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Home > CC3 > Chapter 8 > Lesson 8.2.3 > Problem 8-88

8-88.

Decide which numbers below are correctly written in scientific notation. If they are not, rewrite them. Homework Help ✎

Refer to the rules from the Math Notes box from this lesson:
-The first factor is less than and greater than or equal to .
-The second factor has a base of and an integer exponent.
-The factors are separated by a multiplication sign.

  1. 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 .

  1. Are any of the rules broken by this notation?

  1. Are all of the rules followed by this notation?

    Yes. The second factor has a base of and an integer exponent of .

  1. 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: