Is 13/3 A Rational Number In Decimal Form

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In mathematics, rational numbers are those that can be expressed as the ratio of two integers, i.e., a fraction. The decimal form of a rational number can either be a terminating decimal or a repeating decimal.

Understanding Rational Numbers

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. For example, 3/4, 22/7, and 1/2 are all rational numbers.

Decimal Representation of Rational Numbers

When we divide the numerator by the denominator in a rational number, the result can be either a terminating decimal or a repeating decimal.

• Terminating decimals are those that have a finite number of digits after the decimal point. For example, 3/4 = 0.75, which is a terminating decimal.
• Repeating decimals, on the other hand, have an infinite number of digits after the decimal point, but the digits repeat in a pattern. For example, 1/3 = 0.333..., where the digit 3 repeats infinitely.

Is 13/3 a Rational Number in Decimal Form?

To determine if 13/3 is a rational number in decimal form, we need to divide 13 by 3 and see if the result is a terminating or repeating decimal.

When we divide 13 by 3, we get 4.333..., where the digit 3 repeats infinitely. This means that 13/3 is a repeating decimal, which is a characteristic of rational numbers.

Therefore, 13/3 is indeed a rational number in decimal form.

Key Characteristics of Rational Numbers in Decimal Form

Here are some key characteristics of rational numbers in decimal form:

• Terminating or repeating decimals: Rational numbers can be expressed as either terminating or repeating decimals.
• Finite or infinite digits: Rational numbers can have either a finite number of digits after the decimal point (terminating decimals) or an infinite number of digits that repeat in a pattern (repeating decimals).
• No irrationality: Rational numbers cannot be irrational, meaning they cannot be expressed as a non-repeating, non-terminating decimal.

Examples of Rational Numbers in Decimal Form

Here are some examples of rational numbers in decimal form:

• 1/2 = 0.5 (terminating decimal)
• 1/3 = 0.333... (repeating decimal)
• 2/3 = 0.666... (repeating decimal)
• 3/4 = 0.75 (terminating decimal)

How to Convert a Fraction to a Decimal

To convert a fraction to a decimal, simply divide the numerator by the denominator.

For example, to convert the fraction 2/3 to a decimal, divide 2 by 3, which gives you 0.666....

Conclusion

In conclusion, 13/3 is a rational number in decimal form because it can be expressed as a repeating decimal. Rational numbers can be expressed as either terminating or repeating decimals, and they have key characteristics such as finite or infinite digits and no irrationality.

By understanding rational numbers in decimal form, you can better appreciate the properties and behavior of these numbers in mathematics.

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