2) In one of the most recent silicon industry achievements of 2021, a single transistor takes up a rectangular area on a microchip that measures 10[nm] bv 20[nm]. The early microchips in the 1970's had rectangular transistors that each measured approximately 20[um] by 40[um]. How manv of the new 2021 transistors could fit inside the same area of a single 1970 transistor? A) 400 B) 4000 C) 40,000 D) 400,000 É 4,000,000

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Chapter1: Units, Trigonometry. And Vectors
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**Text Transcription for Educational Website:**

In one of the most recent silicon industry achievements of 2021, a single transistor takes up a rectangular area on a microchip that measures 10 [nm] by 20 [nm]. The early microchips in the 1970's had rectangular transistors that each measured approximately 20 [μm] by 40 [μm]. How many of the new 2021 transistors could fit inside the same area of a single 1970 transistor?

A) 400  
B) 4000  
C) 40,000  
D) 400,000  
E) 4,000,000  

**Explanation of Concepts:**

- **Transistor Size Comparison:** The problem compares the area occupied by transistors from two different eras, 2021 and the 1970s, by using their respective dimensions.
  
- **Measurement Units:** 
  - 2021 transistor dimensions: 10 nanometers (nm) by 20 nanometers (nm).
  - 1970s transistor dimensions: 20 micrometers (μm) by 40 micrometers (μm).

- **Unit Conversion:** To accurately compare the transistor areas, it's essential to convert all measurements to the same units. Note: 1 micrometer (μm) = 1,000 nanometers (nm).

- **Area Calculation:**
  - **2021 transistor area:** \(10 \, \text{nm} \times 20 \, \text{nm} = 200 \, \text{nm}^2\)
  - **1970s transistor area:** After converting dimensions into nanometers, \( (20,000 \, \text{nm}) \times (40,000 \, \text{nm}) = 800,000,000 \, \text{nm}^2 \)

- **Comparison:**
  - The number of 2021 transistors that fit into a 1970s transistor is calculated by dividing the 1970s transistor area by the 2021 transistor area: 
  \[
  \frac{800,000,000 \, \text{nm}^2}{200 \, \text{nm}^2} = 4,000,000
  \]

Thus, the answer is **E) 4,000,000**.
Transcribed Image Text:**Text Transcription for Educational Website:** In one of the most recent silicon industry achievements of 2021, a single transistor takes up a rectangular area on a microchip that measures 10 [nm] by 20 [nm]. The early microchips in the 1970's had rectangular transistors that each measured approximately 20 [μm] by 40 [μm]. How many of the new 2021 transistors could fit inside the same area of a single 1970 transistor? A) 400 B) 4000 C) 40,000 D) 400,000 E) 4,000,000 **Explanation of Concepts:** - **Transistor Size Comparison:** The problem compares the area occupied by transistors from two different eras, 2021 and the 1970s, by using their respective dimensions. - **Measurement Units:** - 2021 transistor dimensions: 10 nanometers (nm) by 20 nanometers (nm). - 1970s transistor dimensions: 20 micrometers (μm) by 40 micrometers (μm). - **Unit Conversion:** To accurately compare the transistor areas, it's essential to convert all measurements to the same units. Note: 1 micrometer (μm) = 1,000 nanometers (nm). - **Area Calculation:** - **2021 transistor area:** \(10 \, \text{nm} \times 20 \, \text{nm} = 200 \, \text{nm}^2\) - **1970s transistor area:** After converting dimensions into nanometers, \( (20,000 \, \text{nm}) \times (40,000 \, \text{nm}) = 800,000,000 \, \text{nm}^2 \) - **Comparison:** - The number of 2021 transistors that fit into a 1970s transistor is calculated by dividing the 1970s transistor area by the 2021 transistor area: \[ \frac{800,000,000 \, \text{nm}^2}{200 \, \text{nm}^2} = 4,000,000 \] Thus, the answer is **E) 4,000,000**.
Expert Solution
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To solve the given question, we will find the area of each transistor in each case and then we will compare.

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