Write each of the following in scientific notation:
c. 0.000 48

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Identify the significant digits in the number 0.00048. These are the non-zero digits, which are 4 and 8.

Determine the position of the decimal point in the original number. In this case, the decimal point is located after the leading zeros and before the significant digits.

Rewrite the number so that it is expressed as a value between 1 and 10. To do this, move the decimal point to the right until it is positioned immediately after the first significant digit. For 0.00048, this becomes 4.8.

Count the number of places the decimal point was moved to achieve the new value. Here, the decimal point was moved 4 places to the right.

Express the number in scientific notation using the format \( a \times 10^b \), where \( a \) is the value between 1 and 10, and \( b \) is the exponent indicating the number of decimal places moved. For this problem, the result is \( 4.8 \times 10^{-4} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 0.00048 can be expressed as 4.8 x 10^-4, where 4.8 is the coefficient and -4 indicates the decimal point has moved four 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

Decimal movement refers to the process of shifting the decimal point in a number to convert it into scientific notation. When moving the decimal to the right, the exponent of ten becomes negative, indicating a smaller number. Conversely, moving the decimal to the left results in a positive exponent, representing a larger number. Understanding this movement is crucial for correctly formatting numbers in scientific notation.