Place the numbers in descending order. 2.3 × 10−10 ; 3.2 × 10−10 ; 2.3 × 10−12 ; 2.3 × 10−8 (2 points) ; ; ;

Answer 1

To place the numbers in descending order, we first need to compare their values. Here are the numbers provided:

1. \(2.3 \times 10^{-10}\)
2. \(3.2 \times 10^{-10}\)
3. \(2.3 \times 10^{-12}\)
4. \(2.3 \times 10^{-8}\)

We can convert these to standard decimal form for easier comparison:

1. \(2.3 \times 10^{-10} = 0.00000000023\)
2. \(3.2 \times 10^{-10} = 0.00000000032\)
3. \(2.3 \times 10^{-12} = 0.0000000000023\)
4. \(2.3 \times 10^{-8} = 0.000000023\)

Now, let's compare them:

• \(2.3 \times 10^{-8} = 0.000000023\) is the largest.
• \(3.2 \times 10^{-10} = 0.00000000032\) comes next.
• \(2.3 \times 10^{-10} = 0.00000000023\) follows.
• \(2.3 \times 10^{-12} = 0.0000000000023\) is the smallest.

Putting these in descending order:

1. \(2.3 \times 10^{-8}\)
2. \(3.2 \times 10^{-10}\)
3. \(2.3 \times 10^{-10}\)
4. \(2.3 \times 10^{-12}\)

So, the numbers in descending order are:

2.3 × 10−8 ; 3.2 × 10−10 ; 2.3 × 10−10 ; 2.3 × 10−12

Answer 2

aniya is taking a road trip. The distance she plans to travel can be written as 3×102 kilometers, 3×105 meters, 3×107 centimeters, or 3×108 millimeters. Which distance uses the most appropriate units?(1 point) Responses 3×102 kilometers 3 times 10 squared kilometers 3×107 centimeters 3 times 10 to the 7th power centimeters 3×108 millimeters 3 times 10 to the 8th power millimeters 3×105 meters

Answer 3

To determine which distance uses the most appropriate units, we can convert all the distances to a common unit, typically kilometers. Here are the conversions for each distance:

1. \(3 \times 10^2\) kilometers: This is already in kilometers.

   • Distance = \(300\) kilometers

2. \(3 \times 10^5\) meters: To convert meters to kilometers, we divide by \(1000\).

   • \(3 \times 10^5\) meters = \(3 \times 10^5 \div 1000 = 3 \times 10^2\) kilometers = \(300\) kilometers

3. \(3 \times 10^7\) centimeters: To convert centimeters to kilometers, we divide by \(100,000\) (since \(1\) kilometer = \(100,000\) centimeters).

   • \(3 \times 10^7\) centimeters = \(3 \times 10^7 \div 100,000 = 3 \times 10^2\) kilometers = \(300\) kilometers

4. \(3 \times 10^8\) millimeters: To convert millimeters to kilometers, we divide by \(1,000,000\) (since \(1\) kilometer = \(1,000,000\) millimeters).

   • \(3 \times 10^8\) millimeters = \(3 \times 10^8 \div 1,000,000 = 3 \times 10^2\) kilometers = \(300\) kilometers

All the distances are equivalent, but using kilometers (the first option, \(3 \times 10^2\) kilometers) is the most appropriate choice for expressing a long road trip, as kilometers are a standard unit for measuring road distances.

Therefore, the most appropriate unit for Aniya's road trip is:

\(3 \times 10^2\) kilometers.

Answer 4

The distance from Venus to the sun is about 67,000,000 miles. The distance from Earth to the sun is about 2.6×107 farther. What is the distance from Earth to the sun? Write your answer in scientific notation to 1 decimal place.(1 point) ×107 miles

Answer 5

To find the distance from Earth to the sun, we will first convert the distance from Venus to the sun and then add the additional distance given in the problem.

1. The distance from Venus to the sun is approximately \(67,000,000\) miles.

   In scientific notation, that is:
   \[ 67,000,000 \text{ miles} = 6.7 \times 10^7 \text{ miles} \]

2. The distance from Earth to the sun is about \(2.6 \times 10^7\) miles farther than the distance from Venus to the sun.

