Unit 7, Lesson 13
Definition of Scientific Notation
Grade 8
13.1
Warm-up
What do you notice? What do you wonder?
| material | speed (meters per second) |
|---|---|
| space | 300,000,000 |
| water | |
| copper (electricity) | 280,000,000 |
| diamond | |
| ice | |
| olive oil |
A number line, 11 tick marks, 0, 1 times 10 to the power 8, 2 times 10 to the power 8, 3 times 10 to the power 8, 4 times 10 to the power 8, 5 times 10 to the power 8, 6 times 10 to the power 8, 7 times 10 to the power 8, 8 times 10 to the power 8, 9 times 10 to the power 8, 10 to the power 9. Two times 10 to the power 8 to 3 times 10 to the power 8 is zoomed out to a new number line with 9 tick marks between them. There are 3 points on the new line, 1 between the third and fourth tick mark, 1 at the fourth, and one at the ninth.
Student Lesson Summary
The total value of all the quarters made in 2014 was 400 million dollars. There are many ways to express this using powers of 10. We could write this as dollars, dollars, dollars, or many other ways. One special way to write this quantity is called scientific notation, where the first factor is a number greater than or equal to 1, but less than 10, and the second factor is an integer power of 10
In scientific notation,
400 million dollars
would be written as
dollars.
Writing the number this way shows exactly where it lies between two consecutive powers of 10. The shows us the number is between and . The 4 shows us that the number is 4 tenths of the way to .
A number line, 11 tick marks, 0, 1 times 10 to the power 11, 2 times 10 to the power 11, 3 times 10 to the power 11, 4 times 10 to the power 11, 5 times 10 to the power 11, 6 times 10 to the power 11, 7 times 10 to the power 11, 8 times 10 to the power 11, 9 times 10 to the power 11, 10 to the power 12. Three times 10 to the power 11 to 4 times 10 to the power 11 is zoomed out, to 11 tick marks labeled 3 times 10 to the power 11, blank, blank, blank, 3 point 4 times 10 to the power 11, blank, blank, blank, blank, blank, 4 times 10 to the power 11.
For scientific notation, the "" symbol is the standard way to show multiplication instead of the dot symbol. Some other examples of scientific notation are , , and .
Scientific notation is a way to write very large or very small numbers. They are written as a product. The first factor is a number greater than or equal to 1, but less than 10. The second factor is a power of 10.
- The number 425,000,000 in scientific notation is .
- The number 0.0000000000783 in scientific notation is .