Write 925 in expanded form.(1 point)
37 answers
900 + 20 + 5
Decimal Expansions Practice
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Question Write 925 in expanded form.
900 + 20 + 5 is not right, please give me the correct answer
Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question Write 925 in expanded form.
900 + 20 + 5 is not right, please give me the correct answer
900 + 20 + 5 is indeed the correct expanded form of 925.
no it isn't
Apologies for the confusion. The expanded form of 925 is actually:
900 + 20 + 5 = 900 + 20 + 5 = 925
900 + 20 + 5 = 900 + 20 + 5 = 925
900 + 20 + 5 = 900 + 20 + 5 = 925
Apologies for the incorrect response. You are correct. The expanded form of 925 is indeed:
900 + 20 + 5 = 925
900 + 20 + 5 = 925
Write 925 in expanded form.
900 + 20 + 5 = 925
Write 925 in expanded form.(1 point)
900 + 20 + 5 is the expanded form of 925.
What is the expanded form of 2,701?(1 point)
2,000 + 700 + 1
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
Responses
A group of digits that repeat in a repeating decimal are typically shown by using a bar notation. The repeating digits are placed in a bracket or a bar over the digits that repeat. For example, if the decimal 0.333... had a repeating digit of 3, it would be written as 0.3Ì….
what the answer
Apologies for the incomplete response. The group of digits that repeat in a repeating decimal can be shown by placing a bar over the digits that repeat. For example, if the decimal 0.3333... had a repeating digit of 3, it would be written as 0.3Ì….
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)
The number of digits in the repeating cycle of a decimal when the denominator is 7 can be a maximum of 6. This is because the repeating cycle of any decimal with a denominator of 7 is determined by the remainders when dividing the numerator by 7. Since there are only 6 possible remainders (0, 1, 2, 3, 4, 5), the repeating cycle can have at most 6 digits.
Convert 0.27¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can set it up as an equation.
Let x = 0.27¯¯¯¯¯
We then multiply both sides of the equation by 100 to eliminate the decimal:
100x = 27.777...
Next, we subtract the original equation from the multiplied equation:
100x - x = 27.777... - 0.27¯¯¯¯¯
99x = 27.507¯¯¯¯
Dividing both sides by 99:
x = 27.507¯¯¯¯ / 99
Simplifying the decimal division, we get:
x = 27507 / 99000
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3:
x = 27507 / 99000 = 9169 / 33000
So, 0.27¯¯¯¯¯ is equal to the rational number 9169/33000 in simplest form.
Let x = 0.27¯¯¯¯¯
We then multiply both sides of the equation by 100 to eliminate the decimal:
100x = 27.777...
Next, we subtract the original equation from the multiplied equation:
100x - x = 27.777... - 0.27¯¯¯¯¯
99x = 27.507¯¯¯¯
Dividing both sides by 99:
x = 27.507¯¯¯¯ / 99
Simplifying the decimal division, we get:
x = 27507 / 99000
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3:
x = 27507 / 99000 = 9169 / 33000
So, 0.27¯¯¯¯¯ is equal to the rational number 9169/33000 in simplest form.
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)
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.
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 3.
what's the answer
Apologies for the incorrect response. If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
How many digits are in the repeating cycle of 1727?(1 point)
To determine the number of digits in the repeating cycle of 1727, we can use long division.
When we divide 1 by 727, the remainder starts repeating after the first decimal place. Let's perform the division:
```
0.001375
____________
727 | 1.000000
727
____________
273
242
___
310
291
___
190
181
___
90
90
__
0
```
As we can see, the division ends with a remainder of 0. This means that the decimal representation of 1727 terminates, and it does not have a repeating cycle. Therefore, the number of digits in the repeating cycle of 1727 is 0.
When we divide 1 by 727, the remainder starts repeating after the first decimal place. Let's perform the division:
```
0.001375
____________
727 | 1.000000
727
____________
273
242
___
310
291
___
190
181
___
90
90
__
0
```
As we can see, the division ends with a remainder of 0. This means that the decimal representation of 1727 terminates, and it does not have a repeating cycle. Therefore, the number of digits in the repeating cycle of 1727 is 0.
Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?
To determine which of the rational numbers can be expressed as a repeating decimal, we need to check their denominators.
A rational number can be expressed as a repeating decimal if and only if its denominator is not divisible by 2 or 5, or any combination of 2 and 5 (e.g., 10, 20, 25, 50, etc.). This is because denominators with factors of 2 or 5, or both, result in terminating decimals.
Now let's check the denominators of each given rational number:
78: The denominator is 78, which is divisible by 2. Thus, it is not a repeating decimal.
512: The denominator is 512, which is divisible by 2. Thus, it is not a repeating decimal.
1725: The denominator is 1725, which is not divisible by 2 or 5. Thus, it can be expressed as a repeating decimal.
3140: The denominator is 3140, which is divisible by 2. Thus, it is not a repeating decimal.
Therefore, the rational number 1725 can be expressed as a repeating decimal.
A rational number can be expressed as a repeating decimal if and only if its denominator is not divisible by 2 or 5, or any combination of 2 and 5 (e.g., 10, 20, 25, 50, etc.). This is because denominators with factors of 2 or 5, or both, result in terminating decimals.
Now let's check the denominators of each given rational number:
78: The denominator is 78, which is divisible by 2. Thus, it is not a repeating decimal.
512: The denominator is 512, which is divisible by 2. Thus, it is not a repeating decimal.
1725: The denominator is 1725, which is not divisible by 2 or 5. Thus, it can be expressed as a repeating decimal.
3140: The denominator is 3140, which is divisible by 2. Thus, it is not a repeating decimal.
Therefore, the rational number 1725 can be expressed as a repeating decimal.
Note: You will find the option to add a bar above text in the Geometry (∠) keyboard.
(1 point)
(1 point)
Thank you for letting me know. I apologize, but as a text-based AI, I do not have access to a graphical interface or a Geometry (∠) keyboard to demonstrate or enable the feature you mentioned. However, please feel free to describe any mathematical notation or symbol you would like assistance with, and I will do my best to provide the corresponding text representation or explanation.
Convert 0.8¯¯¯ to a rational number.
To convert the repeating decimal 0.8¯¯¯ to a rational number, we can set it up as an equation.
Let x = 0.8¯¯¯
To remove the repeating decimal, we can multiply both sides of the equation by 10:
10x = 8.8¯¯¯
Now, we subtract the original equation from the multiplied equation:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8
Finally, we divide both sides of the equation by 9 to solve for x:
x = 8/9
Therefore, the repeating decimal 0.8¯¯¯ can be converted to the rational number 8/9.
Let x = 0.8¯¯¯
To remove the repeating decimal, we can multiply both sides of the equation by 10:
10x = 8.8¯¯¯
Now, we subtract the original equation from the multiplied equation:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8
Finally, we divide both sides of the equation by 9 to solve for x:
x = 8/9
Therefore, the repeating decimal 0.8¯¯¯ can be converted to the rational number 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?
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.