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Chapter 4: Problem 13

Write each Hindu-Arabic numeral in expanded form. 703

Short Answer

Expert verified
The expanded form of the number 703 is \(700 + 0 + 3\).

Step by step solution

01

Identify Digits and Place Values

The number 703 has three digits: 7, 0, and 3. Identify the place value for each digit starting from right to left. The first digit (3) is in the unit's place (10^0), the second digit (0) is in the ten's place (10^1) and the third digit (7) is in the hundred's place (10^2).
02

Convert Each Digit to Its Place Value

Multiply each digit by its place value. This gives: \(7 \times 10^2\), \(0 \times 10^1\), and \(3 \times 10^0\).
03

Write in Expanded Form

Writing these out, we get: \(700 + 0 + 3\)

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Key Concepts

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

Hindu-Arabic numerals
Hindu-Arabic numerals are the number symbols most widely used today. They consist of ten different digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This numeral system is called "Hindu-Arabic" because it originated in India, influenced by Hindu mathematicians, and was later transmitted to the Western world through Arab mathematicians. This system is powerful because it uses a base of ten, known as the decimal system. Using ten digits, we can represent any number, from very small to extremely large. Each position in a number represents a different power of ten. This is what allows us to understand large complexities of numbers in a simple, consistent manner.
Place Value
Understanding place value is crucial in the Hindu-Arabic numeral system. Place value refers to the value of a digit depending on its position in the number. For example, in the number 703, each digit has a unique place value:
  • The digit 3 has a place value of 1 (or 10^0), which is the units or ones place.
  • The digit 0 is in the tens place (or 10^1), though it contributes no value in multiplication.
  • The digit 7 has a place value of 100 (or 10^2), which is the hundreds place.
Place value is what makes it possible to write numbers in expanded form. By multiplying each digit by its place value, the number is expressed as the sum of each individual value.
Mathematical Notation
Mathematical notation involves using symbols and numbers to represent mathematical concepts and operations. In writing numbers, mathematical notation highlights the relationship between digits and their values through multiplication with powers of ten. For instance, in expanded form, the number 703 is written as:
  • 700: This comes from multiplying the digit 7 by its place value (10^2).
  • 0: Even though 0 is in the ten's place, it does not change the value of the number but is noted for correctness.
  • 3: The ones place does not need multiplication with powers of ten, making it simply 3.
Expanded form enables better comprehension of a number's structure and significance, breaking it down into simpler parts through mathematical notation.

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Most popular questions from this chapter

Organize a debate. One side represents people who favor performing computations by hand, using the methods and procedures discussed in this section, but applied to base ten numerals. The other side represents people who favor the use of calculators for performing all computations. Include the merits of each approach in the debate.

Multiply in the indicated base. $$ \begin{array}{r} 543_{\text {seven }} \\ \times \quad 5_{\text {seven }} \\ \hline \end{array} $$

Describe two difficulties that youngsters encounter when learning to add, subtract, multiply, and divide using HinduArabic numerals. Base your answer on difficulties that are encountered when performing these computations in bases other than ten.

Describe how a number is represented in the Egyptian numeration system.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. It takes far more space to represent numbers in the Roman numeration system than in the Egyptian numeration system.
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