Express the following measurements in scientific notation. (a) 453.32 mg

Verified step by step guidance

1. Identify the significant figures in the measurement: 453.32 mg.
2. Determine the position of the decimal point in the original number.
3. Move the decimal point to the right of the first non-zero digit to convert the number to a value between 1 and 10.
4. Count the number of places the decimal point was moved to determine the exponent of 10.
5. Express the number in scientific notation as \( a \times 10^n \), where \( a \) is the number obtained in step 3 and \( n \) is the exponent from step 4.

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 453.32 can be expressed as 4.5332 x 10^2 in scientific notation.

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 maintain the correct number of significant figures to accurately represent the precision of the original measurement.

Unit Conversion

Unit conversion involves changing a measurement from one unit to another while maintaining its value. In this context, converting milligrams (mg) to grams (g) may be necessary, as 1 g equals 1000 mg. Understanding unit conversion is essential for correctly interpreting and expressing measurements in scientific notation.