Homework (Show all work) 1. Convert the following numbers to scientific notation: a. 1,700 b. 0.005 c. $$ 2,300,000 $$ 2. Solve the following problems: a. The height of a building is 450 meters. Write this in scientific notation. b. A rock sample weighs 0.00025 Kilograms. Express this in scientific notation.

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## **1. Convert the following numbers to scientific notation:**

### **a. 1,700**

**Step 1:** Identify the decimal point in the number. For 1,700, it's implicitly after the last zero: 1700.

**Step 2:** Move the decimal point so that only one non-zero digit remains to the left of the decimal.

- Move the decimal 3 places to the left: 
  $$
  1700 \rightarrow 1.700
  $$

**Step 3:** Determine the exponent based on how many places you moved the decimal. Since we moved it 3 places to the left, the exponent is +3.

**Scientific Notation:** 
$$
1.7 \times 10^3
$$

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### **b. 0.005**

**Step 1:** Identify the decimal point: 0.005.

**Step 2:** Move the decimal so that only one non-zero digit remains to the left.

- Move the decimal 3 places to the right:
  $$
  0.005 \rightarrow 5.0
  $$

**Step 3:** Determine the exponent. Since we moved the decimal 3 places to the right, the exponent is -3.

**Scientific Notation:** 
$$
5.0 \times 10^{-3}
$$

*Alternatively, it's common to write it as $$5 \times 10^{-3}$$.*

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### **c. $$2,300,000$$**

**Step 1:** Identify the decimal point: 2300000.

**Step 2:** Move the decimal so that only one non-zero digit remains to the left.

- Move the decimal 6 places to the left:
  $$
  2300000 \rightarrow 2.3
  $$

**Step 3:** Determine the exponent. Since we moved the decimal 6 places to the left, the exponent is +6.

**Scientific Notation:** 
$$
2.3 \times 10^6
$$

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## **2. Solve the following problems:**

### **a. The height of a building is 450 meters. Write this in scientific notation.**

**Step 1:** Identify the number: 450 meters.

**Step 2:** Move the decimal so that only one non-zero digit remains to the left.

- Move the decimal 2 places to the left:
  $$
  450 \rightarrow 4.50
  $$

**Step 3:** Determine the exponent. Since we moved the decimal 2 places to the left, the exponent is +2.

**Scientific Notation:**
$$
4.5 \times 10^2 \text{ meters}
$$

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### **b. A rock sample weighs 0.00025 kilograms. Express this in scientific notation.**

**Step 1:** Identify the number: 0.00025 kilograms.

**Step 2:** Move the decimal so that only one non-zero digit remains to the left.

- Move the decimal 4 places to the right:
  $$
  0.00025 \rightarrow 2.5
  $$

**Step 3:** Determine the exponent. Since we moved the decimal 4 places to the right, the exponent is -4.

**Scientific Notation:**
$$
2.5 \times 10^{-4} \text{ kilograms}
$$

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**Summary of Answers:**

1. **Scientific Notation:**
   - a. $$1,700 = 1.7 \times 10^3$$
   - b. $$0.005 = 5 \times 10^{-3}$$
   - c. $$2,300,000 = 2.3 \times 10^6$$

2. **Problems:**
   - a. Height of building: $$4.5 \times 10^2$$ meters
   - b. Weight of rock sample: $$2.5 \times 10^{-4}$$ kilograms

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Feel free to ask if you have any more questions or need further clarification!
1. **Scientific Notation:** - a. 1,700 = 1.7 × 10³ - b. 0.005 = 5 × 10⁻³ - c. 2,300,000 = 2.3 × 10⁶ 2. **Problems:** - a. 450 meters = 4.5 × 10² meters - b. 0.00025 kg = 2.5 × 10⁻⁴ kg

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