Write each of the following in scientific notation:
d. 530 000

Verified step by step guidance

1. Identify the significant digits in the number. For 530,000, the significant digits are 5.3 (assuming no trailing zeros are significant unless specified).
2. Determine the power of 10 needed to express the number in scientific notation. Count how many places the decimal point would need to move to the left to position it immediately after the first significant digit. In this case, the decimal point moves 5 places.
3. Write the number in the form \( a \times 10^n \), where \( a \) is the significant digits expressed as a decimal and \( n \) is the power of 10. For this problem, \( a = 5.3 \) and \( n = 5 \).
4. Combine the significant digits and the power of 10 to express the number in scientific notation. The result will be \( 5.3 \times 10^5 \).
5. Verify the result by converting \( 5.3 \times 10^5 \) back to standard notation to ensure it equals 530,000.

Key Concepts

Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small in a compact form. It is written as the product of a number between 1 and 10 and a power of ten. For example, the number 530,000 can be expressed as 5.3 x 10^5, where 5.3 is the coefficient and 10^5 indicates the number of places the decimal point has moved.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, only the digits in the coefficient are considered significant. For instance, in the number 5.3 x 10^5, both digits '5' and '3' are significant, which helps convey the accuracy of the measurement or value being represented.

Powers of Ten

Powers of ten are used in scientific notation to indicate the scale of the number. Each power of ten represents a factor of ten multiplied by itself. For example, 10^5 means 10 multiplied by itself five times, equating to 100,000. This concept is crucial for understanding how to convert standard numbers into scientific notation effectively.