Which situation describes opposite quantities that when combined would equal 0?(1 point)
Responses
Eileen moves seven spaces forward, then she moves seven spaces back in a game.
Eileen moves seven spaces forward, then she moves seven spaces back in a game.
Eileen moves seven spaces forward, then she moves two spaces back in a game.
Eileen moves seven spaces forward, then she moves two spaces back in a game.
Sarah is charged a fee of $20 and withdraws $20.
Sarah is charged a fee of $20 and withdraws $20.
Sarah deposits $20 in an account and then deposits another $20.
Sarah deposits $20 in an account and then deposits another $20.
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How many digits could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?
A. infinitely long
B. up to seven digits long
C. up to six digits long
D. any finite length
The repeating cycle of a repeating decimal when the denominator of the rational number is 7 would be up to six digits long. Thus, the correct answer is option C.
Convert 0.27 to a rational number in simplest form.
To convert 0.27 to a rational number in simplest form, we can express it as a fraction.
Let x = 0.27
To convert a decimal to a fraction, we count the decimal places and set the decimal value as the numerator, and the number 1 followed by the same number of zeroes as the decimal places as the denominator.
In this case, there are two decimal places in 0.27, so the denominator will be 100.
x = 0.27 = 27/100
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 1 in this case.
27/100 รท 1/1 = 27/100
Therefore, 0.27 as a rational number in simplest form is 27/100.
To convert 0.264 to a rational number, you would set x equal to 0.264 and then multiply both sides of the equation by what number?
To convert 0.264 to a rational number, we can set x equal to 0.264 and then multiply both sides of the equation by 1000.
When we multiply both sides of the equation by 1000, we move the decimal point three places to the right:
x = 0.264
1000x = 264
So, by multiplying both sides by 1000, we can convert 0.264 to a rational number.
Last one...!!
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
When converting a repeating decimal to a fraction, we set the repeating part as the numerator and a number with a digit "9" repeated as the denominator. Since the repeating cycle has three digits, we use three "9"s in the denominator.
For example, if the repeating decimal is 0.ABC, we would have:
x = 0.abcabcabc...
To convert this decimal to a fraction, we can subtract "x" from "1000x" to eliminate the repeating part:
1000x - x = 0.abcabcabc... - 0.abc
999x = abc
Dividing both sides by 999:
x = abc/999
Thus, if a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.