How do you show the group of digits that repeat in a repeating decimal?
by putting them in parentheses
by putting a bar over them
by underlining them
by printing them in italics
The correct way to show the group of digits that repeat in a repeating decimal is by putting a bar over them.
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?
up to seven digits long
up to six digits long
any finite length
infinitely long
The repeating cycle of a repeating decimal with a denominator of 7 could be up to six digits long.
Convert 0.27
to a rational number in simplest form.
3/11
27/100
1/27
27/99
To convert the decimal 0.27 to a rational number in simplest form, we need to write it as a fraction.
Since there are two digits after the decimal point, we can write 0.27 as 27/100. However, 27/100 is not in simplest form.
To simplify the fraction, we can divide both the numerator (27) and the denominator (100) by their greatest common divisor, which is 1.
Dividing both numbers by 1, we get:
27 ÷ 1 = 27
100 ÷ 1 = 100
Therefore, the simplest form of the rational number representing 0.27 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?
100
999
1,000
10
To convert the decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, we can set x equal to 0.264¯¯¯¯¯¯¯¯ and multiply both sides of the equation by 1000.
x = 0.264¯¯¯¯¯¯¯¯
Multiplying both sides by 1000:
1000x = 264.264¯¯¯¯¯¯¯¯
Now, we can subtract the left side of the equation from the right side:
1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
999x = 264
To isolate x and solve for it, we divide both sides of the equation by 999:
x = 264/999
Hence, to convert 0.264¯¯¯¯¯¯¯¯ to a rational number, we set x equal to it and multiply both sides of the equation by 1000.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator?
999
99
1,000
100