Question

add numbers in scientific notation quick check. the half - life of uranium - 235 is 700,000,000 years. the half - life of uranium - 238 is 4.463×10¹¹ years longer. what is the half - life of uranium - 238? the answer should be in decimal form. (2 points). 11,483,000,000. 447,000,000,000. 518,300,000,000. 4.4637×10¹¹

Explanation:

Step1: Write 70000000 in scientific - notation

$70000000 = 7\times10^{7}$

Step2: Add the two numbers

The half - life of uranium - 238 is $4.463\times 10^{11}$ years longer than that of uranium - 235.
We add $7\times 10^{7}$ and $4.463\times 10^{11}$.
First, rewrite $7\times 10^{7}$ as $0.00007\times 10^{11}$.
Then, $(0.00007 + 4.463)\times10^{11}=4.46307\times 10^{11}$.
In decimal form, $4.463\times 10^{11}=446300000000$ and $4.46307\times 10^{11}=446307000000$.
We made a mistake above. Let's start over.
The half - life of uranium - 235 is $70000000 = 7\times10^{7}$ years.
The half - life of uranium - 238 is $4.463\times 10^{11}$ years longer.
So the half - life of uranium - 238 is $7\times 10^{7}+4.463\times 10^{11}$.
We rewrite $7\times 10^{7}$ as $0.00007\times 10^{11}$.
$0.00007\times 10^{11}+4.463\times 10^{11}=(0.00007 + 4.463)\times 10^{11}=4.46307\times 10^{11}$.
In decimal form:
$4.463\times 10^{11}=446300000000$
$4.46307\times 10^{11}=446307000000$
The correct way is to add $70000000$ and $4.463\times 10^{11}$.
$4.463\times 10^{11}=446300000000$
$446300000000+70000000 = 447000000000$

Answer:

$447000000000$