• Understand and use the rules for exponents
• Change numbers between scientific notation and standard notation
• Solve calculations using scientific notation

Unveiling the Microscopic Universe: Exploring Atoms with Exponents and Scientific Notation

Meet Emma, a curious physicist with a penchant for exploring the intricate details of our universe. Emma, always fascinated by atoms, often contemplates their sizes and the number of atoms required to make up larger items in our world. Let’s join Emma on her atomic explorations. Today you will delve into the minuscule world of atoms, utilizing the rules for exponents, scientific notation, and even some calculations. Ready? Let’s start!

 

One day, Emma was pondering the size of the hydrogen atom. She knows that the diameter of a hydrogen atom is about [latex]10^{-10}[/latex] meters, or [latex]0.000000004[/latex] inches. Emma wonders: what is the correct way to write the diameter of a hydrogen atom, in inches, in scientific notation?

After understanding the size of a hydrogen atom, Emma wants to compare it to a larger atom. She choses the largest known atom, francium.

Intrigued by the difference in size between hydrogen and francium atoms, Emma then wonders about the size of other atoms in comparison to hydrogen. Emma choses to investigate a sucrose molecule next. With a diameter of about [latex]1 \times 10^{-7}[/latex] inches, she ponders how much larger a sucrose molecule is compared to a hydrogen atom ([latex]4 \times 10^{-9}[/latex] inches). Can you assist her in expressing the comparison in scientific notation?