Question

Vocabulary Terms - Define/Illustrate

Metric System as powers of 10
Common US measures in match ups with metric measures:


5 Problems - SHOW ALL WORK!

Convert the speed 1.000m/s (meters/second) to mi/h (miles/hour).
Hint: 1mi = 5280 ft and 1 m = 0.000621371 mi






Use your weight in pounds to calculate into kilograms and then into grams.
Hint: 1kg = 2.205lb.
Write in standard format: 2.146e2




Change 0.000893 x 104 into Scientific Notation
You have a table that measures 62 inches x 86 inches…how would you convert these measurements into feet?


What about miles?



What about Scientific Notation for the miles?

Answer 1

### Vocabulary Terms

**Metric System as Powers of 10:**
The metric system is a decimal-based system of measurement used by most countries worldwide. It is structured around powers of ten, making conversions within the system straightforward and consistent. For example:
- 1 meter (m) = 10 decimeters (dm)
- 1 kilometer (km) = 1,000 meters (m) = 10^3 m
- 1 centimeter (cm) = 0.01 meters (m) = 10^-2 m

**Common US Measures in Match-ups with Metric Measures:**
1. Length:
- 1 inch = 2.54 cm
- 1 foot = 0.3048 m
- 1 mile = 1.60934 km
2. Volume:
- 1 gallon = 3.78541 liters
- 1 quart = 0.946353 liters
3. Weight:
- 1 pound = 0.453592 kg
- 1 ounce = 28.3495 grams

---

### Problems

**1. Convert the speed 1.000 m/s to mi/h (miles/hour).**

To convert from meters per second to miles per hour, we use the conversion factors:
- 1 m = 0.000621371 mi
- 1 hour = 3600 seconds

First, convert 1.000 m/s to miles:
\[
1.000 \text{ m/s} \times 0.000621371 \text{ mi/m} = 0.000621371 \text{ mi/s}
\]
Next, convert seconds to hours:
\[
0.000621371 \text{ mi/s} \times 3600 \text{ s/h} = 2.243 \text{ mi/h}
\]

**Final Answer: 1.000 m/s ≈ 2.243 mi/h**

---

**2. Use your weight in pounds to calculate into kilograms and then into grams. (Example weight: 150 lbs)**

Convert pounds to kilograms:
\[
\text{Weight in kg} = \frac{\text{Weight in lbs}}{2.205}
\]
If your weight is 150 lbs:
\[
\text{Weight in kg} = \frac{150}{2.205} \approx 68.17 \text{ kg}
\]

Convert kilograms to grams:
\[
\text{Weight in grams} = \text{Weight in kg} \times 1000 \text{ g}
\]
\[
\text{Weight in grams} = 68.17 \times 1000 \approx 68170 \text{ g}
\]

**Write in standard format:**
\[
68170 \text{ g} = 6.8170 \times 10^4 \text{ g}
\]

---

**3. Change \(0.000893 \times 10^4\) into Scientific Notation.**

To convert to scientific notation, we want only one non-zero digit to the left of the decimal point.
\[
0.000893 \times 10^4 = 0.00893 \times 10^3
\]
Thus,
\[
\text{Scientific Notation} = 8.93 \times 10^{-3} \text{ (after moving the decimal point)}
\]

---

**4. Convert table measurements into feet: 62 inches x 86 inches.**

Convert inches to feet (1 foot = 12 inches):
\[
\text{Length} = \frac{62 \text{ inches}}{12} \approx 5.1667 \text{ ft}
\]
\[
\text{Width} = \frac{86 \text{ inches}}{12} \approx 7.1667 \text{ ft}
\]

Final dimensions in feet:
- Length: \(5.167 \text{ ft}\)
- Width: \(7.167 \text{ ft}\)

---

**5. Convert table measurements into miles. To calculate: 5.167 feet x 7.167 feet.**

Convert feet to miles (1 mile = 5280 feet):
\[
\text{Length in miles} = \frac{5.167}{5280} \approx 0.000978 \text{ mi}
\]
\[
\text{Width in miles} = \frac{7.167}{5280} \approx 0.001358 \text{ mi}
\]

**Scientific Notation for the miles:**
- Length: \(9.78 \times 10^{-4} \text{ mi}\)
- Width: \(1.358 \times 10^{-3} \text{ mi}\)

---

These calculations illustrate how to effectively convert between different measurement systems and how to express quantities in scientific notation.