At a certain lab, the average mass of one bacterium is measured to be 1.1 x 10^-12 kilograms use scientific notation to express the mass of 65 bateria

Answer 1

To find the mass of 65 bacteria, you can multiply the mass of one bacterium by the number of bacteria.

Given that the mass of one bacterium is \( 1.1 \times 10^{-12} \) kilograms, the mass of 65 bacteria can be calculated as follows:

\[ \text{Mass of 65 bacteria} = 65 \times (1.1 \times 10^{-12}) \]

First, calculate \( 65 \times 1.1 \):

\[ 65 \times 1.1 = 71.5 \]

Now, we can express this in scientific notation. The number \( 71.5 \) can be expressed as \( 7.15 \times 10^{1} \).

Putting this together, we multiply:

\[ \text{Mass of 65 bacteria} = 7.15 \times 10^{1} \times 10^{-12} \]

When multiplying powers of ten, you add the exponents:

\[ 7.15 \times 10^{1 - 12} = 7.15 \times 10^{-11} \]

Therefore, the mass of 65 bacteria in scientific notation is:

\[ \boxed{7.15 \times 10^{-11}} \text{ kilograms} \]

Answer 2

Omar broke a cell sample into 88 batches, each weighing 3.9 x 10^-10 grams. How much did the original sample weigh? Use scientific notation to express your answer

Answer 3

To find the weight of the original sample, you can multiply the weight of one batch by the number of batches.

Given that each batch weighs \( 3.9 \times 10^{-10} \) grams and there are 88 batches, the total weight can be calculated as follows:

\[ \text{Total weight} = 88 \times (3.9 \times 10^{-10}) \]

First, calculate \( 88 \times 3.9 \):

\[ 88 \times 3.9 = 343.2 \]

Now, express \( 343.2 \) in scientific notation. \( 343.2 \) can be expressed as:

\[ 3.432 \times 10^{2} \]

Next, incorporate the \( 10^{-10} \) from the weight of each batch:

\[ \text{Total weight} = 3.432 \times 10^{2} \times 10^{-10} \]

When multiplying powers of ten, you add the exponents:

\[ 3.432 \times 10^{2 - 10} = 3.432 \times 10^{-8} \]

Therefore, the weight of the original cell sample in scientific notation is:

\[ \boxed{3.432 \times 10^{-8}} \text{ grams} \]

Answer 4

Omar broke a cell sample into 8 batches, each weighing 3.9 x 10^-10 grams. How much did the original sample weigh? Use scientific notation to express your answer

Answer 5

To find the weight of the original cell sample, you can multiply the weight of one batch by the number of batches.

Given that each batch weighs \( 3.9 \times 10^{-10} \) grams and there are 8 batches, the calculation is as follows:

\[ \text{Total weight} = 8 \times (3.9 \times 10^{-10}) \]

First, calculate \( 8 \times 3.9 \):

\[ 8 \times 3.9 = 31.2 \]

Next, express \( 31.2 \) in scientific notation:

\[ 31.2 = 3.12 \times 10^1 \]

Now, include the \( 10^{-10} \) from the weight of each batch:

\[ \text{Total weight} = 3.12 \times 10^1 \times 10^{-10} \]

When multiplying powers of ten, you add the exponents:

\[ 3.12 \times 10^{1 - 10} = 3.12 \times 10^{-9} \]

Therefore, the weight of the original cell sample in scientific notation is:

\[ \boxed{3.12 \times 10^{-9}} \text{ grams} \]

Answer 6

The distance from Neptune to Mars is 4.272 x 10^-9 kilometers how long would it take a rocket traveling at 3.88 x 10^4 kilometers per hour to travel from Neptune to Mars? Round your answer to the nearest whole number of hours

Answer 7

To find out how long it would take a rocket traveling at \(3.88 \times 10^4\) kilometers per hour to travel the distance from Neptune to Mars, which is \(4.272 \times 10^{-9}\) kilometers, you can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the given values:

\[ \text{Time} = \frac{4.272 \times 10^{-9} \text{ kilometers}}{3.88 \times 10^{4} \text{ kilometers per hour}} \]

To perform this division, first divide the coefficients:

\[ \frac{4.272}{3.88} \approx 1.10103 \]

Now, when dividing the powers of ten, you subtract the exponent in the denominator from the exponent in the numerator:

\[ 10^{-9} \div 10^{4} = 10^{-9 - 4} = 10^{-13} \]

So, the time can be expressed as:

\[ \text{Time} \approx 1.10103 \times 10^{-13} \text{ hours} \]

Now, converting \(1.10103 \times 10^{-13}\) hours to a more manageable number, since it is a very small number, rounding to the nearest whole number gives:

\[ \text{Time} \approx 0 \text{ hours} \]

Therefore, it would take approximately \( \boxed{0} \) hours for a rocket traveling at \(3.88 \times 10^4\) kilometers per hour to travel from Neptune to Mars.

Answer 8

The approximate areas of California and Puerto Rico are listed below

California: 4.24 x 10^-5 square kilometers
Puerto Rico: 5.33 x 10^3 square kilometers
How many times larger is California than Puerto Rico? Write your answer in standard notation, rounding to the nearest tenth

Answer 9

To find out how many times larger California is than Puerto Rico, you can divide the area of California by the area of Puerto Rico.

Given:

• Area of California: \(4.24 \times 10^{-5}\) square kilometers
• Area of Puerto Rico: \(5.33 \times 10^{3}\) square kilometers

The calculation to determine how many times larger California is than Puerto Rico is:

\[ \text{Ratio} = \frac{\text{Area of California}}{\text{Area of Puerto Rico}} = \frac{4.24 \times 10^{-5}}{5.33 \times 10^{3}} \]

Now, to divide these two numbers, you can divide the coefficients and then subtract the exponents:

1. Divide the coefficients:

\[ \frac{4.24}{5.33} \approx 0.795 \]

2. Subtract the exponents:

\[ 10^{-5} \div 10^{3} = 10^{-5 - 3} = 10^{-8} \]

So, combining these results gives:

\[ \text{Ratio} \approx 0.795 \times 10^{-8} \]

Now, express this in standard notation:

\[ 0.795 \times 10^{-8} = 7.95 \times 10^{-9} \]

However, to find how many times larger California is than Puerto Rico, we need the reciprocal of this ratio:

\[ \text{Reciprocal} = \frac{1}{7.95 \times 10^{-9}} \approx 1.257 \times 10^{8} \]

Rounding \(1.257 \times 10^{8}\) to the nearest tenth gives:

\[ \approx 125700000.0 \]

Thus, the answer in standard notation is:

\[ \boxed{125700000.0} \]

Therefore, California is approximately 125.7 million times smaller than Puerto Rico, making the directly proportional conclusion: Puerto Rico is much larger than California.