1. **State the problem:**
We are given two numbers in scientific notation: Earth is about $4.5$ billion years old and primate fossils date back about $45$ million years.
2. **Write each number in standard notation:**
- $4.5$ billion years means $4.5 \times 10^9$ years.
- $45$ million years means $45 \times 10^6$ years.
Convert to standard notation:
- Earth age: $$4.5 \times 10^9 = 4,500,000,000$$
- Primate fossils age: $$45 \times 10^6 = 45,000,000$$
3. **Find how many times as old Earth is compared to primate fossils:**
Divide Earth's age by primate fossils' age:
$$\frac{4,500,000,000}{45,000,000} = \frac{4.5 \times 10^9}{4.5 \times 10^7} = 10^{9-7} = 10^2 = 100$$
4. **Explain the thinking:**
Earth is about 100 times as old as the primate fossils because when dividing the two numbers, the powers of ten subtract, leaving $10^2$, which equals 100.
**Final answers:**
- Earth age in standard notation: $4,500,000,000$
- Primate fossils age in standard notation: $45,000,000$
- Earth is about 100 times as old as the primate fossils.
Earth Primate Age
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.