Final answer:
True statements about rational numbers include that decimals that can be converted to fractions and repeating decimals are rational numbers, and they can be expressed as one integer divided by another. The false statement is that one divided by zero represents a rational number, as division by zero is undefined. Rational numbers are typically fractions, including those in scientific notation.
Step-by-step explanation:
When identifying which statements are true of rational numbers, it's important to note that these are numbers that can be expressed as fractions, where both the numerator and the denominator are integers, and the denominator is not zero. This type of number can be in the form of a simple fraction, a repeating decimal, or a terminating decimal.
Decimals that can be written as fractions are rational numbers.
Repeating decimals are rational numbers because they can be written as fractions.
A rational number can be written as one integer divided by another integer.
Rational numbers can be written as fractions.
The statement "One divided by zero is an example of a rational number" is not true, as division by zero is undefined. Thus, it doesn't generate a rational number.
Examples of expressing a decimal as a fraction include converting the repeating decimal 0.333... to the fraction 1/3. For scientific notation, the number 4.5 X 10-6, which is a very small number closer to zero than to one, can also be represented as a fraction (4500/1,000,000) since scientific notation itself is just another way of representing numbers, including fractions.