51 Questions
Which is the smallest natural number?
1
In the set of whole numbers, what is the least number?
0
Which statement is true about integers?
Every whole number is an integer
Which of the following sets includes the number 0?
Whole numbers
What does the set of integers include?
All natural numbers and their negatives, including 0
What does the line point represent at 750 units to the left of the origin O?
Negative integer -750
Which of the following is NOT a property of rational numbers?
Innumerable quantity
What is the definition of a rational number provided in the text?
A number that can be written in the form p/q where q is not zero
Which statement regarding natural numbers and integers is correct?
Every natural number and integer is a rational number
What does the term 'rational' in rational numbers derive from?
The word 'ratio'
What is a terminating decimal?
A decimal that ends after a finite number of digits
Which of the following fractions can be expressed as a terminating decimal?
$\frac{2}{5}$
Why can the fractions $\frac{1}{4}$ and $\frac{5}{8}$ be expressed as terminating decimals?
Because their denominators have no primes other than 2 and 5
Which of the following is an example of a terminating decimal obtained from dividing $\frac{5}{8}$?
0.625
Which of the following is NOT a property of terminating decimals?
They always represent irrational numbers
Which of the following is the simplest form of the rational number $\frac{133}{57}$?
$\frac{19}{3}$
Given the rational number $\frac{4}{7}$, which of the following is an equivalent rational number?
$\frac{16}{28}$
How is the rational number $\frac{1}{2}$ represented on the real line in the given content?
By taking midpoint of a unit length from 0
Which of the following is NOT an example of equivalent rational numbers from the content provided?
$\frac{3}{6}$ and $\frac{4}{5}$
According to the content, what are rational numbers?
Numbers that can be expressed as a fraction with integers and non-zero denominators
What is the general method used to find a rational number between two given rational numbers?
Taking the average of the two numbers
If $x = \frac{1}{3}$ and $y = \frac{1}{2}$, what is the rational number lying between them?
$\frac{5}{12}$
What rational number lies between $\frac{1}{3}$ and $\frac{1}{4}$?
$\frac{7}{24}$
Which of the following represents the rational number between $\frac{3}{5}$ and $\frac{2}{3}$?
$\frac{17}{30}$
How would you find a rational number between $\frac{2}{7}$ and $\frac{3}{5}$?
Calculate $\frac{1}{2}(\frac{2}{7} + \frac{3}{5})$
What is the length of the period of the decimal expansion of $rac{1}{7}$?
6
Which of the following fractions has a repeating string of remainders of length 3 in its decimal expansion?
$rac{22}{7}$
Which of the following is true for any rational number?
It can be either terminating or nonterminating recurring decimal
If a rational number has a period length of 1, which of the following could be its decimal representation?
0.777...
The maximum number of repeating entries in the decimal expansion of $rac{1}{13}$ is:
12
Which of the following describes a terminating decimal?
Has a finite number of digits
What is the square root of 961?
31
Which of the following is the closest approximate value for $1275 ÷ 5$?
255
Which of the following pairs is equivalent to 9900?
$33 imes 300$
What is the quotient when 318002 is divided by 66?
4820
Which number is represented as both a Terminative and a Repeating Decimal?
2455
Which property is true for irrational numbers under addition and multiplication?
They satisfy the commutative and associative properties.
What is the outcome when $rac{22}{7}$ is used as a representation of a number?
The number is rational.
What is the result of adding two irrational numbers, such as $rac{1}{3} + rac{4}{3} = 2$?
May be rational.
What does the product of $rac{ posqr{3}}{rac{ posqr{3}}}$ result in?
Rational
Which statement about irrational numbers is incorrect?
Their sum is always irrational.
Which of the following is correct according to the Associative Law of addition for real numbers?
$(a + b) + c = a + (b + c)$
What property guarantees that there are infinitely many real numbers between any two real numbers?
Density Property
Which statement correctly describes the Existence of Additive Inverse?
For each real number $a$, there exists a real number $(-a)$ such that $a + (-a) = 0$
Which of the following is true about rational numbers?
They can be represented by a terminating or repeating decimal.
What is the identity element for multiplication in the set of real numbers?
1
What is the length of OB if OA = 1 unit and AB = 1 unit?
$\sqrt{2}$ units
After constructing OA = 1 unit and AB = 1 unit, what geometric construction is used to find point P?
Draw an arc from point O with radius OB
What is the length of OC if BC = 1 unit?
$\sqrt{3}$ units
What is the representation of $\sqrt{3}$ on the number line?
The point Q
If CD = 1 unit, what is the length of OD?
$2$ units
Study Notes
Decimal Representations of Rational Numbers
- Repeating strings of remainders are observed in decimal representations of rational numbers.
- The number of entries in a repeating string of remainders is less than the divisor.
- In the case of $\frac{2}{3}$, the repeating number is 2, and the divisor is 3.
- In the case of $\frac{15}{7}$, a set of 6 digits (132645) repeats itself, and the divisor is 7.
Length of Period
- The repeated number of decimal places in a rational number is called the length of its period.
- Example: The length of the period of $\frac{15}{7}$ is 6, as it can be expressed as 2.142857.
Special Characteristics of Rational Numbers
- Every rational number can be expressed either as a terminating decimal or as a non-terminating recurring decimal.
- The maximum number of entries in the repeating block of digits in the decimal expansion of $\frac{1}{n}$ is (n-1), where n is the divisor.
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