Divide 3.3×104 by 5.5×10^7 .(1 point) Responses 6×10^−5 6 times 10 to the negative 5 power 6×10^−3 6 times 10 to the negative 3 power 6×10^−4 6 times 10 to the negative 4 power 6×10^−6 6 times 10 to the negative 6 power

Answer 1

To divide \(3.3 \times 10^4\) by \(5.5 \times 10^7\), follow these steps:

1. Divide the coefficients: \[ \frac{3.3}{5.5} = 0.6 \]

2. Subtract the exponents (since you are dividing powers of 10): \[ 10^4 \div 10^7 = 10^{4-7} = 10^{-3} \]

3. Combine the results: \[ 0.6 \times 10^{-3} \]

4. Convert \(0.6\) to scientific notation: \[ 0.6 = 6 \times 10^{-1} \] Thus, \[ 0.6 \times 10^{-3} = 6 \times 10^{-1} \times 10^{-3} = 6 \times 10^{-4} \]

So, the final answer is: \[ \boxed{6 \times 10^{-4}} \]

Answer 2

A city lunch program for seniors received a grant of 1.925×106 dollars. Divide that figure by the cost of $2.75 per lunch to find out how many senior lunches the grant can provide. Write the answer in scientific notation.(1 point) Responses 0.7×106 0.7 times 10 superscript 6 baseline 0.7×105 0.7 times 10 superscript 5 baseline 7×106 7 times 10 superscript 6 baseline 7×105 7 times 10 superscript 5 baseline Skip to navigation page 12 of 12

Answer 3

To find out how many senior lunches the grant can provide, we need to divide the total grant amount by the cost per lunch:

\[ \text{Total Grant} = 1.925 \times 10^6 \text{ dollars} \] \[ \text{Cost per Lunch} = 2.75 \text{ dollars} \]

Now, we perform the division:

\[ \frac{1.925 \times 10^6}{2.75} \]

First, divide the coefficients:

\[ \frac{1.925}{2.75} \] Calculating this gives approximately:

\[ \frac{1.925}{2.75} \approx 0.7 \]

Next, we consider the scientific notation for the number of lunches, which also includes the power of 10:

\[ 10^6 \]

Now combining the results, we have:

\[ 0.7 \times 10^6 \]

To write this in correct scientific notation, we represent \(0.7\) in scientific notation as \(7 \times 10^{-1}\):

\[ 0.7 \times 10^6 = 7 \times 10^{-1} \times 10^6 = 7 \times 10^{5} \]

So the answer is:

\[ \boxed{7 \times 10^5} \]

Answer 4

Solomon needs to distribute 10.5 gallons of perfume among 3.5×102 containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point) Responses 3×10−1 3 times 10 superscript negative 1 baseline 3×102 3 times 10 squared 0.35×10−1 0.35 times 10 superscript negative 1 baseline 3×10−2 3 times 10 negative squared Skip to navigation page 12 of 12

Answer 5

To find out how many gallons of perfume will be in each container, we need to divide the total amount of perfume by the number of containers:

Total perfume: \[ 10.5 \text{ gallons} \]

Number of containers: \[ 3.5 \times 10^2 \text{ containers} \]

Now we perform the division:

\[ \text{Gallons per container} = \frac{10.5}{3.5 \times 10^2} \]

First, we can simplify the division of the coefficients:

\[ \frac{10.5}{3.5} = 3 \]

Now we handle the powers of ten:

\[ \frac{1}{10^2} = 10^{-2} \]

Putting it all together:

\[ \text{Gallons per container} = 3 \times 10^{-2} \]

So, the final answer in scientific notation is:

\[ \boxed{3 \times 10^{-2}} \]

Answer 6

A large pavilion is made of 2.967×105 bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation.(1 point) Responses 4.3×105 4.3 times 10 superscript 5 baseline 0.43×104 0.43 times 10 superscript 4 baseline 4.3×104 4.3 times 10 superscript 4 baseline 2.33×105 2.33 times 10 superscript 5 baseline Skip to navigation page 12 of 12

Answer 7

To find the number of square feet in the pavilion, we will divide the total number of bricks by the number of bricks per square foot.

Total number of bricks: \[ 2.967 \times 10^5 \text{ bricks} \]

Bricks per square foot: \[ 6.9 \text{ bricks/sq ft} \]

Now we perform the division:

\[ \text{Square feet} = \frac{2.967 \times 10^5}{6.9} \]

First, we divide the coefficients:

\[ \frac{2.967}{6.9} \approx 0.43 \]

Now we include the power of ten:

Since the division is purely of numbers, we keep that as it is:

\[ 10^5 \]

So, we have:

\[ \text{Square feet} = 0.43 \times 10^5 \]

To put \(0.43\) into proper scientific notation, we can write:

\[ 0.43 = 4.3 \times 10^{-1} \]

Thus,

\[ 0.43 \times 10^5 = 4.3 \times 10^{-1} \times 10^5 = 4.3 \times 10^{4} \]

Therefore, the final answer in scientific notation is:

\[ \boxed{4.3 \times 10^4} \]