Question

Which statement is true when a rational number in fractional form is converted to a decimal? I. The decimal repeats. II. The decimal terminates.

Answer 1

The statement that is true when a rational number in fractional form is converted to a decimal is that the decimal repeats.

Step-by-step explanation:

When a rational number in fractional form is converted to a decimal, the statement that is true is:

1. The decimal repeats.

For example, when the fraction 1/3 is converted to a decimal, the decimal equivalent is 0.3333... with the 3s repeating indefinitely. Thus, the decimal form of a rational number in fractional form will have a repeating pattern.

Decimals are used to make our calculations easy. We use them to quickly compare fractions without doing many calculations. For example, comparing (675/63) with (463/77) can be very time-consuming. Instead, we write them as decimals 10.71 and 6.01 and compare easily and determine which one is greater than the other. We also use them to shorten the complicated fractional equations.

Answer 2

Answer: The answer is (iii) Either the decimal repeats or terminates.

Step-by-step explanation:

We are familiar with the theory of rational and irrational numbers.

When a rational number is converted to decimal form, then either the digits after the decimals repeats themselves or the decimal terminates.

For example, the fraction 10/3 = 3.333333 . . ., which is rational. Here digits are repeating. And the fraction 5/4=1.25, which terminates. These are the two decimal forms of rational numbers.

In the decimal form of an irrational number, digits after the decimal are non-repeating and non-recurring.

For example, √3 = 1.73205080757 . . .. This is the only decimal form of irrational numbers.

Thus, the correct option is (iii) Either the decimal repeats or terminates.