Problem 37 - Prealgebra

Question

In the following exercises, write each number as a whole number using digits. three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen

Step-by-Step Solution

Answer

3,226,512,017

Step 1: Identify the place values

Recognize the components of the number: billions, millions, thousands, and units.

Step 2: Break down the number

The given number is three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen.

Step 3: Convert each part to digits

Convert each word to its corresponding digit: 'three billion' to 3,000,000,000, 'two hundred twenty-six million' to 226,000,000, 'five hundred twelve thousand' to 512,000, 'seventeen' to 17.

Step 4: Combine all parts

Combine the digits of all parts together: 3,000,000,000 + 226,000,000 + 512,000 + 17.

Step 5: Write the final number

Write the final number as a whole number using digits: 3,226,512,017.

Key Concepts

Place Value

Understanding place value is crucial in writing numbers. Place value refers to the value of each digit in a number based on its position. The right-most digit has the smallest value, known as the 'units' place. As you move left, each position increases in value by a power of ten.

For example, in the number 3,226,512,017, the place values are:

• 3 is in the billions place.
• 2 is in the hundred millions place.
• 2 is in the ten millions place.
• 6 is in the millions place.
• 5 is in the hundred thousands place.
• 1 is in the ten thousands place.
• 2 is in the thousands place.
• 0 is in the hundreds place.
• 1 is in the tens place.
• 7 is in the units place.

Each digit's position determines its value. For example, the 3 in 3,000,000,000 represents three billion, not just three units.

Recognizing place value helps in converting numbers written in words to digits and ensures accuracy when performing arithmetic operations.

Whole Numbers

Whole numbers are numbers without fractions or decimals. They include all the positive integers and zero. Essentially, they are the numbers you use to count objects.

Examples of whole numbers include 0, 1, 2, 3, and so on. They are straightforward but play an essential role in understanding more complex mathematical concepts.

Remember, whole numbers do not include negative numbers, fractions, or decimals. Therefore, the number 3,226,512,017 is a whole number because it is composed of digits only without any decimal or fractional parts.

Understanding this helps students distinguish between different types of numbers and use them correctly in various mathematical contexts.

Number Conversion

Number conversion involves transforming numbers written in words into digits. It requires understanding and correctly interpreting the place values within a number.

Let's break down the process using our example: 'three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen.'

• Identify each section: billions, millions, thousands, and units.
• Convert each word group to its digit form:
  
  • 'Three billion' converts to 3,000,000,000.
  • 'Two hundred twenty-six million' converts to 226,000,000.
  • 'Five hundred twelve thousand' converts to 512,000.
  • 'Seventeen' converts to 17.
• Combine all parts: 3,000,000,000 + 226,000,000 + 512,000 + 17.

The final number in digits is 3,226,512,017.

By following this step-by-step method, students can accurately convert any number written in words into its numeric form. This is an essential skill not only for mathematics but also for real-world applications such as reading financial statements or understanding large quantities.