Number System MCQs with Answers & Explanations

Step 1: Natural numbers are 1, 2, 3, ... and do not include negative numbers. Step 2: Whole numbers are 0, 1, 2, 3, ... and do not include negatives. Step 3: Integers include ..., -2, -1, 0, 1, 2, ... so -7 is an integer. Step 4: Irrational numbers cannot be written as a/b; -7 is rational but the best classification among the options is Integers.

Step 1: sqrt(50) = sqrt(25*2) = 5*sqrt(2). Step 2: sqrt(2) is irrational, so 5*sqrt(2) is irrational. Step 3: 0.125 = 1/8 (rational). Step 4: -2/7 is rational. Step 5: 0.333... repeating equals 1/3 (rational). Therefore the irrational choice is sqrt(50).

Step 1: Normalize decimals to the same number of places: -0.40, -0.50, -0.49. Step 2: Convert -1/2 = -0.50. Step 3: On the number line, the smallest is the most negative. Step 4: -0.50 is the smallest among -0.50, -0.49, -0.40. Therefore -0.50 is smallest.

Step 1: Apply order of operations: multiplication before addition/subtraction. Step 2: 5*2 = 10. Step 3: Compute 3 + 10 - 4 = 13 - 4 = 9.

Step 1: Compute parentheses first: 18 - 6 = 12. Step 2: Divide: 12/3 = 4.

Step 1: Use absolute value: | -12 | = 12 and | 5 | = 5. Step 2: Subtract: 12 - 5 = 7.

Step 1: Compute inside parentheses: 4 - 3 = 1. Step 2: Multiply: 7*1 = 7.

Step 1: The grouping changes but the order remains the same. Step 2: This is the associative property of addition, not commutative (which swaps order) or distributive (which multiplies over addition). Step 3: Identity property involves adding 0.

Step 1: Use exponent rules for same base: 2^3 * 2^4 = 2^(3+4) = 2^7. Step 2: Compute 2^7 = 128.

Step 1: Any nonzero number to the zero power equals 1. Step 2: Therefore 10^0 = 1 by the zero exponent rule.

Step 1: Subtracting a negative is adding: -3 - (-8) = -3 + 8. Step 2: -3 + 8 = 5.

Step 1: The product of two negatives is positive. Step 2: 2*7 = 14. Step 3: Therefore -2 * (-7) = 14.

Step 1: Divide magnitudes: 42/6 = 7. Step 2: A positive divided by a negative is negative. Step 3: Result is -7.

Step 1: 21 = 3*7 (composite). Step 2: 33 = 3*11 (composite). Step 3: 51 = 3*17 (composite). Step 4: 29 has no divisors other than 1 and itself; hence it is prime.

Step 1: Prime factorize: 18 = 2*3^2, 24 = 2^3*3. Step 2: Common primes with lowest powers: 2^1*3^1 = 6. Step 3: Therefore the GCD is 6.

Step 1: Prime factorize: 4 = 2^2, 6 = 2*3. Step 2: Take highest powers: 2^2*3 = 12. Step 3: Therefore the LCM is 12.

Step 1: 0.375 = 375/1000. Step 2: Simplify by dividing numerator and denominator by 125: 375/1000 = 3/8. Step 3: 3/8 is simplest form.

Step 1: Divide 5 by 4: 5/4 = 1.25. Step 2: Because 4 goes into 5 once with remainder 1, 1 + 1/4 = 1.25.

Step 1: 45% = 45 per 100 = 45/100. Step 2: 45/100 = 0.45 in decimal. Step 3: Simplify 45/100 by dividing by 5 to get 9/20. Step 4: All representations are equivalent.

Step 1: 20% = 20/100 = 0.20. Step 2: Multiply 0.20*150 = 30.