Q31. - Algebra 1

Question

Earth has a diameter of about 8000 miles. Jupiter has a dimeter of about 88000 miles. Write in scientific notation the ratio of Earth’s diameter to Jupiter’s diameter.

Step-by-Step Solution

Answer

The required scientific notation is about $9.1\times {10}^{-2}$.

Step 1. Define an integer.

An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

Step 2. Define scientific notation.

A number written in scientific notation is of the form $a\times {10}^n$, where $1\le a<10$ and $n$ is an integer.

Step 3. Calculate the ratio of the diameter of Jupiter to the diameter of Earth.

Diameter of Earth $=8000$ miles

 

Diameter of Jupiter $=88000$ miles

 

Ratio of Earth’s diameter to Jupiter’s diameter is

$$\begin{gathered} \frac{8000}{88000}=\frac{1}{11} \\ =0.09090909 \\ \simeq 0.091 \end{gathered}$$

Step 4. Express the number 0 . 091 in scientific notation.

Move the decimal point until it is right of the first non-zero digit.

$0.091\to 9.1$

So, $a=9.1$.

 

The decimal point is moved 2 places to the right.

 

So, $n=-2$

 

Hence,

$0.091=9.1\times {10}^{-2}$

Therefore the required scientific notation is about $9.1\times {10}^{-2}$.