### Home > MC2 > Chapter 10 > Lesson 10.1.6 > Problem 10-76

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: