Question
Aliyah wants to estimate the value of the quotient of 5.68 times 10 Superscript negative 3 and 8.54 times 10 Superscript negative 9. Which statement about the value is true?
The value will be greater than 1 because (negative 3) divided by (negative 9) is a positive number. A number in scientific notation with a positive exponent has a value greater than 1.
The value will be greater than 1 because (negative 3) minus (negative 9) = 6. A number in scientific notation with a positive exponent is greater than 1.
The value will be less than 1 because 5.68 divided by 8.54 is less than 1. The negative exponents will make it even smaller.
The number will be less than 1 because 5.68 times 10 Superscript negative 3 is a very small number and division always makes the size of a number smaller.
The value will be greater than 1 because (negative 3) divided by (negative 9) is a positive number. A number in scientific notation with a positive exponent has a value greater than 1.
The value will be greater than 1 because (negative 3) minus (negative 9) = 6. A number in scientific notation with a positive exponent is greater than 1.
The value will be less than 1 because 5.68 divided by 8.54 is less than 1. The negative exponents will make it even smaller.
The number will be less than 1 because 5.68 times 10 Superscript negative 3 is a very small number and division always makes the size of a number smaller.
Answers
GPT-4o mini
To evaluate the quotient of \(5.68 \times 10^{-3}\) and \(8.54 \times 10^{-9}\), we can analyze how to work with the scientific notation and the division of the coefficients.
First, we can break down the expression as follows:
\[
\frac{5.68 \times 10^{-3}}{8.54 \times 10^{-9}} = \frac{5.68}{8.54} \times \frac{10^{-3}}{10^{-9}}
\]
For the division of the powers of ten, we know:
\[
\frac{10^{-3}}{10^{-9}} = 10^{-3 - (-9)} = 10^{-3 + 9} = 10^6
\]
Now we need to evaluate \(\frac{5.68}{8.54}\). This value is less than 1 since \(5.68\) is less than \(8.54\).
Putting this together, we have:
\[
\frac{5.68}{8.54} \times 10^{6}
\]
Since \(\frac{5.68}{8.54} < 1\) and we multiply a number less than 1 by \(10^6\) (which is \(1,000,000\)), the overall result will be greater than 1 because the 10 raised to a power (6 in this case) dominates.
Thus, we can conclude that:
**The value will be greater than 1 because (negative 3) minus (negative 9) = 6. A number in scientific notation with a positive exponent is greater than 1.**
First, we can break down the expression as follows:
\[
\frac{5.68 \times 10^{-3}}{8.54 \times 10^{-9}} = \frac{5.68}{8.54} \times \frac{10^{-3}}{10^{-9}}
\]
For the division of the powers of ten, we know:
\[
\frac{10^{-3}}{10^{-9}} = 10^{-3 - (-9)} = 10^{-3 + 9} = 10^6
\]
Now we need to evaluate \(\frac{5.68}{8.54}\). This value is less than 1 since \(5.68\) is less than \(8.54\).
Putting this together, we have:
\[
\frac{5.68}{8.54} \times 10^{6}
\]
Since \(\frac{5.68}{8.54} < 1\) and we multiply a number less than 1 by \(10^6\) (which is \(1,000,000\)), the overall result will be greater than 1 because the 10 raised to a power (6 in this case) dominates.
Thus, we can conclude that:
**The value will be greater than 1 because (negative 3) minus (negative 9) = 6. A number in scientific notation with a positive exponent is greater than 1.**