Math

QuestionIdentify which numbers in the list 5.737737773,26,45,32,0,95.737737773 \ldots, 26, \sqrt{45}, -\frac{3}{2}, 0, 9 are rational and which are irrational.

Studdy Solution

STEP 1

Assumptions1. Rational numbers are numbers that can be expressed as a ratio of two integers. . Irrational numbers are numbers that cannot be expressed as a ratio of two integers.
3. The list of numbers given by Lisa is 5.737737773,26,45,3,0,95.737737773 \ldots,26, \sqrt{45},-\frac{3}{},0,9

STEP 2

We will determine whether each number is rational or irrational.

STEP 3

First, consider the number 5.7377377735.737737773 \ldots. This number is a repeating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

STEP 4

Next, consider the number 2626. This number is an integer, and all integers are rational because they can be expressed as a ratio where the denominator is1. Therefore, 2626 is a rational number.

STEP 5

Next, consider the number 45\sqrt{45}. This number is the square root of 4545, which is not a perfect square. Therefore, 45\sqrt{45} cannot be expressed as a ratio of two integers, and it is an irrational number.

STEP 6

Next, consider the number 32-\frac{3}{2}. This number is a fraction, which means it can be expressed as a ratio of two integers. Therefore, 32-\frac{3}{2} is a rational number.

STEP 7

Next, consider the number 00. This number is an integer, and all integers are rational because they can be expressed as a ratio where the denominator is1. Therefore, 00 is a rational number.

STEP 8

Finally, consider the number .Thisnumberisaninteger,andallintegersarerationalbecausetheycanbeexpressedasaratiowherethedenominatoris1.Therefore,. This number is an integer, and all integers are rational because they can be expressed as a ratio where the denominator is1. Therefore, is a rational number.

STEP 9

Now, we can summarize the results.
a. The rational numbers are 5.737737773,26,32,,95.737737773 \ldots,26, -\frac{3}{2},,9. b. The irrational number is 45\sqrt{45}.

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