Complete step-by-step solutions for DAV Class 7 Secondary Mathematics Chapter 3: Rational Numbers as Decimals (Brain Teasers, HOTS & Value Based Questions). Includes detailed explanations for terminating vs non-terminating decimals, recurring decimals, period and periodicity, conversion of decimals to fractions, Higher Order Thinking Skills (HOTS), and Value-Based Questions (VBQs) strictly matching the DAV Education Board curriculum.
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Q.1. (A) Tick (✓) the correct option
(i) 0.225 expressed as a rational number in simplest form is:
- (a) 1/4
- (b) 45/210
- (c) 9/40
- (d) 225/999
0.225 = 225/1000
Dividing numerator and denominator by 25: (225 ÷ 25)/(1000 ÷ 25) = 9/40.
Correct Option: (c) 9/40
(ii) A rational number p/q can be expressed as a terminating decimal if q has no prime factor other than:
- (a) 2, 3
- (b) 2, 5
- (c) 3, 5
- (d) 2, 3, 5
Correct Option: (b) 2, 5
(iii) −7 8/100 expressed as a decimal number is:
- (a) −7.800
- (b) 7.008
- (c) −7.008
- (d) −7.08
−7 8/100 = −(7 + 0.08) = −7.08.
Correct Option: (d) −7.08
(iv) The recurring decimal 4.01325 (with bar over 25) is equal to:
- (a) 4.013252525…
- (b) 4.01325555…
- (c) 4.0132501325…
- (d) 4.0130132525…
Correct Option: (a) 4.013252525…
(v) The quotient when 0.00639 is divided by 0.213 is:
- (a) 3
- (b) 0.3
- (c) 0.03
- (d) 0.003
0.00639/0.213 = (639 / 100000)/(213 / 1000) = 639/100000 × 1000/213 = 3/100 = 0.03.
Correct Option: (c) 0.03
Q.1. (B) Short Answer Questions
(a) Without actual division, determine if −28/250 is terminating or non-terminating.
2. Prime factors of denominator 125 = 5 × 5 × 5 = 53.
3. Since the denominator has only 5 as its prime factor, it is a Terminating Decimal.
Ans: Terminating Decimal
(b) How many decimal places will the decimal representation of 37/250 terminate after?
Therefore, the decimal representation will terminate after 3 decimal places (37 ÷ 250 = 0.148).
Ans: 3 decimal places
(c) Convert 3.125 into p/q form in lowest terms.
Ans: 25/8
(d) Is the square of 0.2 smaller or greater than 0.2?
Ans: Smaller
Q.2. Convert the following rational numbers into decimals by long division
(i) 13/8
Ans: 1.625
(ii) −17/40
Ans: −0.425
(iii) 5/6
Ans: 0.83 (bar on 3)
🔥 Higher Order Thinking Skills (HOTS)
HOTS Q1: Find the value of x if 0.00032 ÷ x = 0.008.
⇒ x = 0.00032/0.008 = (32 / 100000)/(8 / 1000) = 32/100000 × 1000/8 = 4/100 = 0.04.
Ans: 0.04
HOTS Q2: Express the non-terminating repeating decimal 0.35 (bar on 35) as a rational number p/q.
Since 2 digits are repeating, multiply by 100:
100x = 35.353535… — (2)
Subtract (1) from (2):
100x − x = 35.3535… − 0.3535…
99x = 35 ⇒ x = 35/99.
Ans: 35/99
🌱 Value Based Questions (VBQ)
VBQ: A hospital dispensary measured the liquid antibiotic dosage for child patients up to three decimal places (0.125 mL per kg body weight).
(a) Convert 0.125 into standard fraction form in lowest terms.
0.125 = 125/1000 = 1/8 mL.(b) What core value is exhibited by measuring medicine dosages accurately in decimals?
Core Values Depicted: Precision, medical responsibility, high diligence, and dedication to safeguarding human life and children’s health.Ans: (a) 1/8 mL | (b) Medical Accuracy & Care
📚 DAV Class 7 Maths Chapter 3: Rational Numbers as Decimals – Complete Solutions Index
| Worksheet / Section | Core Concepts Covered | Solution Link |
|---|---|---|
| Worksheet 1 | Terminating Decimals without Actual Division | View Worksheet 1 → |
| Worksheet 2 | Conversion to Decimals using Long Division | View Worksheet 2 → |
| Worksheet 3 | Recurring Decimals, Period & Periodicity | View Worksheet 3 → |
| Brain Teasers, HOTS & VBQs | Comprehensive Review, Exponent Tests & Conversions | Current Page |