Write each of the following in scientific notation:
e. 0.0072

Verified step by step guidance

1. Identify the significant figures in the number. For 0.0072, the significant figures are '7' and '2'.
2. Move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, move the decimal point 3 places to the right, resulting in 7.2.
3. Count the number of places the decimal point was moved. Since it was moved 3 places to the right, the exponent will be negative (-3).
4. Combine the significant figures and the exponent into the format \( a \times 10^n \), where \( a \) is the significant figure (7.2) and \( n \) is the exponent (-3).
5. Write the final result in scientific notation as \( 7.2 \times 10^{-3} \).

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 0.0072 can be expressed as 7.2 x 10^-3, where 7.2 is the coefficient and -3 indicates the decimal point has moved three places to the right.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When converting to scientific notation, it is important to retain the correct number of significant figures to accurately represent the original value, ensuring that 0.0072 is expressed as 7.2 with two significant figures.

Exponent Rules

Exponent rules govern how to manipulate powers of ten in scientific notation. When converting a number to scientific notation, the exponent indicates how many places the decimal point has moved. A negative exponent, like in 7.2 x 10^-3, signifies that the original number is less than one, while a positive exponent indicates a number greater than one. Understanding these rules is essential for accurate conversions.