Planet Earth has a mass of 5.9726 × 10^24 kilograms. And although 70% of the Earth's surface is made of water, the water's mass is only 5 × 10^-4 percent of the Earth's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.

Answer 1

To estimate the mass of water on Earth, we start with the total mass of the Earth:

\[ \text{Mass of Earth} = 5.9726 \times 10^{24} \text{ kg} \]

We know that the mass of the water is given as \( 5 \times 10^{-4} \) percent of the Earth's total mass. First, we need to convert this percentage into a decimal for calculations:

\[ 5 \times 10^{-4} \text{ percent} = \frac{5 \times 10^{-4}}{100} = 5 \times 10^{-6} \]

Next, we calculate the mass of the water by multiplying the Earth's mass by this decimal fraction:

\[ \text{Mass of water} = \text{Mass of Earth} \times \left(5 \times 10^{-6}\right) \]

Substituting the mass of the Earth into the equation:

\[ \text{Mass of water} = (5.9726 \times 10^{24}) \times (5 \times 10^{-6}) \]

Now, we perform the multiplication step-by-step. First, multiply the coefficients:

\[ 5.9726 \times 5 = 29.863 \]

Next, multiply the powers of ten:

\[ 10^{24} \times 10^{-6} = 10^{24 - 6} = 10^{18} \]

Now, combining these results, we find:

\[ \text{Mass of water} = 29.863 \times 10^{18} \text{ kg} \]

We can convert this into scientific notation by writing it as:

\[ 2.9863 \times 10^{19} \text{ kg} \quad (\text{moving the decimal one place to the left increases the exponent by 1}) \]

Thus, the estimated mass of the planet's water is:

\[ \boxed{2.9863 \times 10^{19} \text{ kg}} \]

This calculation includes all of the estimates and steps used to arrive at the final answer.

Answer 2

can you make it a little less advanced and without all the symbols and slashes

Answer 3

Sure! Let's break it down in simpler terms and without using too many symbols.

1. Find the mass of the Earth: The Earth has a mass of about 5.9726 × 10^24 kilograms.

2. Percentage of water: We know that the mass of the water on Earth is 0.0005 percent of the Earth’s total mass. To make this easier to use, we convert the percentage into a decimal.

   • 0.0005 percent can be written as 0.0005 divided by 100 which equals 0.000005, or in scientific notation, that’s 5 × 10^(-6).

3. Calculate the mass of water: To find the mass of the water, we multiply the mass of the Earth by the fraction that represents water.

   So, we take:

   • 5.9726 × 10^24 kilograms (mass of the Earth)
   • and multiply it by 5 × 10^(-6) (the fraction representing water).

4. Calculating the multiplication step:

   • First, multiply the numbers: 5.9726 times 5 is approximately 29.863.
   • Next, for the powers of ten, we take 10^24 times 10^(-6). When you add the exponents, you get 10^(24 - 6) which equals 10^18.

5. Combine the results: This gives us:

   • Approximately 29.863 × 10^18 kilograms.

6. Write in proper scientific notation: To convert 29.863 into proper scientific notation, you would move the decimal point one place to the left, which increases the exponent by 1. So it becomes:

   • 2.9863 × 10^19 kilograms.

Therefore, the estimated mass of all the water on Earth is roughly 2.9863 × 10^19 kilograms.

Answer 4

can you make it just a little bit less advanced

Answer 5

Of course! Let's simplify it further.

1. Earth's Mass: The mass of the Earth is about 5.9726 followed by 24 zeros kilograms.

2. Water Percentage: The water on Earth makes up a very small part: 0.0005 percent. To make it easier to work with, let's change that percentage into a decimal:

   • 0.0005 percent means we divide by 100. This gives us 0.000005, which is the same as saying 5 times 10 to the power of negative 6.

3. Finding the Mass of Water: To find out how much the water weighs, we need to multiply the mass of the Earth by the water percentage.

   • We multiply:
     • Earth's mass: 5.9726 followed by 24 zeros
     • By the decimal for water: 0.000005 (or 5 times 10 to the power of negative 6).

4. Doing the Math:

   • First, multiply 5.9726 by 5, which equals about 29.863.
   • Then, for the part with the zeros, when we multiply:
     • 10 to the power of 24 with 10 to the power of negative 6, we combine the powers. We get 10 to the power of 18.

5. Putting It All Together:

   • Now we have about 29.863 times 10 to the power of 18 kilograms for the mass of the water.

6. Final Adjustment: To write this in a standard way, we adjust 29.863 to get it between 1 and 10 by moving the decimal left, which gives us:

   • 2.9863 times 10 to the power of 19 kilograms.

So, the estimated mass of all the water on Earth is about 2.9863 times 10 to the power of 19 kilograms.