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Chapter 4: Problem 17

Write each Hindu-Arabic numeral in expanded form. 3070

Short Answer

Expert verified
The Hindu-Arabic numeral 3070 in expanded form is 3000 + 0 + 70 + 0.

Step by step solution

01

Identification of digits and their place values

First identify each digit in the Hindu-Arabic numeral and its corresponding place value. In the numeral 3070, the digits are 3, 0, 7, 0. The place values are thousand (3), hundred (0), ten (7) and unit (0).
02

Multiply each digit by its place value

Next, multiply each digit by its corresponding place value. Hence, we have 3000 (which is 3 times 1000), 0 (which is 0 times 100), 70 (which is 7 times 10), and 0 (which is 0 times 1).
03

Write the numeral in expanded form

Write the numeral in expanded form by joining each product obtained in step 2 with a '+' sign. Therefore, 3070 in expanded form equals 3000 + 0 + 70 + 0.

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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, which we use every day, is a decimal positional numeral system. This means it is based on ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These numerals are arranged in a specific way to represent values, from very small to very large numbers.
This system is both simple and efficient because it is built around the concept of place value, allowing us to understand and communicate complex information using just these ten symbols.
For example, the numeral 3070 in the Hindu-Arabic system expresses a combination of different values that are determined by the position of each digit.
Place values
Place value is essential to understanding numbers in the Hindu-Arabic system. Each digit in a number has a place, and each place has a specific value, which increases by a factor of ten as you move from right to left.
For instance:
  • The rightmost digit is in the units place and holds a value between 0 and 9.
  • The next digit to the left is in the tens place and represents a multiple of ten.
  • Further left, a digit is in the hundreds place, representing a multiple of one hundred.
  • Continuing the pattern, thousands, ten thousands, and so on, follow.
In the number 3070, find each digit's place:
  • 3 is in the thousands place; hence its value is 3000.
  • 0 is in the hundreds place; its value is 0 because 0 multiplied by 100 equals 0.
  • 7 is in the tens place; thus, it equates to 70.
  • The last 0 is in the units place, adding no extra value to the number.
Multiplying by place value
Multiplying each digit by its place value is how we construct the expanded form of a number. Start with identifying each digit's place and then perform multiplication to see what each contributes to the overall number.
In the example of 3070:
  • The digit 3 is in the thousands position, so we calculate 3 times 1000, resulting in 3000.
  • The digit in the hundreds place is 0, which results in 0 when multiplied by 100.
  • The number 7 is in the tens place: 7 times 10 equals 70.
  • The units place is again 0, contributing nothing to the total through multiplication.
Finally, to write in expanded form, these products are summed: 3070 becomes 3000 + 0 + 70 + 0. This breakdown shows how each digit contributes individually to form the complete number, reflecting the significance of both place values and multiplication in our numeral system.

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Most popular questions from this chapter

Use Table 4.7 on page 241 to solve Exercises 13-36. Write each Roman numeral as a Hindu-Arabic numeral. MMDCLXXVII

Add in the indicated base. $$ \begin{array}{r} 632_{\text {seven }} \\ +564_{\text {seven }} \\ \hline \end{array} $$

Perform the indicated operations. \(\mathrm{B} 5_{\text {sixteen }} \times 2 \mathrm{C}_{\text {sixteen }}\)

Subtract in the indicated base. $$ \begin{array}{r} 23_{\text {five }} \\ -14_{\text {five }} \\ \hline \end{array} $$

Write each Ionic Greek numeral as a Hindu-Arabic numeral. \(\iota \beta\)
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