Question

quiz instructions
this 2.06 quiz focuses on operations on scientific notation. youll have two attempts, and your highest score w
attempts: 2
time limit: unlimited
question 3
find the product.
(2.5×10^(-10))(7×10^(-6))
express your answer in scientific notation.
1.75×10^16
1.75×10^(-15)
1.75×10^(-16)
1.75×10^(-17)

Explanation:

Step1: Multiply the coefficients

Multiply 2.5 and 7.
$2.5\times7 = 17.5$

Step2: Multiply the powers of 10

Use the rule $a^m\times a^n=a^{m + n}$. Here $a = 10$, $m=-10$ and $n=-6$.
$10^{-10}\times10^{-6}=10^{-10+( - 6)}=10^{-16}$

Step3: Combine the results

The product is $17.5\times10^{-16}$. But in scientific - notation, the coefficient should be between 1 and 10. Rewrite 17.5 as $1.75\times10^1$.
So $17.5\times10^{-16}=1.75\times10^1\times10^{-16}$.
Using the rule $a^m\times a^n=a^{m + n}$ again, we get $1.75\times10^{1+( - 16)}=1.75\times10^{-15}$

Answer:

$1.75\times10^{-15}$