Answer:C1: 3/10, 6/20, 9/30C2: 1/3, 2/6, 3/9C3: not a rational number, cannot be represented by a fractionD1: the rational number 2/7 is a repeating decimal fraction, because the denominator has a factor that is not 2 or 5. The decimal is ...[tex]0.\overline{285714}[/tex]D2: no ratio of rational numbers will be non-terminating, not-repeating. The ratio of numbers, at least one of which is irrational, will have a non-terminating, non-repeating fractional part: (√2)/2, for example.Step-by-step explanation:C1. This is a terminating decimal fraction. In simplest form, it is 3/10. The numerator and denominator can be scaled by any number you like to make an equivalent fraction: 3/10 = (3·2)/(10·2) = 6/20 = (3·3)/(10·3) = 9/30C2. The repeating single-digit decimal fraction 0.3_3 is equivalent to 3/9 = 1/3. As before, you can scale the numerator and denominator by any number you like. 1/3 = (1·2)/(3·2) = 2/6.A repeating decimal can be converted to a fraction by putting the repeating digits over an equivalent number of 9s. The 6-digit repeating decimal of D1, for example is ... 285714/999999 = 2/7C3. The design of this number is such that it has an increasing number of 3s separated by a single 1. By design, it is non-terminating and non-repeating. Hence it is an irrational number and cannot be represented exactly by a fraction consisting of the ratio of two finite integers.___D1. If you continue the division, you will get quotient digits 0.285714 and the remainder after the last step will be 2, the dividend number you started with. This signals the beginning of the repeating of the digits of the quotient.A calculator confirms that 2/7 is the repeating decimal ...[tex]\dfrac{2}{7}=0.285714\overline{285714}[/tex]D2. A "fraction" need not consist of the ratio of two integers. If at least one of the parts of the (reduced) ratio is an irrational number, the decimal equivalent of the fraction will not terminate or repeat. An example is ...[tex]\dfrac{\sqrt{2}}{2}\approx 0.707106781186547524400844362104849039284...[/tex]