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Chapter 10: Problem 47

For Exercises \(33-48,\) convert to scientific notation. $$4920$$

Short Answer

Expert verified
4.920 脳 10鲁

Step by step solution

01

- Identify the Significant Figures

The number provided is 4920. The significant figures in this number are 4, 9, 2, and 0.
02

- Place Decimal Point

To convert to scientific notation, place the decimal point after the first significant figure: 4.920.
03

- Determine the Exponent

Count the number of places the decimal point has moved from its original position (after the last digit) to its new position: The decimal point moved 3 places to the left.
04

- Write in Scientific Notation

Combine the significant figures with the exponent to write the number in scientific notation: \[ 4920 = 4.920 \times 10^3 \]

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Key Concepts

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

Significant Figures
Significant figures are the digits in a number that are meaningful in terms of accuracy or precision. When identifying significant figures in a number, all non-zero digits are always significant. In the number 4920, the significant figures are 4, 9, and 2. The trailing zero in 4920 is also considered significant because it comes after non-zero digits. Significant figures are crucial in scientific notation to ensure that the number's precision remains intact.

Here is a simple rule to remember:
  • All non-zero digits (1-9) are significant.
  • Any zeros between significant digits are significant.
  • Trailing zeros in a decimal number are significant.
  • Leading zeros are never significant.

So for 4920, all digits are significant making it easy to convert to scientific notation accurately.
Decimal Point
The decimal point plays a vital role in determining where each digit is placed in a number. It's crucial when converting a number into scientific notation. In our number, 4920, the original placement of the decimal point is at the end of the number (4920.0).

When converting to scientific notation, we move the decimal point so that it's placed just after the first non-zero digit. This means moving it from its original position to just after the 4, making the number 4.920.

Understanding how to place the decimal correctly helps in determining the correct exponent later in the process.
Exponent
The exponent in scientific notation explains how many places the decimal point has moved to convert the number to a simplified format. In our case, converting 4920 into scientific notation involves moving the decimal point three places to the left.

This movement is represented by the exponent in the notation: \(10^3\). The exponent is positive because we moved the decimal point to the left. If we were dealing with a number less than one and moved the decimal to the right, the exponent would be negative.

So, after moving the decimal point in 4920 to make it 4.920, we combine the significant figures with the exponent, giving us: \[4.920 \times 10^3\].

Remember:
  • Positive exponents: Decimal moved to the left.
  • Negative exponents: Decimal moved to the right.

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Most popular questions from this chapter

Simplify. Write the answers with positive exponents only. $$z^{-4} z^{7}$$

Perform the indicated operations. $$\left(\frac{7}{8} a-4 b-\frac{1}{2} c\right)-\left(-\frac{1}{4} a+\frac{1}{2} b+\frac{3}{8} c\right)$$

Simplify. $$v^{9} v^{30} v^{55}$$

Simplify. Write the answers with positive exponents only. $$\left(p^{4}\right)^{-5}$$

Perform the indicated operations. $$\left(1.2 x^{2}+3.5 x-9.6\right)+\left(2.9 x^{2}-6.7 x-3.5\right)$$
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