Question

The mass of a chlorine molecule is \(1.18 \times 10^{-22} \mathrm{~g} .\) Express the mass as an ordinary number.

Short answer

0.000000000000000000000118 g

Step-by-step solution

Understanding Scientific Notation

Scientific notation is a way to express very large or very small numbers. It consists of a number between 1 and 10 multiplied by a power of ten. In this exercise, the mass of the chlorine molecule is given as \(1.18 \times 10^{-22}\). This means 1.18 is multiplied by 10 raised to the power of -22.

Converting Scientific Notation to Ordinary Number

To convert \(1.18 \times 10^{-22}\) to an ordinary number, we need to shift the decimal point of 1.18 twenty-two places to the left. This is because the exponent is -22, indicating a very small number.

Performing the Conversion

Start with the number 1.18. To move the decimal 22 places left, initially move it 1 place before 1 to get 0.118, then place 21 zeros in front. This results in the ordinary number: \(0.000000000000000000000118\).

Key concepts

Converting Scientific Notation

Scientific notation is a helpful tool in handling extremely large or small numbers with more ease and precision. When converting a number from scientific notation to its ordinary form, the position of the decimal point is altered based on the exponent of ten. If the exponent is positive, move the decimal point to the right, magnifying the number. Conversely, if the exponent is negative, as in our example with the chlorine molecule, the decimal point shifts to the left, indicating a smaller value.

To convert the scientific notation of the mass of a chlorine molecule, given as \(1.18 \times 10^{-22}\), we moved the decimal point 22 places to the left. This step reveals how such a tiny mass is expressed in everyday numbers, beginning with 1.18 and transforming it into an ordinary number packed with zeros: \(0.000000000000000000000118\). This process showcases the practicality of scientific notation in converting between different scales of measurement with clarity.

Chlorine Molecule Mass

In the realm of chemistry, the chlorine molecule's mass serves as a paradigmatic example of how scientific notation functions advantageously. The mass of a single chlorine molecule is extraordinarily small, approximately \(1.18 \times 10^{-22}\) grams.

This succinct representation captures the tiny scale of atomic and molecular masses, which are, by nature, minute. Molecular masses like that of chlorine require a method to effectively and accurately engage with their nuances. Without scientific notation, writing out such small measurements in full would be cumbersome and error-prone. Using scientific notation allows scientists and students alike to work with, compare, and communicate these small numbers with greater ease and understanding.

Expressing Small Numbers

Expressing small numbers, particularly in the field of science, ensures that even minuscule quantities can be communicated clearly and without error. Small numbers like \(0.000000000000000000000118\) for the mass of a chlorine molecule are common in scientific discussions.

When numbers are small, several zeros can precede significant digits. Scientific notation aids in simplifying these otherwise bulky figures into a more digestible form. Here are a few benefits:

• Reduces the likelihood of counting errors when reading or writing.
• Makes it simpler to perform calculations, updates, or comparisons.
• Allows for the easy sharing of data among researchers and students.

By efficiently translating these microscopic numbers into a readable format, scientific notation plays a crucial role in scientific communication, education, and application, offering a bridge between abstract numerical explanations and tangible comprehension.