Question

Vocabulary Terms - Define/Illustrate

List the inequality symbols and their meanings:
What do you look at to compare numbers in Scientific Notation?








5 Problems - SHOW ALL WORK!

Order the following from least to greatest:
6.8 x 10^6 , 6 x 10^6 , 6.6 x 10^-6 ,6.1 x 10^-6






The diameter of the planet Mercury is 4.87 x 10^3 km. The diameter of the planet Venus is 1.21 x 10^4 km. The diameter of Earth is 1.28 x 10^4 km. The diameter of Mars is 6.79 x 10^3km.
Which planet has the smallest diameter?



If you want to change 192.345 x 10^-2 into Scientific Notation, what would you do?







Which is greater,
5.45 x 10^-4 or 6.35 x 10^-4 ?
Why do we look to the number line when deciding greater or less numbers?

Answer 1

### Vocabulary Terms

#### Inequality Symbols and Their Meanings:
- **< (less than)**: Indicates that the number on the left is smaller than the number on the right.
- Example: \( 3 < 5 \) means 3 is less than 5.
- **> (greater than)**: Indicates that the number on the left is larger than the number on the right.
- Example: \( 7 > 4 \) means 7 is greater than 4.
- **≤ (less than or equal to)**: Indicates that the number on the left is either smaller than or equal to the number on the right.
- Example: \( 3 ≤ 3 \) means 3 is less than or equal to 3.
- **≥ (greater than or equal to)**: Indicates that the number on the left is either larger than or equal to the number on the right.
- Example: \( 5 ≥ 4 \) means 5 is greater than or equal to 4.
- **= (equal to)**: Indicates that the number on the left is the same as the number on the right.
- Example: \( 8 = 8 \) means both sides are equal.

#### Comparing Numbers in Scientific Notation:
When comparing numbers in scientific notation, you look first at the exponent of the base 10. Numbers with larger exponents represent larger values, regardless of the coefficients. If the exponents are the same, compare the coefficients directly.

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### Problems

1. **Order the following from least to greatest:**
- \( 6.8 \times 10^6 \)
- \( 6 \times 10^6 \)
- \( 6.6 \times 10^{-6} \)
- \( 6.1 \times 10^{-6} \)

**Comparison:**
- For the numbers with \( 10^6 \):
- \( 6 \times 10^6 = 6,000,000 \)
- \( 6.6 \times 10^6 = 6,600,000 \)
- \( 6.8 \times 10^6 = 6,800,000 \)
- For the numbers with \( 10^{-6} \):
- \( 6.1 \times 10^{-6} = 0.0000061 \)
- \( 6.6 \times 10^{-6} = 0.0000066 \)

**Ordering from least to greatest:**
\[
6.1 \times 10^{-6} < 6.6 \times 10^{-6} < 6 \times 10^{6} < 6.6 \times 10^{6} < 6.8 \times 10^{6}
\]

2. **Smallest Diameter:**
- Mercury: \( 4.87 \times 10^3 = 4,870 \, \text{km} \)
- Venus: \( 1.21 \times 10^4 = 12,100 \, \text{km} \)
- Earth: \( 1.28 \times 10^4 = 12,800 \, \text{km} \)
- Mars: \( 6.79 \times 10^3 = 6,790 \, \text{km} \)

**Comparison:**
- Mercury (4,870 km) is the smallest.

3. **Changing to Scientific Notation:**
- Original: \( 192.345 \times 10^{-2} \)
- To convert to scientific notation:
- Move the decimal point 2 places to the left: \( 1.92345 \)
- Adjust the exponent accordingly: \( 1.92345 \times 10^{0} \) (since we moved the decimal left)
- Final result: \( 1.92345 \times 10^{-0} \):
- Therefore, \( 192.345 \times 10^{-2} = 1.92345 \times 10^{0} \)

4. **Which is greater:**
- Compare \( 5.45 \times 10^{-4} \) and \( 6.35 \times 10^{-4} \).
- Both have the same exponent (−4).
- Compare coefficients: \( 5.45 < 6.35 \).
- Therefore, \( 6.35 \times 10^{-4} \) is greater.

5. **Why Do We Look at the Number Line:**
- A number line visually represents the value of numbers, allowing us to see their relative positions.
- Numbers further to the right are greater, and numbers further to the left are smaller, which helps in understanding and comparing quantities effectively.