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Chapter 5: Problem 38

Write each number without exponents. $$ -6 \times 10^{-4} $$

Short Answer

Expert verified
-0.0006

Step by step solution

01

Understand the Exponent

The exponent tells you how many places to move the decimal point. A negative exponent indicates moving the decimal point to the left.
02

Moving the Decimal Point

Starting with -6, move the decimal point 4 places to the left. This involves adding zeros to the left of the number.
03

Write the Final Number

After moving the decimal point 4 places to the left, -6 becomes -0.0006.

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Key Concepts

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

Exponents
Exponents tell us how many times to multiply a number by itself. For example, in the expression \(2^3\), the exponent is 3, which means we multiply 2 by itself three times: \(2 \times 2 \times 2 = 8\).

Exponents can also be negative or positive. Positive exponents indicate repeated multiplication, while negative exponents often involve moving the decimal point. Understanding basic exponents is crucial for working with both large and small numbers effectively.
Decimal Point
A decimal point separates the whole number part from the fractional part of a number.

For example, in the number 12.34, 12 is the whole number part, and 34 is the fractional part.

When working with exponents, especially negative ones, the decimal point plays a critical role. It helps in determining the placement of the number in relation to powers of ten.

Always keep track of your decimal point when performing operations like multiplication or division with exponents.
Negative Exponent
Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent.

For example, \(10^{-2} \) translates to \( \frac{1}{10^2} = 0.01\).

In other words, we move the decimal point to the left. The original exercise involves \(-6 \times 10^{-4} \), and the negative exponent of -4 means we move the decimal point four places to the left. Starting with -6, this becomes -0.0006.

Mastering the concept of negative exponents allows you to handle very small numbers comfortably by transforming them into a form that is easier to read and understand.

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Most popular questions from this chapter

Perform each division. $$ \frac{y^{3}+1}{y+1} $$

Use scientific notation to calculate the answer to each problem. On February \(17,2009,\) Congress raised the U.S. government's debt limit to \(\$ 1.2 \times 10^{13} .\) When this national debt limit is reached, about how much will it be for every man, women, and child in the country? Use 300 million as the population of the United States.

Simplify by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(2 y^{-1} z^{2}\right)^{2}\left(3 y^{-2} z^{-3}\right)^{3}}{\left(y^{3} z^{2}\right)^{-1}} $$

Multiply. $$ \frac{1}{2}(4 m-8 n) $$

Multiply. $$ (2 c)\left(3 c^{2}\right) $$
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