Express The Given Expanded Form As A Hindu-Arabic Numeral.${ \left(9 \times 10^3\right) + \left(0 \times 10^2\right) + \left(0 \times 10^1\right) + \left(5 \times 1\right) = \square }$(Simplify Your Answer.)
Introduction
In mathematics, the Hindu-Arabic numeral system is a widely used method of representing numbers. It is a decimal system that uses ten distinct symbols, including 0, to represent numbers. In this article, we will explore how to express a given expanded form as a Hindu-Arabic numeral.
Understanding Expanded Form
Expanded form is a way of representing a number as a sum of its place values. Each place value is represented by a coefficient multiplied by a power of 10. For example, the number 1234 can be represented in expanded form as:
(1 × 10^3) + (2 × 10^2) + (3 × 10^1) + (4 × 10^0)
Expressing Expanded Form as Hindu-Arabic Numeral
To express the given expanded form as a Hindu-Arabic numeral, we need to evaluate the coefficients and powers of 10. Let's consider the given expanded form:
(9 × 10^3) + (0 × 10^2) + (0 × 10^1) + (5 × 1)
Step 1: Evaluate the Coefficients
The coefficients are the numbers that are multiplied by the powers of 10. In this case, the coefficients are 9, 0, 0, and 5.
Step 2: Evaluate the Powers of 10
The powers of 10 are the exponents that are multiplied by the coefficients. In this case, the powers of 10 are 10^3, 10^2, 10^1, and 1.
Step 3: Multiply the Coefficients and Powers of 10
Now, we need to multiply the coefficients and powers of 10. This will give us the place values of the number.
(9 × 10^3) = 9000 (0 × 10^2) = 0 (0 × 10^1) = 0 (5 × 1) = 5
Step 4: Add the Place Values
Finally, we need to add the place values to get the Hindu-Arabic numeral.
9000 + 0 + 0 + 5 = 9005
Conclusion
In this article, we have learned how to express a given expanded form as a Hindu-Arabic numeral. We have broken down the process into four steps: evaluating the coefficients, evaluating the powers of 10, multiplying the coefficients and powers of 10, and adding the place values. By following these steps, we can easily convert an expanded form to a Hindu-Arabic numeral.
Example 1: Expressing Expanded Form as Hindu-Arabic Numeral
Let's consider another example:
(7 × 10^4) + (3 × 10^3) + (2 × 10^2) + (1 × 10^1) + (4 × 10^0)
Step 1: Evaluate the Coefficients
The coefficients are 7, 3, 2, 1, and 4.
Step 2: Evaluate the Powers of 10
The powers of 10 are 10^4, 10^3, 10^2, 10^1, and 10^0.
Step 3: Multiply the Coefficients and Powers of 10
Now, we need to multiply the coefficients and powers of 10.
(7 × 10^4) = 70000 (3 × 10^3) = 3000 (2 × 10^2) = 200 (1 × 10^1) = 10 (4 × 10^0) = 4
Step 4: Add the Place Values
Finally, we need to add the place values to get the Hindu-Arabic numeral.
70000 + 3000 + 200 + 10 + 4 = 73114
Example 2: Expressing Expanded Form as Hindu-Arabic Numeral
Let's consider another example:
(9 × 10^2) + (8 × 10^1) + (7 × 10^0)
Step 1: Evaluate the Coefficients
The coefficients are 9, 8, and 7.
Step 2: Evaluate the Powers of 10
The powers of 10 are 10^2, 10^1, and 10^0.
Step 3: Multiply the Coefficients and Powers of 10
Now, we need to multiply the coefficients and powers of 10.
(9 × 10^2) = 900 (8 × 10^1) = 80 (7 × 10^0) = 7
Step 4: Add the Place Values
Finally, we need to add the place values to get the Hindu-Arabic numeral.
900 + 80 + 7 = 987
Conclusion
Frequently Asked Questions
In this article, we will answer some frequently asked questions about expressing expanded form as a Hindu-Arabic numeral.
Q: What is the Hindu-Arabic numeral system?
A: The Hindu-Arabic numeral system is a decimal system that uses ten distinct symbols, including 0, to represent numbers.
Q: What is expanded form?
A: Expanded form is a way of representing a number as a sum of its place values. Each place value is represented by a coefficient multiplied by a power of 10.
Q: How do I express an expanded form as a Hindu-Arabic numeral?
A: To express an expanded form as a Hindu-Arabic numeral, you need to evaluate the coefficients and powers of 10, multiply the coefficients and powers of 10, and add the place values.
Q: What are the steps to express an expanded form as a Hindu-Arabic numeral?
A: The steps to express an expanded form as a Hindu-Arabic numeral are:
- Evaluate the coefficients
- Evaluate the powers of 10
- Multiply the coefficients and powers of 10
- Add the place values
Q: Can you give an example of expressing an expanded form as a Hindu-Arabic numeral?
A: Let's consider the expanded form:
(9 × 10^3) + (0 × 10^2) + (0 × 10^1) + (5 × 1)
To express this expanded form as a Hindu-Arabic numeral, we need to evaluate the coefficients and powers of 10, multiply the coefficients and powers of 10, and add the place values.
(9 × 10^3) = 9000 (0 × 10^2) = 0 (0 × 10^1) = 0 (5 × 1) = 5
Adding the place values, we get:
9000 + 0 + 0 + 5 = 9005
Q: What if the expanded form has negative coefficients?
A: If the expanded form has negative coefficients, you need to multiply the coefficient by -1 and then evaluate the powers of 10.
For example, let's consider the expanded form:
(-3 × 10^2) + (2 × 10^1) + (1 × 10^0)
To express this expanded form as a Hindu-Arabic numeral, we need to evaluate the coefficients and powers of 10, multiply the coefficients and powers of 10, and add the place values.
(-3 × 10^2) = -300 (2 × 10^1) = 20 (1 × 10^0) = 1
Adding the place values, we get:
-300 + 20 + 1 = -279
Q: Can you give an example of expressing an expanded form with decimal coefficients as a Hindu-Arabic numeral?
A: Let's consider the expanded form:
(3.5 × 10^2) + (2.2 × 10^1) + (1.1 × 10^0)
To express this expanded form as a Hindu-Arabic numeral, we need to evaluate the coefficients and powers of 10, multiply the coefficients and powers of 10, and add the place values.
(3.5 × 10^2) = 350 (2.2 × 10^1) = 22 (1.1 × 10^0) = 1.1
Adding the place values, we get:
350 + 22 + 1.1 = 373.1
Conclusion
In this article, we have answered some frequently asked questions about expressing expanded form as a Hindu-Arabic numeral. We have covered the steps to express an expanded form as a Hindu-Arabic numeral, including evaluating the coefficients and powers of 10, multiplying the coefficients and powers of 10, and adding the place values. We have also provided examples of expressing expanded form with negative coefficients and decimal coefficients as a Hindu-Arabic numeral.