What is the expanded form of 285?(1 point)
Responses
(2×100)+(8×10)+(5×1)
left parenthesis 2 times 100 right parenthesis plus left parenthesis 8 times 10 right parenthesis plus left parenthesis 5 times 1 right parenthesis
(8×10)+(2×1)
left parenthesis 8 times 10 right parenthesis plus left parenthesis 2 times 1 right parenthesis
(5×100)+(8×10)+(2×1)
left parenthesis 5 times 100 right parenthesis plus left parenthesis 8 times 10 right parenthesis plus left parenthesis 2 times 1 right parenthesis
(2×100)+(8×10)
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left parenthesis 2 times 100 right parenthesis plus left parenthesis 8 times 10 right parenthesis
so what is it
The expanded form of 285 is (2×100)+(8×10)+(5×1).
Write 1,976 in expanded form.(1 point)
Responses
(9×1,000)+(1×100)+(7×10)+(6×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 1 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
(1×1,000)+(9×100)+(7×10)+(6×1)
left parenthesis 1 times 1,000 right parenthesis plus left parenthesis 9 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
(9×1,000)+(1×100)+(6×10)+(7×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 1 times 100 right parenthesis plus left parenthesis 6 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis
(1×100)+(9×100)+(7×10)+(6×1)
left parenthesis 1 times 1,000 right parenthesis plus left parenthesis 9 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
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Question
What is the expanded form of 23.75?(1 point)
Responses
(2×10)+(3×1)+(7×110)+(5×1100)
left parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 100 End Fraction right parenthesis
(5×10)+(7×1)+(3×110)+(2×1100)
left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 3 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis
(2×10)+(3×1)+(5×110)+(7×1100)
left parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 7 times Start Fraction 1 over 100 End Fraction right parenthesis
(2×10)+(3×1)+(7×1101)+(5×1102)
left parenthesis 2 times 10 right parenthesis plus left parenthesis 3 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 superscript 1 baseline End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 squared End Fraction right parenthesis
The expanded form of 23.75 is (2×10)+(3×1)+(7×110)+(5×1100).
Write the expanded form of 357.25(1 point)
Responses
(3×100)+(5×10)+(7×1)+(2×110)+(5×1100)
left parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 100 End Fraction right parenthesis
(3×100)+(5×10)+(7×1)+(2×1100)
left parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis
(3×100)+(5×10)+(7×1)+(2×110)+(5×11,000)
left parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 2 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 5 times Start Fraction 1 over 1,000 End Fraction right parenthesis
(3×100)+(5×10)+(7×1)+(5×110)+(2×1100)
left parenthesis 3 times 100 right parenthesis plus left parenthesis 5 times 10 right parenthesis plus left parenthesis 7 times 1 right parenthesis plus left parenthesis 5 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 2 times Start Fraction 1 over 100 End Fraction right parenthesis
What is the expanded form of 8,471.716?(1 point)
Responses
(8×103)+(4×102)+(7×101)+(1×100)+(7×1101)+(1×1102)+(6×1103)
left parenthesis 8 times 10 cubed right parenthesis plus left parenthesis 4 times 10 squared right parenthesis plus left parenthesis 7 times 10 superscript 1 baseline right parenthesis plus left parenthesis 1 times 10 superscript 0 baseline right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 superscript 1 baseline End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 10 squared End Fraction right parenthesis plus left parenthesis 6 times Start Fraction 1 over 10 cubed End Fraction right parenthesis
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)
left parenthesis 8 times 1,000 right parenthesis plus left parenthesis 4 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 1 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 100 End Fraction right parenthesis
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×11)+(1×110)+(6×1100)
left parenthesis 8 times 1,000 right parenthesis plus left parenthesis 4 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 1 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 1 End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 6 times Start Fraction 1 over 100 End Fraction right parenthesis
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)+(6×11,000)
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×110)+(1×1100)+(6×11,000)
thank u bot your the best
How many digits are in the repeating cycle of 1727?(1 point)
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To determine the number of digits in the repeating cycle of a decimal, we can convert the decimal to a fraction and examine the denominator.
To start, let's write 1727 as a fraction without the repeating part:
1727 = 1727/1
Since there is no repeating part, the denominator of the fraction is 1. Therefore, the number of digits in the repeating cycle is 0.
its wrong
I apologize for the mistake.
To find the number of digits in the repeating cycle of a decimal, we can convert the decimal into a fraction and then determine the length of the repeating portion of the fraction.
To start, let's represent 1727 as a fraction with the repeating part:
Let X = 1727.777...
Multiply both sides by 10 to eliminate the repeating decimal:
10X = 17277.777...
Subtract the original equation from the new equation to eliminate the repeating part:
10X - X = 17277.777... - 1727.777...
