PACT Exam Mathematics 703 fully solved graded A+ 2023/2024

PACT Exam Mathematics 703Real numbers - correct answer numbers that have a specific value. Rational or irrational. Rational include integer, whole, natural. Rational Numbers - correct answer Numbers that can be expressed as a ratio of two integers a/b where b ≠ 0. Can be written EXACTLY in both fraction and decimal Examples of rational numbers - correct answer Mixed numbers 4½ Decimals 0.25 Repeating decimals 0.727272 or 0.72, or 8/11 Natural Numbers - correct answer pointed to in nature, aka counting numbers... 1 tree, two people, three dogs. Whole Numbers - correct answer natural numbers and 0 Integers - correct answer positive and negative counting numbers and zero Examples of natural numbers - correct answer 1, 2, 3, 4, 5,... Examples of whole numbers - correct answer 0, 1, 2, 3, 4,... Examples of integers - correct answer -3, -2, -1, 0, 1, 2, 3,... Irrational Numbers - correct answer Real numbers that cannot be represented exactly as a ratio of two integers. Must use symbols or be approximated Irrational numbers often written with symbols - correct answer π, e, sqrt2 Exponential notation - correct answer indicate repeated multiplication. 2*2*2*2= 2⁴ Any number raised to the 0 power equals - correct answer 1 Exponential notation magnitude - correct answer Exponents can be positive or negative, or in fraction form. Positive exponential notation magnitude - correct answer multiplies the number by itself as many times as exponent shows: 2*2*2*2= 2⁴ =16 Makes fractions smaller: (1/4)*(1/4)*(1/4) = 1/64 Makes absolute value of integers bigger: (-5)² = -5*-5 = 25 Negative exponential notation magnitude - correct answer Multiplies the number by its inverse fraction as many times as the exponent shows: 2^-4 = (1/2)*(1/2)*(1/2)*(1/2) = 1/16 Makes fractions bigger: (1/4)^-3=4*4*4=64 Makes absolute value of integers smaller: -5^-2=(-1/5)*(-1/5)=1/25 fractional exponential notation magnitude - correct answer shows the root that is being found Scientific notation, Large numbers have positive exponents - correct answer 4,200,000 = 4.2 * 10^6 scientific notation small numbers have negative exponents - correct answer 0.000426 = 4.26 * 10^-4 natural numbers greater than 1 that have no numbers other than 1 and themselves divide into them without a remainder. - correct answer prime numbers