Let's break down the problem step by step.
Part (a): Approximate the number of ounces in 1 ton by rounding to the nearest ten thousand ounces.
We know that there are 3.2 ten thousand ounces in 1 ton. To find the total number of ounces in one ton, we multiply 3.2 by 10,000:
[tex]\[
3.2 \times 10,000 = 32,000
\][/tex]
Thus, the number of ounces in one ton, rounded to the nearest ten thousand ounces, is 32,000 ounces.
Part (b): Write your answer from part (a) as a single digit times a power of 10 in exponential form.
We need to express 32,000 as a single digit times a power of 10. The number 32,000 can be rewritten by moving the decimal point:
[tex]\[
32,000 = 3.2 \times 10,000
\][/tex]
Next, we express 10,000 as [tex]\(10^4\)[/tex] because:
[tex]\[
10,000 = 10^4
\][/tex]
Combining these results, we get:
[tex]\[
32,000 = 3.2 \times 10^4
\][/tex]
Therefore, the base is [tex]\(3.2\)[/tex] and the exponent is [tex]\(4\)[/tex].
To summarize:
- Part (a): The number of ounces in 1 ton is approximately 32,000 ounces.
- Part (b): This amount can be written as [tex]\(3.2 \times 10^4\)[/tex].
