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Chapter 5: Problem 26

Write each number without exponents. $$ 8.8 \times 10^{6} $$

Short Answer

Expert verified
8800000

Step by step solution

01

Understand Exponential Notation

Exponential notation is a way to write numbers that are too large or too small more conveniently. In this case, the exponent of 6 means that we need to move the decimal point 6 places to the right.
02

Move the Decimal Point

Starting with the number 8.8, we need to shift the decimal point 6 places to the right. This means we have to add extra zeros to fill the spaces. Moving the decimal point 6 spaces to the right from 8.8, we get 8800000.

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Key Concepts

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

Decimals
Decimal numbers are a way to represent fractions using the base 10. They include numbers with a decimal point and digits after it, showing parts of a whole. For example, 8.8 is a decimal number, where '8' is the whole number part, and '.8' represents 8 tenths.

When working with decimals in exponential notation, you move the decimal point to transform the number. This manipulation helps in understanding large and small numbers easily through exponentiation.
Large Numbers
Large numbers can be challenging to read and work with. Writing a number like 8800000 in full can be cumbersome.

Exponential notation, like in the given exercise, helps simplify the expression of large numbers. When you move the decimal 6 places to the right for 8.8, you get 8800000.
This shows how principles of place value and zeroes are used to manage and operate with large quantities effectively.
Scientific Notation
Scientific notation is a method of writing numbers that are too large or too small for convenient use. It comprises a decimal part and an exponent indicating the power of 10. For example, in 8.8 脳 10^6:

- 8.8 is the coefficient
- 10 is the base
- 6 is the exponent

This format makes it easier to read, compare, and perform operations on very large or very small numbers. Moving the decimal 6 places to the right from 8.8 gives 8800000, demonstrating how scientific notation converts between compact form and standard form.

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Most popular questions from this chapter

If the distance traveled is \(\left(5 x^{3}-6 x^{2}+3 x+14\right)\) miles and the rate is \((x+1) \mathrm{mph},\) write an expression, in hours, for the time traveled.

Evaluate each expression for \(x=3\) $$ 4 x^{3}-5 x^{2}+2 x-5 $$

Use scientific notation to calculate the answer to each problem. (a) The distance to Earth from Pluto is \(4.58 \times 10^{9} \mathrm{km} .\) In April \(1983,\) Pioneer 10 transmitted radio signals from Pluto to Earth at the speed of light, \(3.00 \times 10^{5} \mathrm{km}\) per sec. How long (in seconds) did it take for the signals to reach Earth? (b) How many hours did it take for the signals to reach Earth?

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.

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