3. To find the distance from Earth to the sun, we add the distance from Venus to the sun and the additional distance: \[ \text{Distance from Earth to the sun} = \text{Distance from Venus to the sun} + \text{Additional distance} \] \[ \text{Distance from Earth to the sun} = 6.7 \times 10^7 + 2.6 \times 10^7 \]

4. Combining the two distances: \[ 6.7 \times 10^7 + 2.6 \times 10^7 = (6.7 + 2.6) \times 10^7 = 9.3 \times 10^7 \]

Thus, the distance from Earth to the sun is:

\[ \boxed{9.3 \times 10^7} \text{ miles} \]

Answer 6

Calculate 4.8×10−3−9.4×10−6 . Express the answer in scientific notation rounding to 2 decimal places.(1 point)

Answer 7

To calculate \(4.8 \times 10^{-3} - 9.4 \times 10^{-6}\), we need to express both numbers with the same exponent. Let's convert \(4.8 \times 10^{-3}\) to have the same exponent as \(9.4 \times 10^{-6}\).

1. Convert \(4.8 \times 10^{-3}\): \[ 4.8 \times 10^{-3} = 4.8 \times 10^{-3} \times \frac{1000}{1000} = 4.8 \times 10^{-3} \times 10^{3} \times 10^{-3} = 4.8 \times 10^{0} \times 10^{-3} = 4800 \times 10^{-6} \]

So, \(4.8 \times 10^{-3}\) can be rewritten as \(4800 \times 10^{-6}\).

2. Now we can rewrite the expression: \[ 4800 \times 10^{-6} - 9.4 \times 10^{-6} = (4800 - 9.4) \times 10^{-6} \] \[ = 4790.6 \times 10^{-6} \]

3. Convert \(4790.6\) into scientific notation: \[ 4790.6 = 4.7906 \times 10^{3} \] Therefore, \[ 4790.6 \times 10^{-6} = 4.7906 \times 10^{-3} \]

4. Final express and rounding: Rounding \(4.7906\) to two decimal places, we get \(4.79\).

So, the final answer in scientific notation rounded to two decimal places is:

\[ \boxed{4.79 \times 10^{-3}} \]

Answer 8

A strand of hair has an average mass of 2.17×10−5 ounces. A grain of rice has an average mass of 0.002 ounces. How much heavier is a grain of rice than a strand of hair? Express your answer in scientific notation.(1 point) × ounces

Answer 9

To find out how much heavier a grain of rice is than a strand of hair, we can subtract the mass of the strand of hair from the mass of the grain of rice.

1. Mass of the strand of hair: \[ 2.17 \times 10^{-5} \text{ ounces} \]

2. Mass of the grain of rice: \[ 0.002 \text{ ounces} = 2.0 \times 10^{-3} \text{ ounces} \]

3. Now we subtract the two masses: \[ 2.0 \times 10^{-3} \text{ ounces} - 2.17 \times 10^{-5} \text{ ounces} \]

To perform this subtraction, we must express both numbers with the same exponent. We can convert \(2.0 \times 10^{-3}\) to have the same exponent as \(2.17 \times 10^{-5}\):

\[ 2.0 \times 10^{-3} = 2.0 \times 10^{-3} \times \frac{100}{100} = 200 \times 10^{-5} \]

Now we can perform the subtraction: \[ 200 \times 10^{-5} - 2.17 \times 10^{-5} = (200 - 2.17) \times 10^{-5} \] \[ = 197.83 \times 10^{-5} \]

4. Convert \(197.83\) to scientific notation: \[ 197.83 = 1.9783 \times 10^{2} \] Therefore: \[ 197.83 \times 10^{-5} = 1.9783 \times 10^{2} \times 10^{-5} = 1.9783 \times 10^{-3} \]

5. Round to the appropriate number of decimal places (if necessary): If we round \(1.9783\) to two decimal places, we get \(1.98\).

Thus, the final answer, representing how much heavier a grain of rice is than a strand of hair, in scientific notation is:

\[ \boxed{1.98 \times 10^{-3}} \text{ ounces} \]

Answer 10

Light travels at an approximate rate of 1.9×105 mi./sec. There are about 3.2×107 seconds in a year. About how many miles does light travel in a year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1 point) miles

Answer 11

To calculate the distance light travels in a year, we will multiply the speed of light by the number of seconds in a year.

1. Speed of light:
   \(1.9 \times 10^5\) miles/second

2. Number of seconds in a year:
   \(3.2 \times 10^7\) seconds

3. Calculate the distance: \[ \text{Distance} = (\text{Speed of light}) \times (\text{Time in seconds}) \] \[ \text{Distance} = (1.9 \times 10^5) \times (3.2 \times 10^7) \]

4. Multiply the coefficients and the powers of 10:

   • Coefficients: \(1.9 \times 3.2 = 6.08\)
   • Powers of 10: \(10^5 \times 10^7 = 10^{5 + 7} = 10^{12}\)

   So, \[ \text{Distance} = 6.08 \times 10^{12} \text{ miles} \]

The final answer, in scientific notation and expressed to the exact decimal place, is:

\[ \boxed{6.08 \times 10^{12}} \text{ miles} \]