
Q15. Write as decimals: (a) \(\tfrac{1}{2}\) (b) \(\tfrac{3}{2}\) (c) \(\tfrac{1}{4}\) (d) \(\tfrac{3}{4}\) (e) \(\tfrac{1}{5}\) (f) \(\tfrac{4}{5}\).
(a) 0.5 (b) 1.5 (c) 0.25 (d) 0.75 (e) 0.2 (f) 0.8.
Chapter Summary
Tenth, Hundredth, Thousandth
One of 10, 100, 1000 equal parts of a whole. Written 1/10, 1/100, 1/1000.
Decimal Point
Separates whole-number places from fractional places. Digits to the right = tenths, hundredths, etc.
Place Value Rule
Each place is 10× the place to its right and 1/10 of the place to its left.
Add & Subtract
Align decimal points. Pad with zeros if needed. Operate column by column.
Unit Conversion
1 km = 1000 m; 1 m = 100 cm; 1 cm = 10 mm. Shift the decimal point to convert.
Comparing Decimals
Compare digit by digit from left after aligning decimal points. More digits ≠ larger.
Key Terms
decimal?, tenth?, hundredth?, thousandth?, decimal point, place value, unit, metric conversion.
Capstone Activity: Decimal Scavenger Hunt
L3 ApplyMaterials: Notebook, ruler, digital kitchen scale (optional).
Predict: How many objects at home have a length or mass stamped in decimal form?
- Find 10 household objects that list a measurement: medicines (5 ml), wires (1.5 m), coins (weight), food packets (500 g).
- Record each measurement as a decimal.
- Express each measurement in a smaller unit (mm, mg, paise) and check that only the decimal point shifts.
You will notice that decimals appear everywhere — pharmacy, groceries, travel, fabric, fuel. Mastery of decimals is a real-world must-have.
Competency-Based Questions
Scenario: A local train from Yahapur to Vahapur stops at three stations at equal distances. The train takes 2 minutes at each station. Total travel time (stopping + running) from Yahapur to Vahapur is 45 minutes. Travel time in minutes between consecutive stations is \(t\).
Q1. Using data given, write an expression for the journey.
L3 ApplyThe train runs 4 equal legs (Y→S1, S1→S2, S2→S3, S3→V) of \(t\) minutes each, and stops at three stations for 2 minutes each. So total time = \(4t + 6\) minutes = 45, giving \(t = 9.75\) minutes.
Q2. Analyse: if stops become 2.5 minutes each instead, what is new \(t\)?
L4 Analyse\(4t + 3\times2.5 = 45 \Rightarrow 4t = 37.5 \Rightarrow t = 9.375\) minutes.
Q3. Evaluate: is the answer 9.75 minutes realistic? How precise is it?
L5 Evaluate9.75 minutes = 9 minutes and 45 seconds — realistic for local train segments. Precision to hundredths (9.75) is meaningful since 0.01 minute = 0.6 s.
Q4. Design a new timetable where the total is still 45 minutes but leg-times are 8.5, 9.0, 9.5, and 10.0 minutes. Check feasibility with 3 stops.
L6 CreateSum of legs = 8.5+9.0+9.5+10.0 = 37.0 min. Plus 3×2 = 6 min for stops. Total = 43 min, not 45. Adjust: 9.0+9.5+10+10.5 = 39 + 6 = 45. Yes, feasible.
Assertion–Reason Questions
A: 0.5 = 0.50 = 0.500.
R: Appending zeros after the last digit to the right of the decimal point does not change the value of a decimal.
R: Appending zeros after the last digit to the right of the decimal point does not change the value of a decimal.
(a)
A: 1 km = 1 000 000 mm.
R: 1 km = 1000 m and 1 m = 1000 mm.
R: 1 km = 1000 m and 1 m = 1000 mm.
(a)
A: 2.05 kg and 2.5 kg differ by 450 g.
R: 2.5 − 2.05 = 0.45 kg and 1 kg = 1000 g.
R: 2.5 − 2.05 = 0.45 kg and 1 kg = 1000 g.
(a)
Frequently Asked Questions
What exercises are in Class 7 Ganita Prakash Chapter 3?
Chapter 3 exercises cover writing fractions as decimals, decimal place value identification, unit conversions with decimals, decimal addition and subtraction, and word problems involving money or measurement. NCERT Class 7 Ganita Prakash gives varied practice.
How do you solve decimal word problems?
Read carefully, identify the given values (with units), write them as decimals with matching units, perform the required operation (add, subtract), and state the final answer with the unit. NCERT Class 7 Chapter 3 exercises build this strategy.
What is the summary of Class 7 decimals chapter?
Key ideas: tenths, hundredths, thousandths use base-10 place value; decimals equal fractions with 10, 100, 1000 denominators; unit conversions shift the decimal point; align decimal points when adding or subtracting. NCERT Class 7 Ganita Prakash Chapter 3 covers these.
How to convert 7/1000 into decimal form?
7/1000 means 7 thousandths. Write 0.007 (zero ones, zero tenths, zero hundredths, seven thousandths). NCERT Class 7 Chapter 3 exercises include many such conversions.
Why do Class 7 students learn decimal exercises?
Decimal exercises cement understanding of base-10 place value, precise measurement, and arithmetic with non-whole numbers. These skills are essential for science, money management, and later maths topics. NCERT Class 7 Chapter 3 builds the foundation.
How many decimal places should answers have?
Keep at least as many decimal places as the most precise given value. For example, 2.5 + 1.25 = 3.75 (two places) because 1.25 has two places. Do not round during intermediate steps. NCERT Class 7 Chapter 3 exercises follow this rule.
Frequently Asked Questions — A Peek Beyond the Point
What is Chapter 3 Exercises in NCERT Class 7 Mathematics?
Chapter 3 Exercises is a key concept covered in NCERT Class 7 Mathematics, Chapter 3: A Peek Beyond the Point. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Chapter 3 Exercises step by step?
To solve problems on Chapter 3 Exercises, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 3: A Peek Beyond the Point?
The essential formulas of Chapter 3 (A Peek Beyond the Point) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Chapter 3 Exercises important for the Class 7 board exam?
Chapter 3 Exercises is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Chapter 3 Exercises?
Common mistakes in Chapter 3 Exercises include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Chapter 3 Exercises?
End-of-chapter NCERT exercises for Chapter 3 Exercises cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 3, and solve at least one previous-year board paper to consolidate your understanding.
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