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Chapter 4: Problem 9

In Exercises 9-22, write each Hindu-Arabic numeral in expanded form. 36

Short Answer

Expert verified
The expanded form of the number 36 is \(30 + 6\).

Step by step solution

01

Identify Place Values

The numeral 36 consists of two digits - 3 and 6. The 3 is in the tens place and the 6 is in the ones place.
02

Expand Using Place Values

In expanded form, a number is represented as the sum of each digit multiplied by its respective place value. Therefore, 36 can be written as (3*10) + (6*1).
03

Complete the Calculation

By multiplying, we get 30 + 6.

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Key Concepts

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

Hindu-Arabic Numerals
The Hindu-Arabic numeral system is the most commonly used numeral system in the world today. It features ten symbols, or digits, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This system originated in India and was later introduced to the Arab world before reaching Europe. Its universal adoption is due to its simplicity and efficiency in performing mathematical calculations.
This numeral system is a decimal-based system, meaning it operates on a base 10. This makes it intuitive and easy to use in everyday life due to our ten fingers.
Another characteristic of the Hindu-Arabic system is its positional property, which provides the foundation for calculating number values.
Place Value
Place value is a fundamental concept when working with numbers. It refers to the value or worth of a digit based on its position in a numeral. For example, in the number 36, each digit carries a different weight depending on where it is located:
  • The digit '3' in 36 is in the tens place, making its value 30.
  • The digit '6' is in the ones place, so its value is 6.
Understanding place value is crucial because it allows us to interpret numbers correctly and perform arithmetic operations effectively.
It isn't only important in simple calculations but also plays a vital role in complex mathematics, such as decimals, where each position to the right of a decimal point represents a decreasing power of ten.
Mathematical Notation
Mathematical notation is a way to represent numbers and operations using symbols, such as digits, plus signs, and multiplication signs. The expanded form is a type of mathematical notation that breaks down numbers into their components based on place value.
For the number 36, we write its expanded form as \(3 \times 10 + 6 \times 1\). This notation is a clear and standardized way to express numbers and ensure there is no ambiguity in their interpretation.
  • The multiplication symbol (\(\times\)) in our example shows that each digit is being multiplied by its place value.
  • The plus symbol (+) indicates that these values are being summed to arrive at the original number.
Learning mathematical notation aids in developing strong arithmetic skills as it provides a consistent method to convey mathematical ideas effectively.

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Most popular questions from this chapter

In Exercises 13鈥�24, subtract in the indicated base. $$ \begin{array}{r} 712_{\text {nine }} \\ -483_{\text {nine }} \\ \hline \end{array} $$

In Exercises 19-32, mentally convert each base ten numeral to a numeral in the given base. 37 to base six

In Exercises 33-48, convert each base ten numeral to a numeral in the given base. 129 to base three

In Exercises 29-36, write each Hindu-Arabic numeral as a Roman numeral. 1896

In Exercises 33-48, convert each base ten numeral to a numeral in the given base. 428 to base nine
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