Question

sea level at the battery in new york is rising by about 2.84×10⁻³ m/year. at this rate, how much will the sea level rise in 20 years? express your answer in scientific notation. enter your answer in the boxes.

Explanation:

Step1: Identify the rate and time

The rate of sea - level rise is $r = 2.84\times10^{-3}$ m/year and the time $t = 20$ years.

Step2: Use the formula for distance (rise in this case)

The formula for the amount of sea - level rise $d$ is $d=r\times t$. Substitute the values: $d=(2.84\times 10^{-3})\times20$.
First, calculate $2.84\times20 = 56.8$.
Then, $d = 56.8\times10^{-3}$.

Step3: Convert to scientific notation

In scientific notation, a number is written as $a\times10^{n}$ where $1\leq a<10$ and $n$ is an integer.
Rewrite $56.8\times10^{-3}$ as $5.68\times10^{1}\times10^{-3}$.
Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $5.68\times10^{1+( - 3)}=5.68\times10^{-2}$ m.

Answer:

$5.68\times 10^{-2}$ m