Write each of the following in scientific notation:
d. 360 000

Verified step by step guidance

1. Identify the significant digits in the number. For 360,000, the significant digits are '36'.
2. Determine the power of 10 needed to express the number in scientific notation. Count the number of places the decimal point would need to move to the left to position it 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 a number between 1 and 10, and $n$ is the power of 10. For 360,000, $a$ is 3.6 and $n$ is 5.
4. Combine the significant digits and the power of 10 to express the number in scientific notation. The result is $3.6\times {10}^5$.
5. Verify the result by converting the scientific notation back to standard form to ensure it matches the original number, 360,000.

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 typically written as a product of a number between 1 and 10 and a power of ten. For example, the number 360,000 can be expressed as 3.6 x 10^5 in scientific notation.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific notation, the significant figures are represented in the coefficient (the number between 1 and 10). For 360,000, if we consider it to have three significant figures, it would be written as 3.60 x 10^5.

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 instance, 10^5 means 10 multiplied by itself five times, which equals 100,000, helping to place the decimal point correctly in scientific notation.