Perfecting Unit 1!

Which of the following numbers is an irrational number?

Answer explanation

The number \( \sqrt{3} \) is irrational because it cannot be expressed as a fraction of two integers. In contrast, 0.25, -7/2, and 5 are all rational numbers.

Tags

CCSS.8.NS.A.1

Which set contains all whole numbers?

Answer explanation

The set of whole numbers includes all non-negative integers starting from 0. Therefore, the correct choice is \{0, 1, 2, 3, ...\}, which includes 0 and all positive integers.

Which of the following numbers is written in scientific notation?

Answer explanation

The number written in scientific notation is 4.5 × 10^{-4}, as it is expressed in the form a × 10^n, where 1 ≤ a < 10 and n is an integer. The other options do not meet this format.

Tags

CCSS.8.EE.A.3

Answer explanation

To order the numbers from least to greatest, we compare their values. -5 is the smallest, followed by -2, then 0, and finally 3. Thus, the correct order is -5, -2, 0, 3.

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

Answer explanation

To find √{50}, note that √{49} = 7 and √{64} = 8. Since 50 is between 49 and 64, √{50} lies between 7 and 8. Thus, the correct integers are 6 and 7.

Tags

CCSS.8.NS.A.2

Which of the following is a subset of the set of rational numbers?

• Irrational numbers

• Whole numbers

• Real numbers

• Complex numbers

Answer explanation

Whole numbers are a subset of rational numbers, as they can be expressed as fractions (e.g., 5 = 5/1). In contrast, irrational numbers, real numbers, and complex numbers include values that are not rational.

Answer explanation

To convert 0.0032 to scientific notation, move the decimal point three places to the right, giving 3.2. This corresponds to multiplying by 10 raised to the power of -3, resulting in 3.2 × 10^{-3}, which is the correct answer.

Answer explanation

To order the numbers from least to greatest, we compare their values. -3 is the smallest, followed by -1.5, then 0, and finally 2. Thus, the correct order is -3, -1.5, 0, 2.

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

Answer explanation

The correct rational approximation for \( \pi \) is \( 3.14 \), which is a simple and widely used representation. The other options, \( 3.1415926535... \) is more precise, while \( e \) and \( \sqrt{2} \) are not approximations of \( \pi \).

Tags

CCSS.8.NS.A.2

Which of the following statements is true about the set of real numbers?

• All real numbers are rational.

• All integers are real numbers.

• All whole numbers are irrational.

• All rational numbers are integers.

Answer explanation

The statement 'All integers are real numbers' is true because integers (like -1, 0, 1) are a subset of real numbers. The other statements are false as not all real numbers are rational, whole numbers are not irrational, and not all rational numbers are integers.