Problem 20 - Prealgebra

Question

In the following exercises, name each number in words. $$62,008,465$$

Step-by-Step Solution

Answer

Sixty-two million eight thousand four hundred sixty-five.

Step 1: Identify the Place Values

Break down the number into its place values: 62,008,465. Format as millions, thousands, and units.

Step 2: Convert Millions

The first part of the number is in the millions place: 62 million.

Step 3: Convert Thousands

Next, the thousands place: 008 thousand, which is 8 thousand.

Step 4: Convert Units

Finally, the units place: 465.

Step 5: Combine the Words

Combine all parts: 62 million 8 thousand 465.

Key Concepts

place value

Place value is a fundamental concept in mathematics. It helps us understand the value of each digit in a number based on its position. Each position in a number has a different place value, like ones, tens, hundreds, thousands, and so on. For example, in the number 62,008,465:

• The digit `6` is in the ten-million place, so its value is 60,000,000
• The digit `2` is in the million place, so its value is 2,000,000
• In the smaller units, the `4` is in the hundreds place (400), `6` is in the tens place (60), and the final `5` is in the units place (5).

Knowing place values is essential to break down and understand large numbers.

reading large numbers

Reading large numbers can seem difficult, but it gets easier with practice. Large numbers in standard form are typically divided into groups of three digits using commas. Each group corresponds to a particular place value category. For example, the number 62,008,465 can be broken down as:

• 62 million
• 008 thousand
• 465 units

This way, each segment of the number becomes more manageable to read. Always start from the left, reading each group by its place value category. This helps in understanding the number easily and accurately.

mathematical notation

Mathematical notation refers to the symbols and formatting used to represent numbers and operations clearly. In numbers, commas and periods play critical roles in readability. For example, 62,008,465 is easier to read and understand than 62008465. Some common notations include:

• Using commas to separate groups of three digits (thousands, millions, etc.)
• Decimal points to denote fractions of a whole
• Parentheses to group operations in equations

These notations help to avoid confusion and ensure clarity in communication.

number decomposition

Decomposing numbers means breaking down a large number into smaller, more manageable parts. This technique is especially useful for understanding and working with large numbers. For instance, the number 62,008,465 is decomposed into:

• 62 million
• 8 thousand
• 465 units

Each part can then be understood in terms of its own place value. This process makes it easier to read, write, and perform operations with large numbers. Decomposing numbers also helps in solving mathematical problems by simplifying complex numbers into more straightforward components.