Problem 52 - Fundamentals of Mathematics

Question

For the following problems, write each number using digits. One hundred trillion, one

Step-by-Step Solution

Answer

100,000,000,000,001

Step 1: Understand Place Value

To write 'one hundred trillion' using digits, we need to understand place value. A trillion has 12 zeros, so 'one hundred trillion' will be 100 followed by 12 zeros.

Step 2: Write the Number with Digits

Since a trillion is represented as 1,000,000,000,000, we multiply this by 100. Thus, one hundred trillion is written as 100,000,000,000,000.

Step 3: Add the Final Number

The number given includes an additional 'one'. We add 1 to the previous number. Therefore, one hundred trillion, one is written as 100,000,000,000,001.

Key Concepts

Understanding Trillion

When you hear the term 'trillion', you’re dealing with a very large number. A trillion is a one followed by 12 zeros in the base-10 number system. In numerical terms, this would be represented as \(1,000,000,000,000\).

Understanding such large numbers can be challenging, but it's crucial for tasks involving big data, astronomy, and national budgets. For clarity, here’s a simple breakdown:

• A trillion is a thousand billion (1,000 x 1,000,000,000).
• It's a million million (1,000,000 x 1,000,000).

By grasping how massive a trillion is, we can better appreciate and manage the significance of numbers on an astronomical scale.

Writing Numbers in Digits

Converting words to numerical digits can be tricky, but it becomes much easier when you understand place value and recognize patterns in numbers.

Take 'one hundred trillion, one' as an example. If you break it down:

• The term 'one hundred trillion' is written as a number by identifying the base value of a trillion and multiplying it by 100: \(100 \times 1,000,000,000,000 = 100,000,000,000,000\).
• Then, add the additional 'one' to this large number: \(100,000,000,000,000 + 1 = 100,000,000,000,001\).

Understanding these steps allows you to transform large numerical expressions into more digestible forms for calculations and comprehension.

Mathematical Notation

Mathematical notation is the symbolic language used for representing numbers, variables, and operations in a concise form. It aids in simplifying complex mathematical thoughts and communication.

• The number one trillion (\(1,000,000,000,000\)) uses standard notation to express the concept of twelve zeros following a one.
• For even larger numbers, scientific notation is often employed. With scientific notation, one trillion is written as \(1 \times 10^{12}\), which clearly shows its magnitude without endless zeros.

The right use of mathematical notation ensures precision and clarity, which is critical for effectively conveying and solving mathematical problems, especially those involving large values like trillions.