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Chapter 7: Problem 47

Convert each number into standard notation. $$0.026 \times 10^{-3}$$

Short Answer

Expert verified
The number in standard notation is 0.000026.

Step by step solution

01

Understand Standard Notation and Scientific Notation

Standard notation is a way of writing numbers without exponents. Scientific notation, such as the number provided, is a way to write very large or very small numbers compactly using powers of 10.
02

Identify the Given Number

The number provided is \(0.026 \times 10^{-3}\) in scientific notation.
03

Convert the Scientific Notation to Standard Notation

To convert from scientific notation to standard notation, multiply the decimal number by the power of 10. Here, \(0.026\) is multiplied by \(10^{-3}\). Moving the decimal point three places to the left converts the number.
04

Perform the Calculation

When moving the decimal point three places to the left, \(0.026\) becomes \(0.000026\). Thus, \begin{aligned} 0.026 \times 10^{-3} &= 0.000026eqeqeqeqeqeqeqeqeq0.eq 000eq 02eq 6.eq531470 eq eq eq which is the number in standard notation.Endian.eq the number}ent of a]Apply methods e contextualize the appropriate perform the accurate representation in standard notation.

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Key Concepts

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

Understanding Scientific Notation
Scientific notation is a method used to write very large or very small numbers in a simple and compact form. This is especially useful in science and engineering. It typically involves two parts: a decimal number and a power of 10.
For example, the number 3,000 can be written as \(3 \times 10^3\). Here, 3 is the decimal number, and \(10^3\) indicates the power of 10. This makes it easier to work with extremely large numbers like the speed of light and very small numbers like the charge of an electron.
The Role of the Decimal Point
A decimal point is a fundamental part of numbers, especially in scientific notation. It separates the whole number part from the fractional part.
When converting between scientific notation and standard notation, moving the decimal point is crucial. For instance, in scientific notation, moving the decimal point to the right or left changes the number significantly.
  • Moving the decimal point to the right makes the number larger.
  • Moving the decimal point to the left makes the number smaller.
So, for \(0.026 \times 10^{-3}\), moving the decimal point three places to the left gives us \(0.000026\).
Exploring Powers of 10
Powers of 10 are the backbone of scientific notation. They show how many times you multiply or divide the base number 10. This is indicated by the exponent, which is the small superscript number.
  • A positive exponent means you move the decimal point to the right, making the number bigger. For example, \(10^3 = 1,000\).
  • A negative exponent means you move the decimal point to the left, making the number smaller. For instance, \(10^{-3} = 0.001\).
In the exercise, \(10^{-3}\) shows that the decimal point in \(0.026\) should move three places to the left, resulting in a very small number: \(0.000026\).

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Most popular questions from this chapter

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(3 y-4 z)^{2}$$

Convert each number into standard notation. $$1.76 \times 10^{5}$$

Perform the indicated operations and simplify. $$\frac{4 x^{2} y}{15 z^{3}} \cdot \frac{12 x z}{x^{2} y}$$

Maria can make five flower arrangements per hour, while Francis can make seven flower arrangements per hour. If Maria starts working at 9: 00 A.M. and is joined by Francis at 11: 00 A.M., at what time will they have made 70 flower arrangements?

Estimate the answer without actually carrying out the computation and make the most appropriate choice. If you multiply 0.00032 by \(420,000,\) the result is closest to (a) 0.12 (b) 1.2 (c) 12 (d) 120 (e) 1200
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