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

Verified step by step guidance

1. Identify the decimal number: 0.0072.
2. Move the decimal point to the right until you have a number between 1 and 10. In this case, move it 3 places to the right to get 7.2.
3. Count the number of places you moved the decimal point. Since you moved it 3 places to the right, the exponent will be negative.
4. Write the number in the form of \( a \times 10^n \), where \( a \) is the number you obtained (7.2) and \( n \) is the negative of the number of places you moved the decimal (\(-3\)).
5. Combine the results to express the number in scientific notation: \( 7.2 \times 10^{-3} \).

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 the precision of the measurement is maintained.

Decimal Movement

In scientific notation, moving the decimal point to the right indicates a negative exponent, while moving it to the left indicates a positive exponent. This movement is crucial for converting standard decimal numbers into scientific notation. For instance, in converting 0.0072 to scientific notation, the decimal moves three places to the right, resulting in a negative exponent of -3, reflecting the original number's position relative to 1.