Question

Some of the prefixes of the SI units have crept into everyday language. ( $a$ ) What is the weekly equivalent of an annual salary of $36\mathrm{K}(=36\mathrm{k}\mathrm{\$})?(b)$ A lottery awards 10 megabucks as the top prize, payable over 20 years. How much is received in each monthly check? ( $c$ ) The hard disk of a computer has a capacity of $30\mathrm{GB}$ ( $=30$ gigabytes). At 8 bytes/word, how many words can it store?

Short answer

The equivalent weekly salary is approximately $692.31. The monthly lottery check equals approximately $41,667. The hard disk can store approximately $3.75\times {10}^9$ words.

Step-by-step solution

Annual Salary Conversion to Weekly Equivalent

The task requests to convert an annual salary of $36k to equivalent weekly salary. An year consists of 52 weeks. Therefore, divide the annual salary by 52 to get the weekly salary. Mathematically this would be $$\frac{36,000}{52}$$ We find that the weekly salary equals approximately $692.31.

Lottery Money Conversion to Monthly Checks

The lottery prize is 10 megabucks which is equivalent to 10 million dollars. This amount is payable over 20 years. There are 12 months in a year, so the total number of payments is $12\times 20$. Dividing 10,000,000 by 240 gives the monthly payment. Mathematically this would be $$\frac{10,000,000}{240}$$ We find that the monthly check equals approximately $41,667.

Hard Disk Storage Calculation

The hard disk has a storage capacity of 30 gigabytes and each word consumes 8 bytes of storage. Since 1 gigabyte is equal to ${10}^9$ bytes, the total number of bytes the hard disk can store is $30\times {10}^9$. To find out how many words it can store, divide the total number of bytes by the number of bytes per word. Mathematically this would be $$\frac{30\times {10}^9}{8}$$ We find that the hard disk can store approximately $3.75\times {10}^9$ words.

Key concepts

Annual Salary Conversion

When converting an annual salary to a weekly equivalent, we need to consider how many weeks are in a year. In most cases, a year is considered to have 52 weeks. To achieve the weekly salary from an annual salary, we simply divide the total annual amount by 52. This way, you can easily calculate how much you earn per week.
For example: Given an annual salary of $36,000 (often written as 36K), the weekly salary can be calculated as follows:

• Annual Salary = 36,000 dollars
• Weeks in a year = 52
• Weekly Salary = $\frac{36,000}{52}\approx 692.31\text{ dollars}$

This calculation is helpful for budgeting monthly expenses or comparing job offers that provide weekly compensation.

Lottery Prize Distribution

In the context of lottery prize distribution, the concept is about how to split a large prize over a certain period of time. If you win a lottery that pays out over several years, the total amount is divided into equal payments. For example, if a lottery awards a prize of 10 million dollars (referred to as 10 megabucks here), payable over a span of 20 years, it must be divided into regular monthly installments to know what amount is received each month.
Here's how it's calculated:

• Total Prize Amount = 10,000,000 dollars
• Years of Payment = 20 years
• Number of Monthly Payments = 20 years $\times 12\text{ months/year}=240\text{ months}$
• Monthly Check = $\frac{10,000,000}{240}\approx 41,667\text{ dollars}$

This approach ensures that the prize money is distributed evenly every month over the period of 20 years.

Hard Disk Storage Calculation

Understanding how to calculate hard disk storage is crucial in knowing how much data a device can hold. Storage capacity is often given in gigabytes (GB), where 1 gigabyte equals ${10}^9$ bytes. When you need to determine how many words a disk can store, you must consider how many bytes each word occupies. In this context, each word takes up 8 bytes.
Given a hard disk with a capacity of 30 gigabytes, you can find out how many words it can store as follows:

• Total Storage in Bytes = 30 GB $\times {10}^9\text{ bytes/GB}=30\times {10}^9\text{ bytes}$
• Bytes per Word = 8 bytes
• Number of Words Stored = $\frac{30\times {10}^9}{8}=3.75\times {10}^9\text{ words}$

This method allows you to understand and plan for the storage needs based on your data consumption habits.