Question

Is 9.373 a repeating decimal? Is it rational? Explain your reasoning.

Answer 1

Answer:

The given number is rational number.

Step-by-step explanation:

We are asked to find whether 9.373 is a repeating decimal.

Since we cannot see a bar on the digits after decimal, so our given number is not a repeating decimal.

We know that a number is rational number, when it can be represented as a fraction.

We can represent our given number as a fraction by multiplying and dividing by 1000 as:

$9.373\times \frac{1000}{1000}=\frac{9373}{1000}$

Therefore, our given number is a rational number.

Answer 2

Using concepts from the set of numbers, it is found that 9.373 is a rational number.

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• Whole numbers: Set of numbers including all positive numbers and 0, so: {0,1,2,...}

• Integer numbers: Number without decimals, that can be positive of negative, so: {...,-2,-1,0,1,2,....}

• 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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9.373 has a finite number of decimal digits, thus it is a rational number. It also can be represented as fraction, considering the number of decimal digits is 3.

$9.373 = 9.373\frac{10^3}{10^3} = \frac{9373}{1000}$

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