Problem 14 - Thinking Mathematically

Question

Write each Hindu-Arabic numeral in expanded form. 902

Step-by-Step Solution

Answer

The expanded form of the Hindu-Arabic numeral 902 is 900 + 0 + 2.

Step 1: Identify the Place Value of Each Digit

Starting from the right, each place is worth ten times as much as the place to its right. In the numeral 902, the 2 is in the 'ones' place, the 0 is in the 'tens' place and the 9 is in the 'hundreds' place.

Step 2: Multiply Each Digit by its Place Value

To express the numeral in expanded form, multiply each digit in the numeral by its place value. The result is 900 (9 * 100), 0 (0 * 10), and 2 (2 * 1).

Step 3: Combine the Place Values

The final step is to present all these multiplied values together, which will give the expanded form. So, 902 in expanded form is 900 + 0 + 2.

Key Concepts

Place Value

Understanding place value is essential when working with numbers. It helps us grasp the significance of each digit in a number.

Place value means that the position of a digit in a number determines its value. The more left a digit is placed in a number, the greater its value. For example, in the number 902:

• The digit 2 is in the ones place.
• The digit 0 is in the tens place.
• The digit 9 is in the hundreds place.

Each place is ten times the value to its immediate right. This scale goes from ones, tens, hundreds, and so on. Knowing the place value allows you to understand and manipulate numbers in various mathematical tasks, like converting to expanded form.

Expanded Form

Expanded form shows a number broken down into the sum of its individual place values. This form highlights the contribution of each digit based on its position.

To write a number like 902 in expanded form, follow these steps:

• First, identify the place value of each digit. For instance, 9 is in the hundreds place, giving it a value of 900.
• Next, the 0 is in the tens place, which would be valued as 0 times 10, which is 0.
• Finally, the 2 in the ones place remains 2.

Adding these values together gives 902 in expanded form: 900 + 0 + 2. Expanded form offers a clear picture of how numbers are structured and helps in understanding components of larger numbers.

Hindu-Arabic Numerals

The Hindu-Arabic numeral system is the decimal system that most of the world uses today. It consists of ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This system is known for its efficiency and ease of use in arithmetic calculations.

Introduced to Europe through translations and the works of mathematicians like Fibonacci, this system replaced cumbersome Roman numerals. It features many key benefits, such as:

• The concept of zero, which acts as a placeholder, making operations like subtraction much more straightforward.
• Its place value system - where the position of each digit affects its value - allowing for simple representation of large numbers.
• Decimal point notation, facilitating representation of fractions and decimal numbers.

Using this system, understanding numbers like 902 or performing numerical operations becomes intuitive and manageable.