How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by printing them in italics
by underlining them
by putting them in parentheses
by putting a bar over them
Yes, the answer is 1,000.
by putting a bar over them
up to six digits long
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 1,000.
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)
Responses
infinitely long
any finite length
up to seven digits long
up to six digits long
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
127
Start Fraction 1 over 27 end fraction
2799
Start Fraction 27 over 99 end fraction
311
Start Fraction 3 over 11 end fraction
27100
Start Fraction 27 over 99 end fraction
Rational Numbers in Different Forms Quick Check
4 of 54 of 5 Items
Question
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?(1 point)
Responses
999
100
1,000
10
so the answer is 1,000?
How many digits are in the repeating cycle of 17/27?(1 point)
The repeating cycle of 17/27 is 17¯¯¯¯¯¯¯¯¯¯¯¯¯. In this case, the digit 17 is repeated infinitely. Therefore, the number of digits in the repeating cycle is 2.
Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?(1 point)
The rational numbers that can be expressed as repeating decimals are:
7/8
5/12
17/25
31/40
All of the given rational numbers can be expressed as repeating decimals.
Express 713 as a repeating decimal. Mark the repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
To express 713 as a repeating decimal, we can rewrite it as 713.000000... Since there are no repeating digits in the original number, there is no need to mark any digits with a bar.
Express 7/13 as a repeating decimal. Mark the repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
To express 7/13 as a repeating decimal, we can perform long division:
0.538461538461538461538...
The repeating digits, in this case, are 538461. To mark them with a bar, we can write the repeating decimal as:
0.538¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Please note that you will find the option to add a bar above text in the Geometry (∠) keyboard or by using the appropriate symbols in a document editor or equation editor.
Convert 0.8¯¯¯ to a rational number.(1 point)
To convert 0.8¯¯¯ to a rational number, we can set x equal to 0.8¯¯¯ and perform the following steps:
Let's multiply both sides of the equation by 10 to eliminate the recurring decimal:
10x = 8.8¯¯¯
Now, let's subtract x from both sides of the equation:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
This simplifies to:
9x = 8
Finally, let's divide both sides of the equation by 9 to solve for x:
9x/9 = 8/9
The rational number in simplest form is:
x = 8/9
To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 100.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
999
1,000
100
99
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 99.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
99
99
1,000
1,000
100
100
999