Problem 612 Multiply and write your answer i... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 612

Multiply and write your answer in decimal form. $$\frac{6 \times 10^{9}}{2 \times 10^{-1}}$$

Short Answer

Expert verified

30000000000

Step by step solution

Understand the Problem

We need to multiply the fraction $\frac{6 \times 10^{9}}{2 \times 10^{-1}}$, and write the answer in decimal form.

Simplify the Expression

First, multiply the coefficients (6 and 2): $ \frac{6}{2} = 3 $

Simplify the Exponent

Next, divide the exponential parts: $ \frac{10^{9}}{10^{-1}} = 10^{9 - (-1)} = 10^{10} $

Combine Results

Now combine the simplified coefficient with the simplified exponent: $ 3 \times 10^{10} $

Convert to Decimal Form

Write the result in decimal form by moving the decimal point 10 places to the right: $ 3 \times 10^{10} = 30000000000 $

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Key Concepts

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

Exponent Rules

When multiplying or dividing numbers with exponents, we apply specific rules. One crucial rule is that when dividing like bases, you subtract the exponent of the denominator from the exponent of the numerator. For example, if you have $ \frac{10^a}{10^b} $, it simplifies to $ 10^{a-b} $. This rule is essential in simplifying expressions, significantly reducing complexity. In the exercise provided, this rule is applied as follows: $ \frac{10^9}{10^{-1}} = 10^{9 - (-1)} = 10^{10} $. Always remember, subtracting a negative number is just like adding a positive. By understanding these rules, you can solve similar problems with ease.

Decimal Notation

Decimal notation is a way to write numbers in a more readable form, especially after calculations involving exponents. To convert an expression like $ 3 \times 10^{10} $ into decimal form, you move the decimal point to the right for positive exponents. The number of times you move the decimal point equals the exponent value. For $ 3 \times 10^{10} $, move the decimal 10 places to the right, resulting in 30,000,000,000. This conversion is straightforward once you get the hang of it. The key is to keep track of how many places you need to move the decimal and apply it correctly.

Simplifying Fractions

Simplifying fractions makes calculations easier and results clearer. It involves reducing a fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number. In the given exercise, the fraction $ \frac{6 \times 10^{9}}{2 \times 10^{-1}} $ is simplified by dividing the coefficients: $ \frac{6}{2} = 3 $. Simplifying fractions early in the problem can help avoid more complex calculations later. Always start by simplifying what you can, one step at a time. This approach keeps your work tidy and manageable.

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91影视

Multiply and write your answer in decimal form. $$\frac{6 \times 10^{9}}{2 \times 10^{-1}}$$

Short Answer

Step by step solution

Understand the Problem

Simplify the Expression

Simplify the Exponent

Combine Results

Convert to Decimal Form

Key Concepts

Exponent Rules

Decimal Notation

Simplifying Fractions

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