Classifying Real Numbers

Rachel states that -5.5 is an integer because it is negative.

Is she correct?

Why or why not?

• Yes, because all negatives are integers.

• Yes, because all integers have decimals.

• No, because integers do not have decimals.

• No, because integers cannot be negative.

Answer explanation

No, because integers do not have decimals.

Classify this number:  6.7

• real

• real      rational

• real      rational        integer

• real   rational   integer   whole

Answer explanation

The number 6.7 is a real and rational number because it can be expressed as a fraction (67/10) and falls within the set of real numbers.

Is ½ a terminating decimal or a repeating decimal?

• terminating decimal

• repeating decimal

Answer explanation

1/2 is a terminating decimal because when expressed as a decimal, it ends after a finite number of digits without repeating.

Tags

CCSS.7.NS.A.2D

CCSS.8.NS.A.1

Classify this number:  -12

• real

• real      rational

• real       irrational

• real         rational        integer

Answer explanation

The number -12 is a real, rational, and integer number. It is real because it exists on the number line, rational because it can be expressed as a fraction, and an integer because it is a whole number.

-4 is not a whole number because:

• It's negative and whole numbers are positive.

• it's irrational.

• it cannot be turned into a fraction.

• it is even.

Answer explanation

It's negative and whole numbers are positive.

A rational number:

• can be turned into a fraction.

• is only positive.

• can't have a decimal.

• is not a real number.

Answer explanation

A rational number can be turned into a fraction, making it the correct choice among the options provided.

Tags

CCSS.7.NS.A.2D

CCSS.8.NS.A.1

8 is a part of the following sets: 

• Whole Number

• Integer

• Rational

• All of the above

Answer explanation

8 is a whole number, an integer, and a rational number, so the correct answer is 'All of the above.'

Which number is an irrational number?

• 2.5

• 5.72314.....

• -17

• 1/2

Answer explanation

The irrational number is 5.72314..... because it cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion.

Tags

CCSS.8.NS.A.1

An example of an integer is...

• 9.1

• 8/9

• -9

• -2.3

Answer explanation

An integer is a whole number that can be positive, negative, or zero. In this case, -9 is an example of an integer as it is a whole number without any decimal or fractional part.

Which word does NOT describe 5?

• Whole

• Integer

• Rational

• Irrational

Answer explanation

The word 'Irrational' does NOT describe 5 because 5 is a whole, integer, and rational number, not an irrational number.