Write each of the following in scientific notation with two significant figures:
d. 0.000 25 cm

Verified step by step guidance

1. Identify the significant figures in the given number. In this case, the number is 0.00025 cm, and the two significant figures are '2' and '5'.
2. Rewrite the number in standard scientific notation format: \( a \times 10^n \), where \( a \) is a number between 1 and 10, and \( n \) is an integer.
3. To express 0.00025 in scientific notation, move the decimal point to the right until the number becomes a value between 1 and 10. Count how many places the decimal point is moved. Here, the decimal point is moved 4 places to the right.
4. Since the decimal point was moved to the right, the exponent \( n \) will be negative. The value of \( n \) is \(-4\).
5. Combine the significant figures and the exponent to write the number in scientific notation: \( 2.5 \times 10^{-4} \) cm.

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, 0.00025 can be expressed as 2.5 x 10^-4, where 2.5 is the significant figure and -4 indicates the decimal place shift.

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. In the case of 0.00025, the significant figures are '2' and '5', which means the number should be expressed in scientific notation with these two digits.

Decimal Place Shift

Decimal place shift refers to the movement of the decimal point in a number to convert it into scientific notation. This shift determines the exponent of ten in the notation. For instance, moving the decimal point in 0.00025 four places to the right results in the exponent -4, indicating that the original number is a small fraction.