Understanding Number Systems

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the following number sets includes all the others?

Rational Numbers
Integers
Real Numbers
Complex Numbers (correct)

A number with a decimal expansion that neither terminates nor repeats is a rational number.

False (B)

Which of the following numbers is NOT a composite number?

17 (correct)
15
25
9

What is the result of converting the decimal number 25 to its binary equivalent?

11001 Signup and view all the answers

A recurring decimal can always be expressed as a fraction where the denominator is a power of 10.

False (B) Signup and view all the answers

The value of a digit based on its position in a number is called its ______.

place value Signup and view all the answers

What is the base of the binary number system?

2 Signup and view all the answers

Match each number system with its appropriate description:

Octal = Base-8 number system, using digits 0-7. Hexadecimal = Base-16 number system, using digits 0-9 and letters A-F. Binary = Base-2 number system, using digits 0 and 1. Decimal = Base-10 number system, commonly used in everyday calculations. Signup and view all the answers

The result of splitting a number into equal parts is known as ______.

division Signup and view all the answers

A set containing elements that are common to all the sets being combined is called:

Intersection (A) Signup and view all the answers

Which of the following is an irrational number?

π (D) Signup and view all the answers

If the difference between the sum of digits at odd places and even places in a number is 11, the number is divisible by 11.

True (A) Signup and view all the answers

What is the decimal equivalent of the hexadecimal number '2A'?

42 (B) Signup and view all the answers

What is the name for a fraction where the numerator is greater than or equal to the denominator?

improper fraction Signup and view all the answers

The binary number 10101011 can be directly converted to hexadecimal by grouping the digits into sets of three, starting from the right.

False (B) Signup and view all the answers

In modular arithmetic, the ______ operation finds the remainder after division.

modulo Signup and view all the answers

Which of the following represents the percentage decrease formula?

<code>[(Old Value - New Value) / Old Value] * 100</code> (D) Signup and view all the answers

Match the sequence type to the correct definition:

Arithmetic Sequence = Sequence with a constant difference between consecutive terms. Geometric Sequence = Sequence with a constant ratio between consecutive terms. Series = The sum of terms in a sequence. Signup and view all the answers

Flashcards

Natural Numbers

Positive integers starting from 1 (1, 2, 3,...). Also known as counting numbers.

Whole Numbers

Natural numbers plus zero (0, 1, 2, 3,...).

Integers

All whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3,...).

Rational Numbers

Numbers expressed as a fraction p/q, where p and q are integers and q is not zero (e.g., 1/2, -3/4, 5, 0.75).