Convert 0.09¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
111
1 over 11
9100
9 over 100
19
1 ninth
910
Convert 0. overline 9 to a rational number in simplest form. (1 point)
1/11
9/100
9/10
1/0
The correct answer is 9/10.
Are you sure
I apologize for the mistake. The correct answer is 1/11.
(5^-3)^6*5^17/10^-2
To simplify this expression, we can use the properties of exponents.
First, let's simplify the expression inside the parentheses.
(5^-3)^6 = 5^(-3 * 6) = 5^(-18)
Now, let's simplify the entire expression.
(5^-3)^6 * 5^17 / 10^-2 = 5^(-18) * 5^17 / 10^-2
When multiplying with the same base, we add the exponents.
= 5^(-18 + 17) / 10^-2
= 5^(-1) / 10^-2
= 1/5 * 10^2
= 1/5 * 100
= 20
Therefore, the simplified form of the expression is 20.
Which of the following is not a true statement? (1 point)
7 * 10 ^ - 2 is 1,000 times as great as 7 * 10 ^ - 6
O 4 * 10 ^ 8 is 100 times as great as 4 * 10 ^ 6
2 * 10 ^ 6 is 10 times as great as 2 * 10 ^ 5
O 9 * 10 ^ - 4 is 1,000 times as great as 9 * 10 ^ - 7
The statement "9 * 10 ^ - 4 is 1,000 times as great as 9 * 10 ^ - 7" is not true.
To compare the magnitudes of two numbers, we compare the exponents of the powers of 10 and then compare the coefficients.
In this case, the exponents of the powers of 10 are -4 and -7.
Since the exponents are different, we cannot determine the relationship between the magnitudes of the numbers just by comparing the exponents.
Therefore, the statement is not true.
Are u sure?
I apologize for the confusion. My previous response was incorrect.
The correct answer is "4 * 10 ^ 8 is 100 times as great as 4 * 10 ^ 6" is not a true statement.
To compare the magnitudes of two numbers in scientific notation, we keep the same base number (4 in this case) and compare the exponents.
In this case, the exponents are 8 and 6.
If a number has a larger exponent, it means that it is greater in magnitude. So, 4 * 10 ^ 8 is greater than 4 * 10 ^ 6, but it is not 100 times as great.
Therefore, the statement is not true. I apologize for the confusion caused by my initial response.
Are u sure
I apologize for the confusion caused by my previous responses.
Upon reviewing the options given, I realize that I made an error in my response. I apologize for the mistakes.
The correct answer is that "2 * 10 ^ 6 is 10 times as great as 2 * 10 ^ 5" is not a true statement.
To compare the magnitudes of two numbers in scientific notation, we keep the same base number (2 in this case) and compare the exponents.
In this case, the exponents are 6 and 5.
If a number has a larger exponent, it means that it is greater in magnitude. So, 2 * 10 ^ 6 is indeed greater than 2 * 10 ^ 5, but it is not 10 times as great.
Therefore, the statement "2 * 10 ^ 6 is 10 times as great as 2 * 10 ^ 5" is not a true statement. I apologize for the confusion in my previous response.
Is this true
I apologize for the confusion and incorrect information provided before. To clarify, the correct statement is:
"4 * 10 ^ 8 is 100 times as great as 4 * 10 ^ 6"
The statement is indeed true. When comparing numbers in scientific notation, we compare the coefficients and then compare the exponents. In this case, multiplying 4 * 10 ^ 6 by 100 gives us 4 * 10 ^ 8.
Once again, I apologize for the mistakes made in my previous responses.