Question

Vocabulary Terms - Define/Illustrate

What is this notation on the calculator:
1.388e-2

Why does the calculator create this notation?



Why come up with a new notation like Scientific Notation? What is the point?







5 Problems - SHOW ALL WORK!

What does a positive integer exponent tell you when a number is written in scientific notation?


Give an example:



What does a negative integer exponent tell you when a number is written in scientific notation?


Give an example:
Write 872,010,000,000 in scientific notation.




Write 0.00000000026 in scientific notation.
A company reported a net income for the quarter as $2.75 billion. Last quarter, the income was reported as $1.76 billion. How much did the income increase?


What operation are you going to use?


What is your reasoning to come up with the increase in income?

Answer 1

### Vocabulary Terms

#### 1. Notation on the Calculator: 1.388e-2
The notation "1.388e-2" represents a number in scientific notation, more specifically, it can be read as \(1.388 \times 10^{-2}\). In this case, "e" stands for "exponent," so "e-2" indicates that we are multiplying by \(10^{-2}\).

#### 2. Why does the calculator create this notation?
Calculators use this notation primarily for two reasons:
1. **Space Efficiency**: It allows for compact representation of very large or very small numbers without using excessive digits, making it easier to read and manage calculations.
2. **Precision Maintenance**: It accurately represents numbers that may otherwise be cumbersome to display fully or that require many digits, ensuring that the precision of the values is maintained.

#### 3. Why come up with a new notation like Scientific Notation? What is the point?
Scientific notation simplifies calculations and communication of very large or very small numbers. The benefits include:
- **Simplicity**: It allows easier multiplication and division of large numbers by focusing on the exponents.
- **Clarity**: It reduces the risk of errors in reading or writing very large or small values.
- **Standardization**: It provides a common framework for scientists, mathematicians, and engineers, facilitating clearer communication of numeric data.

---

### Problems

#### 1. Positive Integer Exponent in Scientific Notation
A positive integer exponent tells you how many places to move the decimal point to the right when converting from scientific notation to standard form. For example, \(5.0 \times 10^3\) means you move the decimal 3 places to the right, resulting in 5000.

**Example:**
- \(3.2 \times 10^4 = 32,000\)

#### 2. Negative Integer Exponent in Scientific Notation
A negative integer exponent tells you how many places to move the decimal point to the left when converting from scientific notation to standard form. For example, \(4.5 \times 10^{-3}\) means you move the decimal 3 places to the left, resulting in 0.0045.

**Example:**
- \(2.1 \times 10^{-2} = 0.021\)

---

#### 3. Write 872,010,000,000 in Scientific Notation
To convert, you place the decimal after the first non-zero digit and count how many places you move it to the left.
- \(872,010,000,000 = 8.7201 \times 10^{11}\)

---

#### 4. Write 0.00000000026 in Scientific Notation
To convert, you place the decimal after the first non-zero digit and count how many places you move it to the right.
- \(0.00000000026 = 2.6 \times 10^{-10}\)

---

#### 5. A company reported a net income for the quarter as $2.75 billion. Last quarter, the income was reported as $1.76 billion. How much did the income increase?
To find the increase in income, subtract the last quarter's income from the current quarter's income.

**Operation:**
- Subtraction

**Reasoning:**
To find the increase, I will calculate \(2.75 \, \text{billion} - 1.76 \, \text{billion}\).

**Calculations:**
- \(2.75 - 1.76 = 0.99\)

**Conclusion:**
The income increased by $0.99 billion, or $990 million.