Write each of the following in scientific notation:
a. 0.024

Verified step by step guidance

1. Identify the decimal number that needs to be converted into scientific notation. In this case, the number is 0.024.
2. Determine the position of the decimal point and count how many places it needs to move to create a number between 1 and 10. For 0.024, the decimal point needs to move 2 places to the right.
3. Rewrite the number as a product of the adjusted number and a power of 10. After moving the decimal point, the adjusted number becomes 2.4. The power of 10 corresponds to the number of places the decimal point was moved, which is -2 (since the original number is less than 1).
4. Express the number in scientific notation using the format \( a \times 10^b \), where \( a \) is the adjusted number and \( b \) is the exponent. For this problem, the scientific notation is \( 2.4 \times 10^{-2} \).
5. Double-check your work to ensure the adjusted number is between 1 and 10 and the exponent correctly reflects the movement of the decimal point.

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 0.024 can be expressed as 2.4 x 10^-2, where 2.4 is the coefficient and -2 indicates the decimal shift.

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. For instance, in the number 2.4 x 10^-2, both digits '2' and '4' are significant, indicating the precision of the measurement.

Exponent Rules

Exponent rules govern how to manipulate powers of ten in scientific notation. When multiplying or dividing numbers in scientific notation, you add or subtract the exponents, respectively. Understanding these rules is essential for correctly converting and calculating numbers in scientific notation.