Question

Use scientific notation to estimate the number of inches in 1,225 miles. Include all calculations in your final answer.

1 inch ≈ 1.578 × 10 -5 miles.

Answer 1

can you make it without all the symbols and slashes. and can you make it less advanced

Answer 2

can you use less words and make it less advanced

Answer 3

To estimate the number of inches in 1,225 miles using scientific notation, we start with the given conversion factor:

1 inch ≈ \(1.578 \times 10^{-5}\) miles.

To find the number of inches in 1,225 miles, we first set up the relationship:

\[
\text{Number of inches} = \frac{\text{miles}}{\text{miles per inch}}
\]

Substituting in the known values:

\[
\text{Number of inches} = \frac{1,225 \text{ miles}}{1.578 \times 10^{-5} \text{ miles per inch}}
\]

Now, we perform the division. In scientific notation, dividing by a number in scientific notation can be done as follows:

1. First, compute the reciprocal of the conversion factor:

\[
\frac{1}{1.578 \times 10^{-5}} = \frac{1}{1.578} \times 10^{5}
\]

Calculating \(\frac{1}{1.578}\):

\[
\frac{1}{1.578} \approx 0.634 \implies 6.34 \times 10^{-1}
\]

So, we have:

\[
\frac{1}{1.578 \times 10^{-5}} \approx 6.34 \times 10^{-1} \times 10^{5} = 6.34 \times 10^{4}
\]

2. Now, we multiply by 1,225:

\[
\text{Number of inches} \approx 1,225 \times (6.34 \times 10^{4})
\]

To perform this multiplication, we first convert 1,225 into scientific notation:

\[
1,225 = 1.225 \times 10^{3}
\]

Now, we can multiply:

\[
1.225 \times 10^{3} \times 6.34 \times 10^{4} = (1.225 \times 6.34) \times (10^{3} \times 10^{4})
\]

Calculating \(1.225 \times 6.34\):

\[
1.225 \times 6.34 \approx 7.77
\]

And for the powers of ten:

\[
10^{3} \times 10^{4} = 10^{7}
\]

Thus:

\[
\text{Number of inches} \approx 7.77 \times 10^{7}
\]

Therefore, the estimated number of inches in 1,225 miles is:

\[
\boxed{7.77 \times 10^{7}}
\]

Answer 4

Sure! Let's break it down step by step without using too many symbols or advanced notation.

**Step 1: Understanding the Conversion**
We need to convert 1,225 miles into inches. We know that **1 inch is approximately equal to 0.00001578 miles**.

**Step 2: Finding How Many Inches in a Mile**
First, we want to find out how many inches there are in one mile. Since **1 mile is equal to 63,360 inches** (because there are 12 inches in a foot and 5,280 feet in a mile):

- So, 1 mile = 12 inches/foot × 5,280 feet = 63,360 inches.

**Step 3: Calculating Inches for 1,225 Miles**
Now, we want to find the total number of inches in 1,225 miles.

To do that, we multiply the total number of inches in one mile (63,360) by the number of miles (1,225):

1. First, calculate the product:
- 1,225 miles × 63,360 inches per mile.

**Step 4: Performing the Multiplication**
Let's do the multiplication:

- 1,225 × 63,360 = 77,520,000 inches.

**Step 5: Converting to Scientific Notation**
Now, let's convert 77,520,000 into scientific notation.
- This number can be written as 7.752 × 10^7.

**Final Answer:**
So, the estimated number of inches in 1,225 miles is **approximately 7.77 × 10^7 inches**.

This means there are about **77,700,000 inches in 1,225 miles**.

Answer 5

Absolutely! Here’s a simpler version:

1. **Conversion Info:**
- 1 mile = 63,360 inches.

2. **Calculate for 1,225 miles:**
- 1,225 miles × 63,360 inches/mile = 77,520,000 inches.

3. **Convert to Scientific Notation:**
- 77,520,000 inches = 7.752 × 10^7 inches.

**Final Answer:**
Approximately **7.77 × 10^7 inches** in 1,225 miles.