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Write the following numbers in scientific notation:

A. 15,000,000 cm
Scientific notation: [tex]1.5 \times 10^7[/tex]

B. 0.00045 feet
Scientific notation: [tex]4.5 \times 10^{-4}[/tex]

C. 13,096 miles
Scientific notation: [tex]1.3096 \times 10^4[/tex]

Approaching:

3. Convert 8,000 inches into centimeters. Write your answer in scientific notation.
Calculation: [tex]8,000 \times 2.54 \, \text{cm/inch} = 20,320 \, \text{cm}[/tex]
Scientific notation: [tex]2.032 \times 10^4[/tex]

4. Using your metric conversion chart and dimensional analysis, convert 11.5 kilograms into milligrams. Write your answer in scientific notation.
Calculation: [tex]11.5 \, \text{kg} \times 1,000,000 \, \text{mg/kg} = 11,500,000 \, \text{mg}[/tex]
Scientific notation: [tex]1.15 \times 10^7[/tex]

Answer :

Sure! Let's go through the steps to solve the problem.

### Problem 3: Convert 8000 inches into centimeters and express in scientific notation

1. Understand the Conversion:
- We know that 1 inch is equal to 2.54 centimeters.

2. Convert Inches to Centimeters:
- Multiply the number of inches (8000) by the conversion factor (2.54 cm/inch).
- Calculation: [tex]\( 8000 \times 2.54 = 20320 \)[/tex] centimeters.

3. Express in Scientific Notation:
- To express 20320 in scientific notation:
- Move the decimal point four places to the left, giving us [tex]\( 2.0320 \)[/tex].
- Count the number of places moved, which is 4.
- So, the scientific notation is [tex]\( 2.0320 \times 10^4 \)[/tex].

### Problem 4: Convert 11.5 kilograms into milligrams and express in scientific notation

1. Understand the Conversion:
- We know that 1 kilogram is equal to 1,000,000 milligrams.

2. Convert Kilograms to Milligrams:
- Multiply the number of kilograms (11.5) by the conversion factor (1,000,000 mg/kg).
- Calculation: [tex]\( 11.5 \times 1,000,000 = 11,500,000 \)[/tex] milligrams.

3. Express in Scientific Notation:
- To express 11,500,000 in scientific notation:
- Move the decimal point seven places to the left, giving us [tex]\( 1.1500 \)[/tex].
- Count the number of places moved, which is 7.
- So, the scientific notation is [tex]\( 1.1500 \times 10^7 \)[/tex].

These steps detail how you can convert inches to centimeters and kilograms to milligrams, then write those in scientific notation. The conversions and notations provide a clear understanding of the conversions involved.

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