Math  /  Numbers & Operations

QuestionThe atmospheric pressure on the surface of Venus is 90 . atm. Calculate the atmospheric pressure in kPa . Be sure your answer has the right number of significant digits. kPa ×10

Studdy Solution

STEP 1

What is this asking? We need to convert a pressure given in atmospheres (atm) to kilopascals (kPa). Watch out! Don't forget about significant figures and make sure to use the correct conversion factor!

STEP 2

1. Conversion Setup
2. Calculation
3. Significant Figures

STEP 3

Alright, let's **get started**!
We're given a pressure in **atmospheres**, and we want to convert it to **kilopascals**.
The conversion factor we need is 1 atm=101.325 kPa1 \ atm = 101.325 \ kPa.
This tells us that one atmosphere is *exactly* equal to 101.325 kilopascals.
Remember that!

STEP 4

We're given 90 atm90 \ atm.
To convert, we'll multiply our given value by a fraction that's equal to one.
Why one?
Because multiplying by one doesn't change the *value* of what we started with, only the *units*.

STEP 5

Our magic fraction will have kilopascals on top and atmospheres on the bottom.
This way, the atmospheres will divide to one, and we'll be left with kilopascals.
It looks like this: 101.325 kPa1 atm\frac{101.325 \ kPa}{1 \ atm}.
See how the units will work out?

STEP 6

Let's **do the math**!
We multiply our given pressure by our conversion fraction: 90 atm101.325 kPa1 atm90 \ atm \cdot \frac{101.325 \ kPa}{1 \ atm}

STEP 7

Notice how the units of *atm* divide to one, leaving us with *kPa*.
That's exactly what we wanted!
Now, we just multiply the numbers: 90101.325 kPa=9119.25 kPa90 \cdot 101.325 \ kPa = 9119.25 \ kPa

STEP 8

Almost there!
Now, let's consider **significant figures**.
Our original value, 90 atm90 \ atm, has one significant figure (the 9).
Since we're multiplying, our final answer should also have one significant figure.

STEP 9

To round 9119.25 kPa9119.25 \ kPa to one significant figure, we look at the first digit, which is 9.
The next digit is 1, which is less than 5, so we round down.
Our final answer will be 9000 kPa9000 \ kPa.

STEP 10

The atmospheric pressure on Venus is 9000 kPa9000 \ kPa.

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