Number System
Punjab Board · Class 9 · Mathematics
Flashcards for Number System — Punjab Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedIs zero a rational number? Express it in the form p/q.
Answer
Yes, zero is a rational number. We can write it as 0/1, 0/2, 0/3, etc., where p = 0 and q ≠ 0. Since zero can be expressed as the ratio of two integers, it satisfies the definition of a rational numbe…
Find five rational numbers between 3 and 4.
Answer
Method: Write 3 and 4 with denominator 6 (5+1): 3 = 18/6 and 4 = 24/6. The five numbers between them are: 19/6, 20/6 = 10/3, 21/6 = 7/2, 22/6 = 11/3, 23/6. Simplified answers: 19/6, 10/3, 7/2, 11/3, 2…
Find three rational numbers between 3/5 and 4/5.
Answer
Method 1 - Midpoint method: Between 3/5 and 4/5, find (3/5 + 4/5)/2 = 7/10. Between 3/5 and 7/10, find (3/5 + 7/10)/2 = (6/10 + 7/10)/2 = 13/20. Between 7/10 and 4/5, find (7/10 + 4/5)/2 = (7/10 + 8/1…
Determine if these statements are true or false: (i) Every whole number is a natural number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number.
Answer
(i) FALSE - Zero is a whole number but NOT a natural number. Natural numbers = {1, 2, 3, ...}, Whole numbers = {0, 1, 2, 3, ...}. (ii) FALSE - Negative integers like -5, -10 are NOT whole numbers. Who…
Convert 10/3 to decimal form and describe its pattern.
Answer
Performing long division: 10 ÷ 3 = 3.333... The pattern shows: Remainder 1 repeats indefinitely. Decimal form: 10/3 = 3.3̄ (bar over 3 indicates repetition). This is a non-terminating recurring decima…
Convert 1/7 to decimal form and identify the repeating block.
Answer
Performing long division: 1 ÷ 7 = 0.142857142857... Step-by-step remainders: 1→10→3→2→6→4→5→1 (cycle repeats). Decimal form: 1/7 = 0.1̄4̄2̄8̄5̄7̄ (bar over all six digits). Repeating block: 142857 (pe…
Convert 7/8 to decimal and explain why it terminates.
Answer
Performing long division: 7 ÷ 8 = 0.875 Remainders: 7→2→4→0 (stops here). Decimal form: 7/8 = 0.875 (terminating). Why it terminates? The denominator 8 = 2³, which is a power of 2 only. Rule: A fracti…
Express 0.3̄ (where 3 repeats) as a fraction p/q.
Answer
Let x = 0.3̄ = 0.3333... Step 1: Multiply by 10 → 10x = 3.3333... Step 2: Notice that 10x = 3 + 0.3333... = 3 + x Step 3: Solve → 10x - x = 3 → 9x = 3 → x = 3/9 = 1/3 Answer: 0.3̄ = 1/3 Verification: …
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