Problem 6 - Fundamentals of Mathematics

Question

Express each number using digits. Twenty trillion, three billion, eighty million, one hundred nine thousand, four hundred two.

Step-by-Step Solution

Answer

The number is expressed as 20,003,080,109,402.

Step 1: Identify Place Values

Understand the different place values specified in the number: trillion, billion, million, thousand, and hundreds.

Step 2: Write Place Values with Zeros

Convert each place value into digits, noting its specific number of zeros. A trillion has 12 zeros, a billion has 9 zeros, a million has 6 zeros, a thousand has 3 zeros, and hundreds do not have zeros.

Step 3: Express Each Part Numerically

Write each part of the number using digits: - Twenty trillion as 20,000,000,000,000 - Three billion as 3,000,000,000 - Eighty million as 80,000,000 - One hundred nine thousand as 109,000 - Four hundred two as 402.

Step 4: Combine All Parts Together

Add all these parts together, aligning them properly according to their place value to form the complete number. Thus, 20,000,000,000,000 + 3,000,000,000 + 80,000,000 + 109,000 + 402 is written as a single number.

Key Concepts

Understanding Number Notation

Number notation is a way to express numbers using digits. In this context, understanding how large numbers are composed is crucial. Numbers can be written in words or digits. Writing numbers in digit form allows for easy readability and quick understanding. For instance, in the exercise, numbers like "twenty trillion" are broken down into their digit form to make their size more comprehensible.

• Writing numbers in digit form involves using place values.
• Each category, like trillions or millions, has a specific number of zeros associated with it.
• Proper number notation makes it easier to handle mathematical operations.

Number notation using digits is especially valuable in various fields like finance and science, where dealing with large numbers is commonplace.

Dealing with Large Numbers

Large numbers can seem daunting at first glance, especially when written in words. However, when expressed through digits, these numbers can be managed more easily. It's all about understanding their place values. For instance, a trillion has 12 zeros. Knowing this helps in converting worded numbers into numerical form more accurately.

• Breaking down a large number into smaller parts helps in understanding it better.
• For example, the number "twenty trillion, three billion" can be expressed by enhancing focus on each segment individually first.
• Always start by identifying the largest place value to maintain order.

Converting large numbers from words to digits requires practice, but is a valuable skill that improves clarity in communication and computation.

Digit Representation and Place Value

Digit representation involves expressing each part of a number based on its position or place value. Each digit in a number has a specific place value that determines its contribution to the whole number. For large numbers, understanding place value is key. Once you know how many zeros each place value carries, combining these correctly forms the large number accurately. For example:

• "Twenty trillion" can be represented with 20 at the beginning followed by 12 zeros.
• "Three billion" is 3 followed by 9 zeros.
• Align each number expression in place, especially when adding them together.
• This keeps all digits in their correct positions, ensuring the total value is correct.

The clear understanding of digit representation and place value solidifies one's ability to handle and work with both small and large numbers effectively.