Number System
Gujarat Board · Class 9 · Mathematics
Flashcards for Number System — Gujarat Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedExpress -25 as a rational number in the form p/q where p and q are integers and q ≠ 0.
Answer
Step 1: Recall that any integer can be written as a rational number by placing it over 1. Step 2: Write -25 = -25/1 Answer: -25/1 (where p = -25, q = 1, and q ≠ 0) Verification: -25 ÷ 1 = -25 ✓…
Find five rational numbers between 1 and 2.
Answer
Method: Write 1 and 2 with denominator 6 → 6/6 and 12/6 Step 1: 1 = 6/6 and 2 = 12/6 Step 2: Numbers between 6/6 and 12/6 are: 7/6, 8/6, 9/6, 10/6, 11/6 Step 3: Simplify if needed: 7/6, 4/3, 3/2, 5/3,…
Determine if 1/3 is a rational number. Justify your answer.
Answer
Answer: Yes, 1/3 is a rational number. Justification: By definition, a number is rational if it can be written as p/q where p and q are integers and q ≠ 0. For 1/3: p = 1 (integer), q = 3 (integer), a…
Find the decimal expansion of 1/3 by long division. What type of decimal is it?
Answer
Long division: 1 ÷ 3 1.000... ÷ 3 Step 1: 10 ÷ 3 = 3 remainder 1 → quotient digit is 3 Step 2: 10 ÷ 3 = 3 remainder 1 → quotient digit is 3 (pattern repeats) Result: 1/3 = 0.333... = 0.3̄ Type: Non-te…
Find the decimal expansion of 1/8 by long division. What type of decimal is it?
Answer
Long division: 1 ÷ 8 Step 1: 10 ÷ 8 = 1 remainder 2 → quotient is 0.1 Step 2: 20 ÷ 8 = 2 remainder 4 → quotient is 0.12 Step 3: 40 ÷ 8 = 5 remainder 0 → quotient is 0.125 Result: 1/8 = 0.125 Type: Ter…
Convert 0.333... (non-terminating recurring) to the form p/q where p and q are integers.
Answer
Let x = 0.333... Step 1: Multiply both sides by 10 → 10x = 3.333... Step 2: Subtract original equation from new equation: 10x - x = 3.333... - 0.333... 9x = 3 Step 3: Solve for x → x = 3/9 = 1/3 Answe…
Convert 0.142857̄ (where 142857 repeats) to the form p/q.
Answer
Let x = 0.142857142857... Step 1: The repeating block has 6 digits, so multiply by 10⁶ = 1,000,000 1,000,000x = 142857.142857... Step 2: Subtract: 1,000,000x - x = 142857.142857... - 0.142857... 999,9…
Classify √2, √3, π, and 0.123456... (non-terminating non-recurring) as rational or irrational.
Answer
√2: Irrational (non-terminating non-recurring decimal: 1.41421356...) √3: Irrational (non-terminating non-recurring decimal: 1.73205080...) π: Irrational (non-terminating non-recurring decimal: 3.1415…
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