Converting numbers to and from scientific notation (a×10k)
Scientific notation is a useful way to write large or small numbers in a compact form. It uses powers of 10 to "condense" a lot of digits. Numbers written in scientific notation are of the form
where 1≤a<10 and k∈Z.
Scientific notation is sometimes called "standard form."
Let x=3×105,y=4×106, and suppose we want to find x+y.
Since the powers of 10 are different, we cannot simply add 3+4. Instead, we rewrite y so it is multiplying 105:
Now we can add:
Finally, we convert back to scientific form, since 43>10:
Basically, we took the higher power of 10 and "split" it so that it matched the smaller power of 10.
We can multiply and divide numbers in scientific form as follows:
Multiplying and dividing numbers in scientific notation relies heavily on exponent rules.
Nice work completing Scientific Notation, here's a quick recap of what we covered:
Exercises checked off
Converting numbers to and from scientific notation (a×10k)
Scientific notation is a useful way to write large or small numbers in a compact form. It uses powers of 10 to "condense" a lot of digits. Numbers written in scientific notation are of the form
where 1≤a<10 and k∈Z.
Scientific notation is sometimes called "standard form."
Let x=3×105,y=4×106, and suppose we want to find x+y.
Since the powers of 10 are different, we cannot simply add 3+4. Instead, we rewrite y so it is multiplying 105:
Now we can add:
Finally, we convert back to scientific form, since 43>10:
Basically, we took the higher power of 10 and "split" it so that it matched the smaller power of 10.
We can multiply and divide numbers in scientific form as follows:
Multiplying and dividing numbers in scientific notation relies heavily on exponent rules.
Nice work completing Scientific Notation, here's a quick recap of what we covered:
Exercises checked off