Hey Bot, I need help with one math question.
Of course! I'll do my best to assist you. Please go ahead and ask your math question.
What is the expanded form of 23.75?(1 point)
The expanded form of 23.75 is:
20 + 3 + 0.7 + 0.05
can you write that in a different way?
Certainly! Here's an alternative way to write the expanded form of 23.75:
(2 * 10) + (3 * 1) + (7 * 0.1) + (5 * 0.01)
Oh sorry, but can your write that in expanded factors form
Certainly! Here's the expanded factors form of 23.75:
(2 * 10) + (3 * 1) + (7 * (1/10)) + (5 * (1/100))
Sorry I have another question.
Write the expanded form of 357.25(1 point)
Can you write the answer in expanded factors form
Certainly! Here's the expanded form of 357.25:
(3 * 100) + (5 * 10) + (7 * 1) + (2 * (1/10)) + (5 * (1/100))
And here it is in expanded factors form:
(3 * 10^2) + (5 * 10^1) + (7 * 10^0) + (2 * 10^(-1)) + (5 * 10^(-2))
okay one last question
What is the expanded form of 8,471.716?(1 point)
and can you also write this in expanded factors form
Sure! Here's the expanded form of 8,471.716:
(8 * 1000) + (4 * 100) + (7 * 10) + (1 * 1) + (7 * (1/10)) + (1 * (1/100)) + (6 * (1/1000))
And here it is in expanded factors form:
(8 * 10^3) + (4 * 10^2) + (7 * 10^1) + (1 * 10^0) + (7 * 10^(-1)) + (1 * 10^(-2)) + (6 * 10^(-3))
Thanks bot for help with those last question, but I have more
You're welcome! I'm here to help. Please feel free to ask any additional questions you have, and I'll do my best to assist you.
How many digits are in the repeating cycle of 1727?(1 point)
To determine the number of digits in the repeating cycle of a number when expressed as a fraction, we need to find its prime factors.
Let's start by considering 1727. We notice that it is not divisible by 2, so we move on to 3. Dividing 1727 by 3, we get 575 remainder 2.
Next, we try dividing by 7, but it doesn't divide evenly. Another prime number to consider is 11. After dividing 1727 by 11, we get 157 remainder 0.
So, we have prime factors of 3, 11, and 157.
Now, let's analyze the prime factors to determine the length of the repeating cycle. Both 3 and 11 are factors of 10 (3 * 11 = 33), which implies that the decimal expansion will repeat every 10 digits. However, 157 is prime and does not divide evenly into 10.
Therefore, the repeating cycle of 1727 when expressed as a decimal would be 10 digits.
sorry bot I meant to put
How many digits are in the repeating cycle of 17/27?(1 point)
No problem! The repeating cycle of a fraction can be determined by its denominator. To find the repeating cycle of 17/27, we need to prime factorize the denominator, which is 27.
27 can be factorized as 3 * 3 * 3 or 3^3.
The length of the repeating cycle in a fraction with a denominator of 3^n is n. In the case of 27, n is equal to 3.
Therefore, the repeating cycle of 17/27 is 3 digits long.
Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?(1 point)
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to check their denominators for any factors other than 2 and 5, since those factors result in a terminating decimal.
Let's check the denominators for each given rational number:
- 7/8: The denominator, 8, only contains 2 as a factor, so it can be expressed as a terminating decimal.
- 5/12: The denominator, 12, contains 2 and 3 as factors, so it can be expressed as a repeating decimal.
- 17/25: The denominator, 25, only contains 5 as a factor, so it can be expressed as a terminating decimal.
- 31/40: The denominator, 40, contains 2 and 5 as factors, so it can be expressed as a terminating decimal.
Based on this analysis, the only rational number that can be expressed as a repeating decimal is 5/12.
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.
(1 point)
To express 7/13 as a repeating decimal, we need to perform long division:
0.
13 | 7.000
- 6.50
------
50
-39
----
110
-104
----
60
- 52
----
80
- 78
----
20
The remainder 20 repeats.
Therefore, 7/13 as a repeating decimal is 0.538461538461... with the digits 538461 repeating.
Convert 0.8¯¯¯ to a rational number.(1 point)
To convert the repeating decimal 0.8¯¯¯ to a rational number, we can represent it as a fraction.
Let's use the variable x to represent the repeating decimal:
x = 0.8¯¯¯
To eliminate the repeating part, we multiply x by a power of 10 that moves the decimal point just before the repeating part:
10x = 8.¯¯¯
Next, we subtract x from 10x to eliminate the repeating part:
10x - x = 8.¯¯¯ - 0.¯¯¯
This simplifies to:
9x = 8
Now, we solve for x by dividing both sides of the equation by 9:
x = 8/9
Therefore, 0.8¯¯¯ can be expressed as 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?(1 point)
To convert the repeating decimal 0.82¯¯¯¯¯ to a rational number, we begin by setting x equal to 0.82¯¯¯¯¯.
x = 0.82¯¯¯¯¯
To eliminate the repeating part, we need to multiply x by a power of 10 that moves the decimal point just before the repeating part. Since there are two repeating digits (82), we need to multiply by 100 (10^2):
100x = 82.82¯¯¯¯¯
Therefore, to eliminate the repeating part of the decimal, we multiply both sides of the equation by 100.