How do you show the group of digits that repeat in a repeating decimal?

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

If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 99.

The correct way to show the group of digits that repeat in a repeating decimal is by putting them in parentheses. When a decimal number has a repeating digit or group of digits, we use parentheses to indicate which digits are repeating. For example, if we have the repeating decimal 0.333..., we would write it as 0.(3). Similarly, if we have 0.123123123..., we would write it as 0.(123). The parentheses help to clearly identify the digits that are repeated.