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Update page 'Day 1 homework - Xuanyi Wang (Sloetjes)'

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Day 1 homework - Xuanyi Wang (Sloetjes).md
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# Xuanyi Wang\_Day-1\_Homework\_03/30/23 # Xuanyi Wang\_Day-1\_Homework\_03/30/23
### 1. What is the name of the international standard for floating-point representation? #### 1. What is the name of the international standard for floating-point representation?
**IEEE 754** **IEEE 754**
### 2. How many bits are the floating point numbers defined by that standard allowed to be? #### 2. How many bits are the floating point numbers defined by that standard allowed to be?
####Single-precision format (32-bits) ####Single-precision format (32-bits)
@@ -23,7 +23,7 @@ Double-precision floating-point numbers are represented using 64 bits, with 1 bi
* However, these formats are less commonly used than the single-precision and double-precision formats. * However, these formats are less commonly used than the single-precision and double-precision formats.
### 3. Does your computer support all those formats? Can you think of an easy way to check with only one line of Python? #### 3. Does your computer support all those formats? Can you think of an easy way to check with only one line of Python?
@@ -33,7 +33,7 @@ import platform
platform.architecture()[0] platform.architecture()[0]
``` ```
### 4. Why doesn't this code give the same answers to the two multiplications? #### 4. Why doesn't this code give the same answers to the two multiplications?
``` ```
mport pandas as pd mport pandas as pd
import numpy as np import numpy as np
@@ -60,7 +60,7 @@ print(df)
`num1` and `num2` are both 64-bit integers, which means that ` num1 * num2` is performed using 64-bit integer arithmetic. However,`df[‘Number1’] ` and `df[‘Number2’] ` are Pandas Series objects and they are 64-bit floating point numbers so `df[‘Number1’] * df[‘Number2’] ` is performed using floating-point arithmetic which involves approximations and rounding errors. `num1` and `num2` are both 64-bit integers, which means that ` num1 * num2` is performed using 64-bit integer arithmetic. However,`df[‘Number1’] ` and `df[‘Number2’] ` are Pandas Series objects and they are 64-bit floating point numbers so `df[‘Number1’] * df[‘Number2’] ` is performed using floating-point arithmetic which involves approximations and rounding errors.
### 1. You can use sys.getsizeof to see how large a Python object is. Does the size of a Python floating-point number change as it gets larger? Why or why not? #### 1. You can use sys.getsizeof to see how large a Python object is. Does the size of a Python floating-point number change as it gets larger? Why or why not?
**The size of a Python floating-point number does not change as it gets larger.** **The size of a Python floating-point number does not change as it gets larger.**
@@ -71,14 +71,14 @@ Regardless of the magnitude of the float, the number of bytes used to represent
However, it's worth noting that as the magnitude of a floating-point number grows larger, the number of significant digits it can represent decreases. This is due to the limited precision of floating-point arithmetic, and can result in rounding errors when performing calculations with very large or very small floating-point numbers. However, it's worth noting that as the magnitude of a floating-point number grows larger, the number of significant digits it can represent decreases. This is due to the limited precision of floating-point arithmetic, and can result in rounding errors when performing calculations with very large or very small floating-point numbers.
### 2. We already know that the precision of floating-point numbers decreases as their magnitude increases. Using Pandas, create a dataframe representing a large amount of US Dollars. What is the smallest number of dollars where adding one cent begins to yield wrong results? #### 2. We already know that the precision of floating-point numbers decreases as their magnitude increases. Using Pandas, create a dataframe representing a large amount of US Dollars. What is the smallest number of dollars where adding one cent begins to yield wrong results?
Assuming double-precision floating-point numbers (64 bits), the smallest number of dollars that can be represented is $0.01 divided by 2 to the power of 52 (the number of bits used to represent the fraction part of a double-precision number). This equals approximately **$0.0000000000002384**. Assuming double-precision floating-point numbers (64 bits), the smallest number of dollars that can be represented is $0.01 divided by 2 to the power of 52 (the number of bits used to represent the fraction part of a double-precision number). This equals approximately **$0.0000000000002384**.
Therefore, any calculation involving adding 0.01 to a dollar amount smaller than **$0.0000000000002384** may yield wrong results due to the limited precision of floating-point arithmetic. Therefore, any calculation involving adding 0.01 to a dollar amount smaller than **$0.0000000000002384** may yield wrong results due to the limited precision of floating-point arithmetic.
### 3. Name three practical differences between Python strings and bytes. Using sys.getsizeof, see how the sizes may be different. Do emoji change this answer? #### 3. Name three practical differences between Python strings and bytes. Using sys.getsizeof, see how the sizes may be different. Do emoji change this answer?
** Encoding**: Python strings are used to represent text data, while bytes are used to represent binary data. Strings are typically encoded using a character encoding such as UTF-8 or ASCII, which maps each character to a sequence of bytes, while bytes represent raw binary data that may not necessarily correspond to any particular character encoding. ** Encoding**: Python strings are used to represent text data, while bytes are used to represent binary data. Strings are typically encoded using a character encoding such as UTF-8 or ASCII, which maps each character to a sequence of bytes, while bytes represent raw binary data that may not necessarily correspond to any particular character encoding.
@@ -116,7 +116,7 @@ Size of s2: 104
``` ```
### 4. Given this sample CSV file (tomato_sales.csv): #### 4. Given this sample CSV file (tomato_sales.csv):
``` ```
Store,Region,Tomato_Sales Store,Region,Tomato_Sales
Store1,East,300 Store1,East,300