Decide which numbers below are correctly written in scientific notation. If they are not, rewrite them.
Refer to the rules from the Math Notes box from this lesson:
-The first factor is less than
-The second factor has a base of
-The factors are separated by a multiplication sign.
This is not written in scientific notation.
Which one of the rules is not followed in this notation?
The first factor is more than
. We can move the decimal one digit to the left so that the number is between and . How will that change the second factor?
By moving the decimal one digit to the left to make
, we must add to the exponent of . If we move the decimal to the right, we must subtract from the exponent of .
Are any of the rules broken by this notation?
Are all of the rules followed by this notation?
Yes. The second factor has a base of
and an integer exponent of .
The first and second rules for scientific notation are both broken. How can you rewrite each factor to satisfy both rules?
is . This value is . How many times do you have to multiply 10 by itself to get ? , so times.
Now we have
We need to change
to a number between and . Move the decimal point one digit to the right. What does this do to the exponent of ?
We have to subtract
from the exponent of . So now we have: