Question

3. A dime is approximately 1.35 x 10-1cm thick. The thickness of a dollar bill is approximately 1.2 x 10-2

How many times greater is the thickness of a dime than the thickness of a dollar bill?








4. A corporation earned a profit of $2.5 x 104 for 1 x 103 days in a row.

What was the corporation’s total profit during this time period?

Answer 1

3. To find out how many times greater the thickness of a dime is compared to a dollar bill, we can divide the thickness of the dime by the thickness of the dollar bill:

\[
\text{Thickness of a dime} = 1.35 \times 10^{-1} \, \text{cm}
\]
\[
\text{Thickness of a dollar bill} = 1.2 \times 10^{-2} \, \text{cm}
\]

Now, we perform the division:

\[
\text{Ratio} = \frac{1.35 \times 10^{-1}}{1.2 \times 10^{-2}}
\]

Now calculate this step by step:

1. Compute the coefficient:
\[
\frac{1.35}{1.2} = 1.125
\]

2. Compute the powers of ten:
\[
10^{-1} \div 10^{-2} = 10^{-1 - (-2)} = 10^{1} = 10
\]

Now combine both results:
\[
1.125 \times 10 = 11.25
\]

So, the thickness of a dime is **approximately 11.25 times greater** than the thickness of a dollar bill.

---

4. To find the total profit of the corporation over a period of days, we multiply the profit per day by the number of days:

\[
\text{Profit per day} = 2.5 \times 10^{4}
\]
\[
\text{Number of days} = 1 \times 10^{3}
\]

Now, calculate the total profit:

\[
\text{Total profit} = (2.5 \times 10^{4}) \times (1 \times 10^{3})
\]

To compute this step by step:

1. Multiply the coefficients:
\[
2.5 \times 1 = 2.5
\]

2. Add the exponents of ten:
\[
10^{4} \times 10^{3} = 10^{4 + 3} = 10^{7}
\]

Now combine the results:
\[
\text{Total profit} = 2.5 \times 10^{7}
\]

Thus, the corporation’s total profit during this time period is **$2.5 \times 10^{7}**.