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Chapter 5: Problem 133

Write each number in scientific notation. $$ 530 $$

Short Answer

Expert verified
5.30 \times 10^2

Step by step solution

01

- Identify the Significant Figures

Determine the significant figures in the number given. For 530, the significant figures are 5, 3, and 0.
02

- Place the Decimal Point

Move the decimal point in the number so that there is only one non-zero digit to the left of the decimal. For 530, moving the decimal two places to the left gives 5.30.
03

- Multiply by the Power of 10

Express the number as a product of the new decimal and a power of 10. Since the decimal was moved 2 places to the left, the power of 10 will be raised to 2. Therefore, 530 in scientific notation is written as: \[ 5.30 \times 10^2 \]

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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 carry meaningful information about its precision. They include all non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal number. In the number 530, there are three significant figures: 5, 3, and 0. These figures show the precision of the measurement and are crucial when converting to scientific notation. Understanding which digits are significant ensures that we maintain the accuracy and precision of the original number during mathematical operations.
decimal point
The decimal point is a dot used to separate the whole number part from the fractional part of a number. It's a key element in converting numbers to scientific notation. When converting a number like 530 to scientific notation, we move the decimal point so that there is only one non-zero digit to its left. For 530, we move the decimal point two places to the left to get 5.30. This step helps simplify the number while retaining its value, making it easier to handle large or small numbers in calculations.
power of 10
The power of 10 expresses how many times the decimal point has been moved to convert the number to scientific notation. It is written as an exponent. In the case of 530, the decimal point is moved two places to the left, resulting in a power of 10 of 2. This gives us \(5.30 \times 10^2\). Using the power of 10 helps in dealing with extremely large or small numbers by keeping them manageable and preserves the number's accuracy. It鈥檚 an essential part of scientific notation, enabling comparison and calculation of vastly different magnitudes.

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