A Quiz On Rational Numbers! Trivia

Explanation
To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. In this case, we have 2 as the whole number, 1 as the numerator, and 4 as the denominator. Multiplying 2 by 4 gives us 8, and adding 1 gives us 9. Therefore, 2 1/4 as an improper fraction is 9/4.

Explanation
The given list of rational numbers is correctly ordered from least to greatest because 9 9/13 is the smallest number, followed by 9 5/7, then 9.72, 9.74, and finally 9 3/4, which is the largest number.

Explanation
The numbers are ordered from least to greatest by comparing their values. -0.8 is the smallest number, followed by -3/4 which is larger than -0.8. Next is 0, which is larger than both -0.8 and -3/4. Finally, 1.25 is the largest number among the given options.

Explanation
The rational number 4 is greater than the rational number 0.0410.

Explanation
When a fraction is converted to a decimal through long division, a terminating decimal is formed when the remainder is zero. This means that there are no more digits to add after the decimal point, and the decimal representation of the fraction ends.

Explanation
To convert a fraction to a decimal, we divide the numerator by the denominator. In this case, 1 divided by 9 is equal to 0.111111... However, since we are asked to provide the decimal in the given options, the closest option to 0.111111... is 0.1.

Explanation
A rational number is any number that can be expressed as the ratio of two integers. Among the options, 4/7 is a ratio of two integers, making it a rational number. √2, π, and Euler’s number (e) are all irrational numbers because they cannot be written as exact fractions of integers.

Explanation
When a repeating decimal is converted to a fraction, the denominator will always be 9. This is because when a decimal repeats, it indicates that the digits after the decimal point continue infinitely in a repeating pattern. To convert this decimal to a fraction, we can set up an equation where the repeating part of the decimal is equal to x, and multiply both sides by a power of 10 that has the same number of digits as the repeating part. This allows us to eliminate the repeating part and solve for x. The resulting fraction will have the repeating part as the numerator and the number of 9s in the denominator equal to the number of digits in the repeating part. Therefore, the denominator will always be 9.