  ### Home > CC3MN > Chapter 8 > Lesson 8.2.3 > Problem8-88

8-88.

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 $10$ and greater than or equal to $1$.
-The second factor has a base of $10$ and an integer exponent.
-The factors are separated by a multiplication sign.

1. $92.5 × 10^{−2}$

This is not written in scientific notation.
Which one of the rules is not followed in this notation?

The first factor is more than $10$. We can move the decimal one digit to the left so that the number is between $1$ and $10$. How will that change the second factor?

By moving the decimal one digit to the left to make $9.25$, we must add $1$ to the exponent of $10$. If we move the decimal to the right, we must subtract $1$ from the exponent of $10$.

$9.25 × 10^{−1}$

1. $6.875 × 10^{2}$

Are any of the rules broken by this notation?

1. $2.8 × 10$

Are all of the rules followed by this notation?

Yes. The second factor has a base of $10$ and an integer exponent of $1$.

$10^{1} = 10$

1. $0.83 × 100^{2}$

The first and second rules for scientific notation are both broken. How can you rewrite each factor to satisfy both rules?

$100^{2}$ is $\left(100\right)\left(100\right)$. This value is $10,000$. How many times do you have to multiply 10 by itself to get $10,000$?

$\left(10\right)\left(10\right)\left(10\right)\left(10\right) = 10,000$, so $4$ times.
Now we have $0.83 · 10^{4}$.

We need to change $0.83$ to a number between $1$ and $10$. Move the decimal point one digit to the right. What does this do to the exponent of $10$?

We have to subtract $1$ from the exponent of $10$. So now we have:

$8.3 × 10^{3}$