Problem 50 - Fundamentals of Mathematics

Question

For the following problems, write each number using digits. Twenty-three billion

Step-by-Step Solution

Answer

The number is 23,000,000,000.

Step 1: Understand the Place Value System

The number naming system in English uses units like 'thousands,' 'millions,' 'billions,' etc. Here, 'twenty-three billion' suggests a number that has 'billion' as its highest place value.

Step 2: Identify the Value of a Billion

One billion is equivalent to 1,000,000,000 (a 1 followed by 9 zeros). In numeric form, this is 10^9.

Step 3: Find the Value of Twenty-three Billion

Since 'twenty-three' is the number of billions, multiply 23 by the numeric value of a billion. Thus, twenty-three billion is equal to 23 x 1,000,000,000.

Step 4: Write Out the Digits

Perform the multiplication: 23 times 1,000,000,000 equals 23,000,000,000. This is the numeric representation of 'twenty-three billion.'

Key Concepts

Billion

The word 'billion' is a key term in understanding our number system, especially when dealing with large numbers. In the place value system, 'billion' represents a significant unit that helps us to organize and comprehend large figures easily. It is crucial to understand that a billion in numeric terms is expressed as 1,000,000,000, which means it is a whopping 1 followed by 9 zeros.
This large number falls under the category known as the 'thousands' system, where each unit increases in multiples of thousands. This is different from the European system, which once used 'billion' to represent a million million (or a thousand million in scientific notation).

• A single billion can be expressed as \(10^9\) in scientific notation, which simplifies the understanding and computation for large numbers.
• When we speak of 'billion' in contexts such as economics or population, we are referring to this exact value.

Understanding 'billion' is not just about knowing how many zeros follow the 1, but also about knowing where it sits in the larger framework of our number system.

Numeric Representation

Numeric representation involves writing numbers in a precise and clear format using digits. For instance, the problem "twenty-three billion" requires us to understand how this verbal description translates into numbers. This involves recognizing not just the values themselves but the positions they hold in the place value system.
To convert words into numbers, follow these steps:

• Identify the base unit, in this case, 'billion.'
• Recognize the multiplier, which is 'twenty-three.'
• Combine them using multiplication to obtain digits. This means taking 23 and multiplying it by a billion resulting in 23,000,000,000.

This practice is vital in contexts from accounting and finance to computer science, where precise numeric representation is needed to avoid errors.
Words and numbers convertibility play a central role in learning how to write down large numbers swiftly. Doing so efficiently helps in reducing the risk of mistakes when dealing with extensive datasets or accounting figures.

Multiplication

Multiplication is a fundamental operation in math, used to find the total of repeated additions or in this context, to scale numbers effectively within the place value system. When converting 'twenty-three billion' into digits, multiplication allows us to apply the quantity 'twenty-three' to the base unit 'billion'.
The process for solving involves:

• Recognizing that 'billion' is equivalent to 1,000,000,000.
• Multiplying it by 23, as 'twenty-three' indicates how many units of one billion we have.
• Conducting the multiplication: \(23 \times 10^9\).

By multiplying these numbers, you end up with a product of 23,000,000,000.
Multiplication isn't merely about finding totals; it's about scaling up units effectively. This is why it is so crucial in word problems where numbers must be written, compared, or calculated according to certain standards and systems.