Use scientific notation to determine which of these numbers has the least value: 98,789,000;

Question

987,890,000; or 89,987,000. Write your answer in scientific notation, expressed to the exact decimal
place.(1 point)

Answer 1

To compare the numbers 98,789,000; 987,890,000; and 89,987,000 in scientific notation, we will first convert each number into scientific notation.

1. 98,789,000: \[ 98,789,000 = 9.8789 \times 10^7 \]

2. 987,890,000: \[ 987,890,000 = 9.8789 \times 10^8 \]

3. 89,987,000: \[ 89,987,000 = 8.9987 \times 10^7 \]

Now we compare the numbers in scientific notation:

• \( 9.8789 \times 10^7 \) (98,789,000)
• \( 9.8789 \times 10^8 \) (987,890,000)
• \( 8.9987 \times 10^7 \) (89,987,000)

The powers of 10 indicate that \( 10^8 \) is larger than \( 10^7 \). Therefore, both \( 9.8789 \times 10^8 \) and \( 9.8789 \times 10^7 \) are larger than \( 8.9987 \times 10^7 \), but we need to determine which of the numbers with \( 10^7 \) is smaller.

Comparing the coefficients:

• \( 9.8789 \) (from 98,789,000)
• \( 8.9987 \) (from 89,987,000)

Since \( 8.9987 < 9.8789 \), the number with the least value is:

\[ \boxed{8.9987 \times 10^7} \]

Answer 2

is this correct?

Answer 3

Yes, let's double-check the conversions and comparisons step by step:

1. Convert each number to scientific notation:

   • For 98,789,000: \[ 98,789,000 = 9.8789 \times 10^7 \]

   • For 987,890,000: \[ 987,890,000 = 9.8789 \times 10^8 \]

   • For 89,987,000: \[ 89,987,000 = 8.9987 \times 10^7 \]

2. Compare the scientific notation representations:

   • 98,789,000: \( 9.8789 \times 10^7 \)
   • 987,890,000: \( 9.8789 \times 10^8 \)
   • 89,987,000: \( 8.9987 \times 10^7 \)

3. Identifying the least value:

   • \( 9.8789 \times 10^8 \) is the largest because of the \( 10^8 \) power.
   • Now we can compare \( 9.8789 \times 10^7 \) and \( 8.9987 \times 10^7 \).

The coefficients (when the powers of ten are the same) tell us which is smaller:

• \( 9.8789 \) is greater than \( 8.9987 \).

Since \( 8.9987 < 9.8789 \), it shows that 89,987,000 is indeed the smallest number.

Therefore, the number with the least value in scientific notation is: \[ \boxed{8.9987 \times 10^7} \]

So yes, the assessment is correct. Thank you for prompting the check!

Answer 4

Place the numbers in descending order
2.3 X 10^-10; 3.2 X 10^-10; 2.3 X 10^-12; 2.3 X 10^-8

Answer 5

To place the numbers \(2.3 \times 10^{-10}\), \(3.2 \times 10^{-10}\), \(2.3 \times 10^{-12}\), and \(2.3 \times 10^{-8}\) in descending order, we can compare their magnitudes by considering both the coefficients and the powers of 10.

1. Numbers:

   • \(2.3 \times 10^{-10}\)
   • \(3.2 \times 10^{-10}\)
   • \(2.3 \times 10^{-12}\)
   • \(2.3 \times 10^{-8}\)

2. Compare by powers of 10:

   • The number with the highest power (least negative exponent) is the largest. So first note the powers:
     • \(10^{-8}\) (largest)
     • \(10^{-10}\)
     • \(10^{-12}\) (smallest)

Based on that, we can rank the numbers:

• \(2.3 \times 10^{-8}\) is the largest because \(10^{-8}\) is the greatest exponent.
• \(3.2 \times 10^{-10}\) is next because it has a power of \(10^{-10}\) and a coefficient of \(3.2\), which is greater than \(2.3\).
• \(2.3 \times 10^{-10}\) follows since it also has a power of \(10^{-10}\) but a smaller coefficient than \(3.2\).
• \(2.3 \times 10^{-12}\) is the smallest because it has the greatest negative exponent.

