Question

Choose the best description for the real number 34 over 3.

A.Irrational, because it is a fraction
B.Irrational, because it is a repeating decimal
C.Rational, because it is a fraction
D.Rational, because it is a terminating decimal

Answer 1

Hello!

First of all let's eliminate the answers that do not make sense. For A. numbers are NOT irrational because they are a fraction. Numbers are also not irrational because they are a repeating number. C and D are both correct as fractions and terminating decimals are both rational numbers.

34/3≈11.33333333

By using a certain formula you can convert repeating decimals to a fraction. But most people know that .3333333 is 1/3. This gives us 11 1/3 as our answer. So what does it match? It is not a terminating decimal. It repeats but can be written as a fraction. Therefore our answer is C) Rational, because it is a fraction.

I hope this helps!

Answer 2

Using number sets, the correct option is:

C. Rational, because it is a fraction

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• Rational numbers: Integer plus decimals that can be represented by fractions, that is, they either have a pattern, or have a finite number of decimal digits, for example, 0, 2, 0,45(finite number of decimal digits), 0.3333(3 repeating is the pattern), 0.32344594459(4459 repeating is the pattern).

• Irrational numbers: Decimal numbers that are not represented by patterns, that is, for example, 0.1033430290339.

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• In this question, we have $\mathbf{\frac{34}{3}}$, which is a fraction.
• Fraction is rational, thus, the correct option is C.
• Also, the value of the division is:

$\frac{34}{3} = 11.3333...$

Which is a repeating decimal.

A similar problem is given at https://brainly.com/question/10814303