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

The correct answer 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 six digits long

any finite length

infinitely long

up to seven digits long

The correct answer is up to six digits long.

Convert 0.bar(27)

to a rational number in simplest form.(1 point)

3/11

27/99

1/27

27/100

To convert the repeating decimal 0.bar(27) to a rational number in simplest form:

Let x = 0.bar(27)
Multiply x by 100 to shift the decimal point two places to the right:
100x = 27.bar(27)
Subtract the original equation from the above equation to eliminate the repeating part:
100x - x = 27.bar(27) - 0.bar(27)
99x = 27
x = 27/99

Therefore, the rational number in simplest form equivalent to 0.bar(27) is 27/99.

To convert 0.bar(264)to a rational number, you would set x equal to 0.bar(264) and then multiply both sides of the equation by what number?

999

10

1,000

100

To convert 0.bar(264) to a rational number, you would set x equal to 0.bar(264) and then multiply both sides of the equation by 1000.

Setting x = 0.bar(264), we can multiply both sides by 1000 as follows:

1000x = 264.bar(264)

Next, subtract x from both sides to eliminate the repeating part:

1000x - x = 264.bar(264) - 0.bar(264)

Simplifying the equation yields:

999x = 264

Dividing both sides by 999 gives:

x = 264/999

Therefore, the rational number equivalent to 0.bar(264) is 264/999.

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

100

99

999

1,000

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

Since the 1800s, which human activity has changed land use and led to the growth of large cities in many countries?

industrialization

colonization

pollution

rural population growth

The human activity since the 1800s that has changed land use and led to the growth of large cities in many countries is industrialization.

Fill in the black

Rapid population growth can result in large increases in the infant mortality rate if there is _______

A. a shortage of clean food and water
B. a higher cosumption of goods and services
C. deforestation
D. increased migration

The correct answer is A. a shortage of clean food and water.

Fill in the blank

______ are renewable resources because they can be replaced in a short time. _____ are nonrenewable resources because they cannot be replaced or can only be replaced over millions of years.

1st blank space

A. Fossil fuels
B. Metal ores
C. Minerals
D. Plants

2nd blank space

A. Animals
B. Fossil fuels
C. Plants
D. Water sources

The correct answers are:

1st blank space: D. Plants

2nd blank space: B. Fossil fuels