Notice that writing 1.3 billion and 300 million in scientific notation meant that we didn’t need to enter long strings of zeros into our calculator. This is an advantage, since it is very easy to accidentally include too many or too few zeros!
Let’s use scientific notation to help us estimate the number of words in War and Peace as millions, billions, trillions, or some other size. Using an internet search, we found that sample pages of an e-book version of War and Peace have about 300 words on each page. This e-book version is 1307 pages long.
The amount of money needed to send all adults in the United States to a public college for four years. Assume there are about 258 million adults in the United States and that the cost of tuition and fees to a public college is about $25,000.
The amount of money needed per year to raise wages in the US to $15 per hour. Assume that there are 800 thousand full-time US workers making the federal minimum wage of $7.25 or less 1
If the U.S. national debt was $36 trillion in June of 2025 and was evenly divided among the 342 million people living in the United States in 2025, estimate how much each person’s share would be.
Below is a table that describes some small numbers in standard decimal notation, and scientific notation. Notice that for small numbers:
Scientific notation keeps track of the number of decimal places to the left of the second nonzero digit, but after the decimal point, using the exponent.
This notation may look strange, but it is how many calculators write \(5.6 \times 10^{-8}\text{.}\) It may be helpful to think of the “e” as standing for “exponent”.
