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Chapter 5: Problem 83

Convert to decimal notation. $$ 4.92 \times 10^{5} $$

Short Answer

Expert verified
492000

Step by step solution

01

Identify the components

Identify the base number and the exponent in the scientific notation. Here, the base number is 4.92 and the exponent is 5.
02

Interpret the exponent

The exponent tells how many places to move the decimal point. Since the exponent is 5, move the decimal point 5 places to the right.
03

Move the decimal point

Move the decimal point in 4.92 five places to the right. This will add zeros as needed: 4.92 -> 492 -> 4920 -> 49200 -> 492000.

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Key Concepts

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

decimal notation
Decimal notation is a way of writing numbers that uses a base-10 system. In decimal notation, each digit in a number represents a power of ten. For instance, in the number 123.45, the digit 1 represents 100, the digit 2 represents 20, the digit 3 represents 3, the digit 4 represents 0.4, and the digit 5 represents 0.05. This system is straightforward and widely used, making it easy for everyone to understand and perform calculations.
exponent
An exponent is a small number written above and to the right of a base number, indicating how many times the base number is to be multiplied by itself. For example, in the expression \(10^3\), 3 is the exponent, and it means that 10 should be multiplied by itself three times: \(10 \times 10 \times 10\). This makes 1000. Exponents are especially useful for representing very large or very small numbers in a compact form, such as in scientific notation.
base number
The base number is the main number that is raised to a power by the exponent. In the scientific notation \(4.92 \times 10^5\), the base number is 4.92. It is the starting point of the number. When you multiply the base number by 10 raised to the exponent, you get the final number in decimal notation. The base number helps to show the number's scale and precision before it is expanded by the exponent.

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Most popular questions from this chapter

Computer spreadsheet applications allow values for cells in a spreadsheet to be calculated from values in other cells. For example, if the cell Cl contains the formula $$ =\mathrm{A} 1+2 * \mathrm{B} 1 $$ the value in Cl will be the sum of the value in Al and twice the value in B1. This formula is a polynomial in the two variables Al and B1. The cell D6 contains the formula $$ =\mathrm{Al}-0.2 * \mathrm{B} 1+0.3^{*} \mathrm{Cl} $$ What is the value in \(\mathrm{D} 6\) if the value in \(\mathrm{Al}\) is \(10,\) the value in \(\mathrm{B} 1\) is \(-3,\) and the value in \(\mathrm{Cl}\) is \(30 ?\)

For each pair of functions \(f\) and \(g\), determine the domain of \(f / g\) $$ \begin{aligned} &f(x)=3 x-2\\\ &g(x)=2 x-8 \end{aligned} $$

Computer spreadsheet applications allow values for cells in a spreadsheet to be calculated from values in other cells. For example, if the cell Cl contains the formula $$ =\mathrm{A} 1+2 * \mathrm{B} 1 $$ the value in Cl will be the sum of the value in Al and twice the value in B1. This formula is a polynomial in the two variables Al and B1. The cell D4 contains the formula $$ =2 * \mathrm{A} 4+3 * \mathrm{B} 4 $$ What is the value in \(\mathrm{D} 4\) if the value in \(\mathrm{A} 4\) is 5 and the value in \(\mathrm{B} 4\) is \(10^{2}?\)

Simplify. \(\frac{1}{2} x-\frac{1}{4}-\left(\frac{3}{2} x+\frac{3}{4}\right)\)

To prepare for Section \(5.2,\) review operations with integers (Sections \(1.5-1.7)\) Perform the indicated operations. $$ -3(5) $$
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