Question

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 7×105 7 times 10 superscript 5 baseline 0.7×106 0.7 times 10 superscript 6 baseline 0.7×105 0.7 times 10 superscript 5 baseline 7×106

Answer 1

To find out how many senior lunches the grant can provide, you divide the total grant amount by the cost per lunch.

The grant amount is \(1.925 \times 10^6\) dollars, and the cost per lunch is $2.75.

Now, perform the division:

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

First, divide \(1.925\) by \(2.75\):

\[ 1.925 \div 2.75 \approx 0.7 \]

Now, we multiply that result by \(10^6\):

\[ 0.7 \times 10^6 \]

To express this in proper scientific notation, we can convert \(0.7\) to \(7\) by shifting the decimal point one place to the right, which means we need to decrease the exponent of \(10\) by 1:

\[ 0.7 \times 10^6 = 7 \times 10^5 \]

Thus, the number of senior lunches the grant can provide, expressed in scientific notation, is:

\[ 7 \times 10^5 \]

So the correct answer is 7×10^5.

Answer 2

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 3×10−2 3 times 10 negative squared 0.35×10−1 0.35 times 10 superscript negative 1 baseline 3×102

Answer 3

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.

1. Convert the number of containers to standard form: \[ 3.5 \times 10^2 = 350 \]

2. Now perform the division: \[ \text{Gallons per container} = \frac{10.5 \text{ gallons}}{350 \text{ containers}} \]

3. Calculate the division: \[ \frac{10.5}{350} = 0.03 \]

4. Convert 0.03 into scientific notation: \[ 0.03 = 3.0 \times 10^{-2} \]

Thus, the amount of perfume per container, expressed in scientific notation, is:

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

So the correct answer is 3×10−2.

Answer 4

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 2.33×105 2.33 times 10 superscript 5 baseline 4.3×104 4.3 times 10 superscript 4 baseline 4.3×105 4.3 times 10 superscript 5 baseline 0.43×104

Answer 5

To find out how many square feet the pavilion is, we need to divide the total number of bricks by the number of bricks per square foot.

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

2. Bricks per square foot: \[ 6.9 \text{ bricks/square foot} \]

3. Calculate the number of square feet: \[ \text{Square feet} = \frac{2.967 \times 10^5 \text{ bricks}}{6.9 \text{ bricks/square foot}} \]

4. Perform the division: \[ \frac{2.967}{6.9} \approx 0.430 \]

5. Now we multiply by \(10^5\): \[ 0.430 \times 10^5 \]

6. Convert \(0.430\) to proper scientific notation: \[ 0.430 = 4.30 \times 10^{-1} \]

   So: \[ 0.430 \times 10^5 = 4.30 \times 10^{-1} \times 10^5 = 4.30 \times 10^{4} \]

Thus, the number of square feet the pavilion covers, expressed in scientific notation, is:

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

So the correct answer is 4.3×10^4.

Answer 6

For what value of a will 8×103 be 40 times larger than a×102 ?(1 point)

Answer 7

To find the value of \( a \) such that \( 8 \times 10^3 \) is 40 times larger than \( a \times 10^2 \), we can set up the equation:

\[ 8 \times 10^3 = 40 \times (a \times 10^2) \]

Now, simplify the equation:

\[ 8 \times 10^3 = 40a \times 10^2 \]

Next, we can divide both sides by \( 10^2 \) to eliminate it:

\[ \frac{8 \times 10^3}{10^2} = 40a \]

This simplifies to:

\[ 8 \times 10^{3-2} = 40a \]

\[ 8 \times 10^1 = 40a \]

\[ 80 = 40a \]

Now, divide both sides by 40 to solve for \( a \):

\[ a = \frac{80}{40} = 2 \]

Thus, the value of \( a \) is:

\[ \boxed{2} \]

Answer 8

One second is approximately 0.0000115741 of a day. What is this number in scientific notation?(1 point)

Answer 9

To convert the number \(0.0000115741\) to scientific notation, you can follow these steps:

1. Move the decimal point to the right until you have a number between 1 and 10. In this case, you would move the decimal point 5 places to the right.

   \[ 0.0000115741 = 1.15741 \]

2. Since you moved the decimal point 5 places to the right, you will represent this as a negative exponent for 10.

   \[ 0.0000115741 = 1.15741 \times 10^{-5} \]

Therefore, the number \(0.0000115741\) in scientific notation is:

\[ \boxed{1.15741 \times 10^{-5}} \]

Answer 10

The temperature of the sun at its center is about 2.7×107 degrees Fahrenheit. What is this temperature written in decimal notation?(1 point) degrees Fahrenheit

Answer 11

To convert the temperature of the sun at its center from scientific notation \(2.7 \times 10^7\) degrees Fahrenheit to decimal notation, follow these steps:

1. Identify the base number and the exponent. The base is \(2.7\), and the exponent is \(7\).
2. Move the decimal point in \(2.7\) seven places to the right.

Here's how to do that step by step:

• Start with \(2.7\).

• Moving the decimal point seven places to the right means you will have to add zeros.

• Counting the places:

  • 1st place: \(27\)
  • 2nd place: \(270\)
  • 3rd place: \(2700\)
  • 4th place: \(27000\)
  • 5th place: \(270000\)
  • 6th place: \(2700000\)
  • 7th place: \(27000000\)

So,

\[ 2.7 \times 10^7 = 27000000 \]

Thus, the temperature of the sun at its center in decimal notation is

\[ \boxed{27000000} \text{ degrees Fahrenheit.} \]