Question

the atomic radius of a cesium atom is 0.000298 micrometers. round this atomic radius to the nearest ten thousandth micrometer. enter your answer in scientific notation.

Explanation:

Step1: Identify the ten - thousandths place

The ten - thousandths place of a decimal number is the fourth digit after the decimal point. In 0.000298, the digit in the ten - thousandths place is 2 and the digit to its right (the hundred - thousandths place) is 9.

Step2: Apply the rounding rule

Since the digit in the hundred - thousandths place (9) is greater than or equal to 5, we round up the digit in the ten - thousandths place. So 0.000298 rounds to 0.0003.

Step3: Convert to scientific notation

To convert 0.0003 to scientific notation, we write it as \(a\times10^{n}\), where \(1\leqslant|a|\lt10\) and \(n\) is an integer. For 0.0003, \(a = 3\) and \(n=-4\). So the number in scientific notation is \(3\times 10^{-4}\).

Answer:

\(3\times 10^{-4}\)