Problem 56 For Exercises $49-64$, convert... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 10: Problem 56

For Exercises $49-64$, convert to standard form. $$5.5 \times 10^{3}$$

Short Answer

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Step by step solution

Understanding the scientific notation

The given number is in scientific notation: $5.5 \times 10^{3}$. This format represents the number as a product of a coefficient and a power of 10.

Identify the components

In the notation $5.5 \times 10^{3}$, the coefficient is 5.5, and we need to multiply this by $10^{3}$ (which equals 1000).

Perform the multiplication

To find the standard form, multiply the coefficient by the power of 10: $5.5 \times 10^{3} = 5.5 \times 1000 = 5500$.

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Key Concepts

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

Standard Form

Standard form, also known as scientific notation, is a way to express very large or very small numbers in a simplified manner. This notation involves two main components: a coefficient and a power of 10. For instance, in the number given in the exercise, 5.5 is the coefficient and $10^{3}$ is the power of 10. Using this method helps avoid writing out long strings of zeros. By converting to standard form, mathematical operations become easier and more manageable. Always remember the basic structure: Coefficient $\times$ $10^{power}$.

Multiplying Powers of Ten

When transforming a number in scientific notation to its standard form, you must multiply the coefficient by the power of 10. Here, we have 5.5 as the coefficient and $10^{3}$ as the power of 10. To understand powers of 10, let's see what $10^{3}$ means. This translates to 10 multiplied by itself three times (10 $\times$ 10 $\times$ 10), which equals 1000. Thus, multiplying 5.5 by 1000, we get: $$5.5 \times 1000 = 5500.$$ This final product, 5500, is the number in its standard form. By breaking down the multiplication process, we realize how large numbers become more comprehensible.

Converting Scientific Notation

Converting scientific notation to a standard form involves a few steps that simplify complex numbers. Start with identifying the coefficient and the power of 10 in the scientific notation. In our example, $5.5 \times 10^{3}$, 5.5 is your coefficient and $10^{3}$ is your power. To convert, follow these steps:

First, rewrite the power of 10 as a whole number (i.e., $10^{3} = 1000$).
Next, multiply the coefficient by this number: $5.5 \times 1000 = 5500$.

This deliver the number in standard form, 5500. Practicing these steps ensures accurate and quick conversions, making complex calculations simpler and faster.

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91影视

For Exercises \(49-64\), convert to standard form. $$5.5 \times 10^{3}$$

Short Answer

Step by step solution

Understanding the scientific notation

Identify the components

Perform the multiplication

Key Concepts

Standard Form

Multiplying Powers of Ten

Converting Scientific Notation

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