Write each of the following in scientific notation:
c. 0.000 62

Verified step by step guidance

1. Identify the significant digits in the number 0.00062. These are the non-zero digits, which in this case are '6' and '2'.
2. Determine the position of the decimal point in the original number. The decimal point is located after the leading zeros and before the significant digits.
3. Count how many places the decimal point needs to move to the right to position it immediately after the first significant digit (6). In this case, the decimal point moves 4 places to the right.
4. Express the number in the form \( a \times 10^n \), where \( a \) is the significant digits written as a decimal (6.2), and \( n \) is the number of places the decimal point moved (negative because the original number is less than 1).
5. Write the final expression in scientific notation as \( 6.2 \times 10^{-4} \).

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 0.00062 can be expressed as 6.2 x 10^-4, where 6.2 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 maintain the correct number of significant figures to accurately represent the original value, ensuring clarity and precision in scientific communication.

Decimal Movement

Decimal movement refers to the process of shifting the decimal point in a number to convert it into scientific notation. This movement determines the exponent of ten; moving the decimal to the right results in a negative exponent, while moving it to the left results in a positive exponent. Understanding how to correctly move the decimal is crucial for accurately expressing numbers in scientific notation.