Simplifying, we get:
9X = 15550
Dividing both sides by 9, we find:
X = 1727/9
The fraction 1727/9 has a repeating cycle of 6 digits (777777), so the number of digits in the repeating cycle of 1727 is 6.
Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point)
To determine which of the given numbers can be expressed as a repeating decimal, we need to check their divisibility by prime numbers other than 2 and 5 (since a decimal repeats if and only if the denominator has prime factors other than 2 and 5).
Let's analyze each number:
78: 78 is divisible by 2 and 3, so it can be expressed as a repeating decimal.
512: 512 is divisible by 2, so it can be expressed as a terminating decimal.
1725: 1725 is divisible by 3 and 5, so it can be expressed as a terminating decimal.
3140: 3140 is divisible by 2 and 5, so it can be expressed as a terminating decimal.
Therefore, the number that can be expressed as a repeating decimal is 78.
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.
(1 point)
To express 713 as a repeating decimal, we can convert it into a fraction by placing it over a power of 10.
713 can be written as 713/1.
To convert this to a fraction with a repeating decimal, we will divide 713 by a number that ends with one or more 9s.
Let's divide 713 by 999:
713 ÷ 999 = 0.713713713...
The repeating portion is 713, so we can express 713 as a repeating decimal by placing a bar over the digits 713:
0.713¯
whats the anwser
The answer is 0.713¯¯¯. The bar should be placed over the digits 713 to indicate that the sequence repeats indefinitely.
Convert 0.8¯¯¯ to a rational number.
To convert 0.8¯¯¯ to a rational number, we can use the concept of an infinite geometric series.
Let x = 0.8¯¯¯.
Multiplying both sides by 10, we get:
10x = 8.8¯¯¯.
Subtracting the original equation from the new equation, we eliminate the repeating part:
10x - x = 8.8¯¯¯ - 0.8¯¯¯.
Simplifying, we have:
9x = 8.
Dividing both sides by 9, we find:
x = 8/9.
Therefore, the rational number equivalent to 0.8¯¯¯ is 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:
100x = 82.82¯¯¯¯¯
This multiplication by 100 is done to shift the repeating decimal point to the right, so that when we subtract the original equation from the new equation, the repeating part is eliminated.
Subtracting the original x = 0.82¯¯¯¯¯ equation from the new equation, we get:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
Simplifying, we have:
99x = 82
Finally, dividing both sides of the equation by 99, we find:
x = 82/99
Therefore, the rational number equivalent to 0.82¯¯¯¯¯ is 82/99.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by printing them in italics
by printing them in italics
by putting a bar over them
by putting a bar over them
by putting them in parentheses
by putting them in parentheses
by underlining them
The correct response 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?(1 point)
Responses
any finite length
any finite length
infinitely long
infinitely long
up to six digits long
up to six digits long
up to seven digits long
The correct response is: up to six digits long.
When the denominator of a rational number is 7, the repeating cycle of the decimal can have a maximum length of 6. This is because the repeating cycle cannot have a longer length than the denominator itself.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
27100
Start Fraction 27 over 100 end fraction
127
Start Fraction 1 over 27 end fraction
311
Start Fraction 3 over 11 end fraction
2799
Start Fraction 27 over 99 end fraction
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we can set it equal to x and use the method of infinite geometric series.
Let x = 0.27¯¯¯¯¯.
To remove the repeating part, we can multiply both sides of the equation by 100:
100x = 27.27¯¯¯¯¯.
Now, subtracting the original equation from the new equation, we get:
100x - x = 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯.
Simplifying, we have:
99x = 27.
Dividing both sides by 99, we find:
x = 27/99.
To express this rational number in simplest form, we can further simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = 3/11.
Therefore, the rational number equivalent to 0.27¯¯¯¯¯ in simplest form is 3/11.
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
999
1,000
1,000
10
10
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 1000:
1000x = 264.264¯¯¯¯¯¯¯¯
This multiplication by 1000 is done to shift the repeating decimal point to the right, so that when we subtract the original equation from the new equation, the repeating part is eliminated.
Subtracting the original x = 0.264¯¯¯¯¯¯¯¯ equation from the new equation, we get:
1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
Simplifying, we have:
999x = 264
Finally, dividing both sides of the equation by 999, we find:
x = 264/999
Therefore, the rational number equivalent to 0.264¯¯¯¯¯¯¯¯ is 264/999.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
100
100
999
999
1,000
1,000
99
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with the denominator of 999.
Show an example of an irrational number between 9 and 11.(1 point)
Responses
10−−√
start root 10 end root
100−−−√
start root 100 end root
99−−√
start root 99 end root
20−−√
An example of an irrational number between 9 and 11 is √10.
Note: The symbol "√" represents the square root.