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Scientific notation review

Review the basics of scientific notation and try some practice problems. 

Scientific notation

A number is written in scientific notation when there is a number greater than or equal to 1 but less than 10 multiplied by a power of 10.
The following numbers are written in scientific notation:
  • 5, point, 4, times, 10, cubed
  • 8, point, 013, times, 10, start superscript, minus, 6, end superscript
Want to learn more about scientific notation? Check out this video.

Writing numbers in scientific notation

Numbers greater than 10

If we have a number greater than 10, we move the decimal point to the left until we have a number between 1 and 10. Then, we count the number of times we moved the decimal and write that as an exponent over a base of 10. Finally, we write our number multiplied by the power of 10.
Example
Let's write 604, comma, 000 in scientific notation.
If we move the decimal left once, we get 60, comma, 400, point, 0. We need to keep moving the decimal until we get a number between 1 and 10.
We have to move the decimal left a total of start color #a75a05, 5, end color #a75a05 times.
Now, we have 6, point, 04.
Finally, we multiply 6, point, 04 times 10, start superscript, start color #a75a05, 5, end color #a75a05, end superscript:
604, comma, 000 in scientific notation is 6, point, 04, times, 10, start superscript, start color #a75a05, 5, end color #a75a05, end superscript.

Numbers less than 1

If we have a number less than 1, we move the decimal point to the right until we have a number between 1 and 10. Then, we count the number of times we moved the decimal and write that as a negative exponent over a base of 10. Finally, we write our number multiplied by the power of 10.
Example
Let's write 0, point, 0058 in scientific notation.
If we move the decimal right start color #1fab54, 3, end color #1fab54 times, we get a number between 1 and 10.
Now, we have 5, point, 8.
Finally, we write 5, point, 8 times 10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript:
0, point, 0058 in scientific notation is 5, point, 8, times, 10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript.

Practice

Problem 1
Express this number in scientific notation.
245, comma, 600, comma, 000, comma, 000

Want to try more problems like this? Check out this exercise.

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