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Chapter 5: Problem 47

\(8 \times 10^{5}+3 \times 10^{4}\)

Short Answer

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Step by step solution

01

Understand the Problem

The task is to evaluate the expression involving scientific notation: \(8 \times 10^{5}+3 \times 10^{4}\)
02

Break Down Each Term

Write each term in standard form. \(8 \times 10^{5} = 800,000\) \(3 \times 10^{4} = 30,000\)
03

Add the Two Terms

Now add the two standard form numbers together:\(800,000 + 30,000 = 830,000\)

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Key Concepts

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

Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a compact form. It simplifies calculations and makes it easier to read and understand numbers that have many zeros. In scientific notation, a number is written as the product of two parts: a coefficient and a power of ten. For example, the number 800,000 can be written in scientific notation as \(8 \times 10^{5}\). The coefficient (8) is a number between 1 and 10, and the exponent (5) shows how many times the coefficient should be multiplied by 10.
Standard Form
Standard form refers to writing out numbers without using exponents, which is typically how we see and use numbers in everyday life. For instance, a number like \(8 \times 10^{5}\) in scientific notation translates to 800,000 in standard form. Converting from scientific notation to standard form is straightforward: multiply the coefficient by ten raised to the given exponent. Here are some examples to make it clearer:
* \(3 \times 10^{4}\) becomes 30,000.
* \(2.5 \times 10^{6}\) becomes 2,500,000.
This process involves moving the decimal point to the right for positive exponents or to the left for negative exponents.
Addition of Large Numbers
When adding large numbers, especially those in scientific notation, it's helpful to first convert them to standard form. Consider the addition problem in the exercise: \(8 \times 10^{5}\) + \(3 \times 10^{4}\). We first convert these numbers to their standard forms: 800,000 and 30,000. Then, we simply add these numbers as usual: 800,000 + 30,000 = 830,000. Afterward, we could write the result back in scientific notation if needed. This step-by-step approach ensures accuracy and makes it easier to handle and combine large values.

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