PACT Exam Mathematics 703 Exam With Verified
Solutions Graded A+
Real numbers Answer numbers that possess some exact value.
Rational or irrational.
Rational include integer, whole, natural.
Rational Numbers Answer Numbers that can be expressed as the quotient of two
integers a/b where b ≠ 0.
Can be written EXACTLY in both fraction and decimal
Examples of rational numbers Answer Mixed numbers 4½
Decimals 0.25
Repeating decimals 0.727272 or 0.72, or 8/11
Natural Numbers - Answer indicated in nature, aka counting numbers. 1 tree, two
people, three dogs.
Whole Numbers - Answer natural numbers and 0
Integers - Answer positive and negative counting numbers and zero
Examples of natural numbers - Answer 1, 2, 3, 4, 5,.
Examples of whole numbers - Answer 0, 1, 2, 3, 4,.
, Examples of integers - Answer -3, -2, -1, 0, 1, 2, 3,.
Irrational Numbers - Real numbers that cannot be expressed exactly as a ratio of two
integers.
Must use symbols or be approximated
Irrational numbers commonly written with symbols - π, e, \\\sqrt2
Exponential notation - Show repeated multiplication.
2*2*2*2= 2⁴
Any number raised to the 0 power equals - 1
Magnitude of exponential notation - Exponents can be positive or negative, or in fraction
form.
Positive exponential notation magnitude-Answer: Multiplies the number by itself as many
times as exponent shows: 2*2*2*2=2 ⁴ =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-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 - Answer shows the root that is being found
Solutions Graded A+
Real numbers Answer numbers that possess some exact value.
Rational or irrational.
Rational include integer, whole, natural.
Rational Numbers Answer Numbers that can be expressed as the quotient of two
integers a/b where b ≠ 0.
Can be written EXACTLY in both fraction and decimal
Examples of rational numbers Answer Mixed numbers 4½
Decimals 0.25
Repeating decimals 0.727272 or 0.72, or 8/11
Natural Numbers - Answer indicated in nature, aka counting numbers. 1 tree, two
people, three dogs.
Whole Numbers - Answer natural numbers and 0
Integers - Answer positive and negative counting numbers and zero
Examples of natural numbers - Answer 1, 2, 3, 4, 5,.
Examples of whole numbers - Answer 0, 1, 2, 3, 4,.
, Examples of integers - Answer -3, -2, -1, 0, 1, 2, 3,.
Irrational Numbers - Real numbers that cannot be expressed exactly as a ratio of two
integers.
Must use symbols or be approximated
Irrational numbers commonly written with symbols - π, e, \\\sqrt2
Exponential notation - Show repeated multiplication.
2*2*2*2= 2⁴
Any number raised to the 0 power equals - 1
Magnitude of exponential notation - Exponents can be positive or negative, or in fraction
form.
Positive exponential notation magnitude-Answer: Multiplies the number by itself as many
times as exponent shows: 2*2*2*2=2 ⁴ =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-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 - Answer shows the root that is being found