3. Final order in descending order:

• \(2.3 \times 10^{-8}\)
• \(3.2 \times 10^{-10}\)
• \(2.3 \times 10^{-10}\)
• \(2.3 \times 10^{-12}\)

Therefore, the numbers in descending order are:

\[ \boxed{2.3 \times 10^{-8}, 3.2 \times 10^{-10}, 2.3 \times 10^{-10}, 2.3 \times 10^{-12}} \]

Answer 6

Janiya is taking a road trip. the distance she plans to travel can be written as 3 X 10^2 kilometers, 3 X 10^5 meters, 3 X 10^7 centimeters, or 3 X 10^8 millimeters. which distance uses the most appropriate units

Answer 7

To determine which distance uses the most appropriate units for a road trip, we need to convert all the distances into the same unit (e.g., kilometers) to compare them directly.

1. Convert 3 x 10² kilometers: \[ 3 \times 10^2 \text{ kilometers} = 300 \text{ kilometers} \]

2. Convert 3 x 10⁵ meters to kilometers: \[ 3 \times 10^5 \text{ meters} = 3 \times 10^5 \div 1000 = 3 \times 10^2 = 300 \text{ kilometers} \]

3. Convert 3 x 10⁷ centimeters to kilometers: \[ 3 \times 10^7 \text{ centimeters} = 3 \times 10^7 \div 100,000 = 3 \times 10^2 = 300 \text{ kilometers} \]

4. Convert 3 x 10⁸ millimeters to kilometers: \[ 3 \times 10^8 \text{ millimeters} = 3 \times 10^8 \div 1,000,000 = 3 \times 10^2 = 300 \text{ kilometers} \]

Summary of Distances

• 3 x 10² kilometers = 300 kilometers
• 3 x 10⁵ meters = 300 kilometers
• 3 x 10⁷ centimeters = 300 kilometers
• 3 x 10⁸ millimeters = 300 kilometers

Conclusion

While all four distances represent the same value of 300 kilometers, the most appropriate unit for a road trip is kilometers because it is a commonly used unit for larger distances typically encountered when traveling by car. Therefore, the most appropriate option is:

\[ \boxed{3 \times 10^2 \text{ kilometers}} \]

Answer 8

a national park covers an area of 1.42 X 10^6 acres. A nearby national forest covers an area of 1.2 X 10^6 acres. what is the total number of acres in the park and the forest combined

Answer 9

To find the total area covered by the national park and the national forest, we’ll simply add the two areas together, given in scientific notation:

1. Area of the national park: \(1.42 \times 10^6\) acres
2. Area of the national forest: \(1.2 \times 10^6\) acres

Step 1: Align the powers of ten

Since both areas are expressed with the same exponent (\(10^6\)), we can directly add the coefficients.

Step 2: Add the coefficients

\[ 1.42 + 1.2 = 2.62 \]

Step 3: Combine the result with the common exponent

Now, put the coefficient back with the common exponent: \[ 2.62 \times 10^6 \]

Final Result

The total area covered by the national park and the national forest combined is:

\[ \boxed{2.62 \times 10^6 \text{ acres}} \]

Answer 10

The distance from Venus to the sun is about 67,000,000 miles. The distance from Earth to the sun is about 2.6 X 10^7 farther. What is the distance from earth to the sun? Write your answer in scientific notation to 1 decimal place.

_X10^7 miles

Answer 11

To find the distance from Earth to the sun, we need to add the distance from Venus to the sun with the additional distance given.

1. Distance from Venus to the sun: \[ 67,000,000 \text{ miles} = 6.7 \times 10^7 \text{ miles} \]

2. Additional distance from Earth to the sun: \[ 2.6 \times 10^7 \text{ miles} \]

3. Add the two distances together: \[ \text{Distance from Earth to the sun} = \text{Distance from Venus to the sun} + \text{Additional distance} \] \[ = 6.7 \times 10^7 + 2.6 \times 10^7 \] \[ = (6.7 + 2.6) \times 10^7 \] \[ = 9.3 \times 10^7 \text{ miles} \]

Final Result

The distance from Earth to the sun is: \[ \boxed{9.3 \times 10^7 \text{ miles}} \]