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Chapter 4: Problem 10

Write each Hindu-Arabic numeral in expanded form. 65

Short Answer

Expert verified
The expanded form of 65 is 60 + 5.

Step by step solution

01

Identify the Digits and Their Place Values

The number 65 has two digits. The first digit is 6, which is in the tens place. The second digit is 5, which is in the ones place.
02

Write Each Digit in Terms of Its Place Value

The digit 6 represents 6 tens, or 60, and the digit 5 represents 5 ones, or 5.
03

Write the Number in Expanded Form

Combine the values found in the previous step to form the expanded notation of the number. So, 65 becomes 60 + 5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Values
Understanding place values is essential when breaking down numbers. Each digit in a number has a specific place value that determines its worth. This is based on its position within the number. For example, in the number 65, there are two digits: 6 and 5.
  • 6 is in the tens place, which means it represents 60 because the place value of tens is 10.
  • 5 is in the ones place, which simply means 5, as the place value of ones is 1.
By knowing the place values, you can understand how much each digit contributes to the total value of the number.
Hindu-Arabic Numeral
The Hindu-Arabic numeral system is the number system most commonly used today. It consists of ten digits from 0 to 9 and allows for an easy representation of any number, no matter how large. This system uses the concept of place values to distinguish between different magnitudes of numbers.

When we write a number like 65, we rely on this numeral system. It enables us to understand that 65 is more than just a combination of digits. It represents sixty and five through its place value logic. Without the Hindu-Arabic system, representing numbers succinctly and efficiently would be quite challenging!
Number Decomposition
Number decomposition involves breaking down a number into its individual components. This makes it easier to understand and work with. To decompose the number 65, you start by identifying each digit and its place value.

1. **Identify the Digits:** In 65, identify 6 and 5. 2. **Understand their Place Values:**
- 6 is in the tens place, contributing 60 to the number. - 5 is in the ones place, contributing 5 to the number.
3. **Combine for Expanded Form:** With this decomposition, 65 can be represented as 60 + 5 in expanded form. Understanding number decomposition is helpful in many mathematics problems, as it allows students to see numbers as the sum of their parts.

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Most popular questions from this chapter

Write each Hindu-Arabic numeral as a Roman numeral. 96

Describe how to add two numbers in a base other than ten. How do you express and record the sum of numbers in a column if that sum exceeds the base?

Arrange from smallest to largest: $$ 11111011_{\text {two }}, 3 \mathrm{~A} 6_{\text {twelve }}, 673_{\text {eight }} \text {. } $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Bases greater than ten are not possible because we are limited to ten digit symbols.

Multiply in the indicated base. $$ \begin{array}{r} 32_{\text {four }} \\ \times 23_{\text {four }} \\ \hline \end{array} $$
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