Problem 37 - Chemistry Matter and Change

Question

The text tells you that, “1 trillion atoms could fit onto a period at the end of this sentence.” Write out the number 1 trillion using the correct number of zeros.

Step-by-Step Solution

Answer

1 trillion is written as \(1,000,000,000,000\).

Step 1: Understanding the meaning of 1 trillion

Trillion is a large number which is represented as 1 followed by 12 zeros. In other words, 1 trillion equals 1,000,000,000,000.

Step 2: Write the number 1 trillion with the correct number of zeros

We will now write the number 1 trillion using the knowledge from step 1. 1 trillion = 1,000,000,000,000 So, 1 trillion written with the correct number of zeros is 1,000,000,000,000.

Key Concepts

Magnitude of Atoms

When we hear that 1 trillion atoms can fit onto a period, it's hard to imagine such a scale. Atoms are extremely small particles, the basic units of matter. Everything around us is made of atoms. To give you an idea of their scale, an individual atom is about 0.1 nanometers in diameter.

Considering that a typical period at the end of a sentence is around 0.5mm in diameter, fitting a trillion atoms on it means we are dealing with incredibly tiny magnitudes. Just how small these atoms are highlights the importance of using appropriate measuring methods for such tiny scales, and one such method is using scientific notation, which allows us to express large quantities of atoms, or other very small particles, in manageable terms.

Scientific Numeric Representation

Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It's based on powers of ten. For example, the number 1 trillion, can be written as 1,000,000,000,000 or, using scientific notation, as \(1 \times 10^{12}\).

In scientific notation, we use the format \(M \times 10^n\), where \(M\) is a number greater than or equal to 1 but less than 10, and \(n\) is an integer. The 'n' represents how many places you would move the decimal point. This compact form is extremely useful when dealing with the vast quantities or minuscule measurements often found in scientific work, like the number of atoms in a certain volume.

Scale and Measurement

Measuring things correctly is crucial in science. When dealing with quantities and objects ranging from the enormity of galaxies to the minuteness of atoms, it becomes necessary to adopt a scale that allows for precise measurement at any level. This is why we use different units of measurement, such as meters for length, kilograms for mass, and seconds for time.

However, when it comes to atoms, even the smallest standard unit of length, the millimeter, is not nearly precise enough. Instead, we use nanometers or even picometers. It's a question of picking the right tool for the job. For example, when expressing the size of an atom, or the vast number of atoms on the tip of a pencil, using standard units would be impractical and imprecise. Hence, adopting scientific numeric representation and understanding the scale involved is integral to the field of study in physics, chemistry, and beyond.