Irrational numbers, like 0.01020304...., can be written as a fraction.(1 point)

Question

Responses

False, any decimal that does not terminate or repeat is rational.
False, any decimal that does not terminate or repeat is rational.

True, all decimals can be written as a fraction
True, all decimals can be written as a fraction

​​​​​​​False, any decimal that does not terminate or repeat cannot be written as a fraction.
​​​​​​​ False, any decimal that does not terminate or repeat cannot be written as a fraction.

True, decimals that do not terminate can always be written as a fraction

A repeating decimal, like 0.327327327..., can be written as a fraction.(1 point)
Responses

False, any decimal that repeats cannot be written as a fraction
False, any decimal that repeats cannot be written as a fraction

False, any decimal that does not terminate cannot be written as a fraction
False, any decimal that does not terminate cannot be written as a fraction

True, a repeating decimal is irrational, so can be written as a ratio
True, a repeating decimal is irrational, so can be written as a ratio

True, a repeating decimal is rational, so can be written as a ratio

Match the number set or type of number with the correct category.(5 points)
Integers
Repeating decimals (0.454545...)
Non-Repeating decimal (.44454647....)
Whole numbers {0, 1, 2, 3, 4, ....}
{1/2, 1/4, 1/8, 1/16, 1/32}
responses
rational ratio >_ 0 with a denominator = 1
irrational decimals
rational whole numbers and their opposites
rational decimals
rational ratios with a denominator =/ 1

Rational numbers cannot _____________.(1 point)
Responses

be negative
be negative

be square roots of non-perfect squares
be square roots of non-perfect squares

go on forever and ever
go on forever and ever

repeat digits in the decimal

Choose the correct term to fill in the blanks.(4 points)
Square roots and Cube roots can be rational or irrational. The square root of a (Response area)square (√7 = 2.6457...) is always irrational. The square root of a (Response area) square (√25 = 5) is a rational, whole number. This means that √36 is (Response area) and √10 is (Response area)

responses
rational
irrational
perfect
non-perfect

Answer 1

Let's go through your questions one by one:

1. Irrational numbers, like 0.01020304...., can be written as a fraction.
   Response: False, any decimal that does not terminate or repeat cannot be written as a fraction.
   (Irrational numbers cannot be expressed as a fraction.)

2. A repeating decimal, like 0.327327327..., can be written as a fraction.
   Response: True, a repeating decimal is rational, so can be written as a ratio.
   (Repeating decimals are classified as rational numbers.)

3. Match the number set or type of number with the correct category.

   • Integers: rational whole numbers and their opposites
   • Repeating decimals (0.454545...): rational decimals
   • Non-Repeating decimal (.44454647....): irrational decimals
   • Whole numbers {0, 1, 2, 3, 4, ....}: rational whole numbers and their opposites (same as integers)
   • {1/2, 1/4, 1/8, 1/16, 1/32}: rational ratios with a denominator =/ 1

4. Rational numbers cannot _____________.
   Response: be square roots of non-perfect squares
   (Rational numbers are defined as numbers that can be expressed as a fraction, and the square root of non-perfect squares is irrational.)

5. Choose the correct term to fill in the blanks.

   • The square root of a non-perfect (√7 = 2.6457...) is always irrational.
   • The square root of a perfect (√25 = 5) is a rational, whole number.
   • This means that √36 is rational and √10 is irrational.

If you have any additional questions, feel free to ask!