How many digits are in the repeating cycle of 17/27?(1 point)
The repeating cycle of 17/27 can be calculated by dividing the numerator (17) by the denominator (27) and observing the decimal representation.
17 ÷ 27 = 0.629629629629...
We can see that the decimal representation has a repeating cycle of 629. Therefore, there are three digits (6, 2, and 9) in the repeating cycle of 17/27.
Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point
Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?(1 poin
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to check if the denominators have factors other than 2 and 5, as repeating decimals occur when there are prime factors other than 2 and 5 in the denominator.
The prime factorization of each denominator is:
8 = 2^3
12 = 2^2 * 3
25 = 5^2
40 = 2^3 * 5
None of the given denominators have prime factors other than 2 and 5, so none of the rational numbers can be expressed as a repeating decimal.
Therefore, none of the given rational numbers, 7/8, 5/12, 17/25, or 31/40, can be expressed as a repeating decimal.
Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
To express 7/13 as a repeating decimal, we divide the numerator (7) by the denominator (13):
7 ÷ 13 = 0.538461538461...
We can see that the decimal representation has a repeating cycle of 538461. Therefore, 7/13 can be expressed as a repeating decimal as 0.538461 with the digits 538461 repeating.
So, 7/13 can be written as 0.538461 with a bar over the repeating digits: 0.538461
Convert 0.8¯¯¯ to a rational number.(1 point)
Let's denote the repeating decimal 0.8¯¯¯¯ as x.
To convert this repeating decimal to a rational number, we'll multiply x by a power of 10 to eliminate the repeating part.
We can multiply both sides of the equation by 10:
10x = 8.8¯¯¯¯
Next, we can subtract x from both sides of the equation:
10x - x = 8.8¯¯¯¯ - 0.8¯¯¯¯
Simplifying, we have:
9x = 8
Finally, we can solve for x by dividing both sides of the equation by 9:
x = 8/9
So, 0.8¯¯¯¯ can be expressed as the rational number 8/9.
To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by a power of 10.
In this case, we have:
x = 0.82¯¯¯¯¯
To eliminate the repeating part, we can multiply both sides of the equation by 100, since there are two repeating digits:
100x = 82.82¯¯¯¯¯
Therefore, you would multiply both sides of the equation by 100 to convert 0.82¯¯¯¯¯ to a rational number.