Write each of the following in scientific notation with two significant figures:c. 100 000 m

Verified step by step guidance

1. Identify the significant figures in the number 100,000. Since the number is written as 100,000, it has one significant figure.
2. To express the number with two significant figures, we need to consider the first two non-zero digits. In this case, we can write it as 1.0.
3. Determine the power of 10 needed to express 100,000 in scientific notation. Since 100,000 is 10^5, we use this as the exponent.
4. Combine the significant figures and the power of 10 to express the number in scientific notation. This will be in the form of a \( a \times 10^n \) where \( a \) is the significant figures and \( n \) is the exponent.
5. Write the final expression in scientific notation with two significant figures as \( 1.0 \times 10^5 \).

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 100,000 can be expressed as 1.0 x 10^5 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 round the number to the specified number of significant figures, which in this case is two.

Rounding Rules

Rounding rules dictate how to adjust numbers to meet a specified level of precision. When rounding to two significant figures, if the digit following the last significant figure is 5 or greater, the last significant figure is increased by one. This ensures that the number accurately reflects the desired precision in scientific notation.