Express each fraction the first three terms of this pattern as a repeating decimal.
1/11, 2/11, 3/11...
a) describe the pattern
b) Use the pattern to predict the decimal equivalents for 6/11 and 9/11
1/11 = .090909...
now just multiply that by 2 or 3 or 6 or 9
a) The pattern in this sequence is that each fraction is one greater than the preceding fraction, while the denominator remains the same (11, in this case).
b) To find the decimal equivalent, we divide the numerator by the denominator:
1/11 = 0.09 (repeating)
2/11 = 0.18 (repeating)
3/11 = 0.27 (repeating)
We can extend this pattern to predict the decimal equivalents of 6/11 and 9/11.
6/11 = 0.54 (repeating)
9/11 = 0.81 (repeating)
a) The pattern in the given fractions is that the numerator increases by 1 with each term while the denominator remains the same (11 in this case). So, the pattern can be described as a sequence of fractions with a numerator that increases by 1 each time.
b) To convert the fractions to decimal equivalents, we divide the numerator by the denominator. Let's calculate the decimal equivalents for 6/11 and 9/11 using the pattern:
To find the decimal equivalent for 6/11:
6 divided by 11 equals 0.545454... (the ellipsis (...) indicates the repeating decimal pattern).
To find the decimal equivalent for 9/11:
9 divided by 11 equals 0.818181... (again, the ellipsis (...) indicates the repeating decimal pattern).
Therefore, the decimal equivalents for 6/11 and 9/11 are 0.545454... and 0.818181... respectively.