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 number 0.000 25 cm. Here, the significant figures are '25'.
2. To express the number in scientific notation, move the decimal point to the right until you have a number between 1 and 10. In this case, move the decimal point 4 places to the right to get 2.5.
3. Count the number of places you moved the decimal point. This will be the exponent of 10. Since you moved the decimal 4 places to the right, the exponent will be -4.
4. Combine the number from step 2 with the exponent from step 3 to express the number in scientific notation: 2.5 \times 10^{-4}.
5. Ensure that the number is expressed with two significant figures, which is already achieved with 2.5 in this case.

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 Movement

When converting a number to scientific notation, the decimal point is moved to create a new number between 1 and 10. The number of places the decimal is moved determines the exponent of ten. For 0.00025, moving the decimal four places to the right results in a negative exponent (-4), indicating the original number is less than one.