Question

Place the numbers in descending order. 2.3 × 10^−10; 3.2 × 10^−10; 2.3 × 10^−12; 2.3 × 10^−8

Show all work and explain.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To place the numbers in descending order, we need to compare the values of the exponents and the base numbers.

First, let's compare the exponents:
-10, -10, -12, -8

The exponents are -10, -10, -12, -8. In descending order, it will be -8, -10, -10, -12.

Next, let's compare the base numbers:
2.3, 3.2, 2.3, 2.3

Since all the base numbers are the same, we don't need to compare them further.

Now, we can arrange the numbers according to the descending order of the exponents:

2.3 × 10^-8, 2.3 × 10^-10, 3.2 × 10^-10, 2.3 × 10^-12

Final descending order: 2.3 × 10^-8, 2.3 × 10^-10, 3.2 × 10^-10, 2.3 × 10^-12

Answer 2

[AI-generated answer — Explain Bot]

To place the numbers in descending order, we need to compare their magnitudes by looking at their exponents.

Let's compare the exponents of the numbers:

2.3 × 10^−10
3.2 × 10^−10
2.3 × 10^−12
2.3 × 10^−8

The higher the exponent, the larger the number. Therefore, the first step is to compare the exponents to order the numbers.

From least to greatest, the exponents are:
10^−12, 10^−10, 10^−10, 10^−8

As we can see, 10^−12 is the smallest exponent, and 10^−8 is the largest exponent.

Now, let's compare the coefficient (the number in front of the exponent).

For the two numbers with an exponent of 10^−10, they have the same exponent, so we compare their coefficients:

2.3 × 10^−10
3.2 × 10^−10

Since 3.2 is greater than 2.3, we can conclude:

3.2 × 10^−10 is greater than 2.3 × 10^−10

Now, we can order the numbers:

2.3 × 10^−12
2.3 × 10^−10
3.2 × 10^−10
2.3 × 10^−8

So, the numbers in descending order are:
3.2 × 10^−10, 2.3 × 10^−10, 2.3 × 10^−12, 2.3 × 10^−8

Answer 3

[AI-generated answer — Step-by-Step Bot]

To place the numbers in descending order, we need to compare the coefficients of the numbers first. The coefficients are 2.3, 3.2, 2.3, and 2.3.

Since 3.2 is the largest coefficient among them, we can start by placing it first. So, the order becomes: 3.2 × 10^−10; ___; ___; ___

Next, we need to compare the exponents of the numbers. The exponents are -10, -10, -12, and -8.

Since -8 is the largest exponent among them, the number 2.3 × 10^−8 should come next. So, the order becomes: 3.2 × 10^−10; 2.3 × 10^−8; ___; ___

Now, we can compare the remaining two numbers' exponents. The exponents are -10 and -12.

Since -10 is larger than -12, the number 2.3 × 10^−10 should come next. So, the order becomes: 3.2 × 10^−10; 2.3 × 10^−8; 2.3 × 10^−10; ___

Finally, the remaining number 2.3 × 10^−12 goes last.

Therefore, the numbers in descending order are: 3.2 × 10^−10, 2.3 × 10^−8, 2.3 × 10^−10, 2.3 × 10^−12.

Answer 4

Janiya found that her playlist will play for 3.8×102 seconds, 6.3¯¯¯ ×10^5 minutes, 1.05¯¯¯¯¯ ×10^4 hours, or 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days. Which answer uses the most appropriate units?

Show all work and explain.

Answer 5

[AI-generated answer — Bot GPT 3.5]

To determine which answer uses the most appropriate units, we need to compare the values of the exponents and the base numbers.

Let's compare the values:

3.8×102 seconds
6.3¯¯¯¯ ×10^5 minutes
1.05¯¯¯¯¯ ×10^4 hours
4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days

First, let's compare the exponents:

102, 10^5, 10^4, 10^2

The exponents are 2, 5, 4, and 2. In descending order, it will be 5, 4, 2, 2.

Now, let's compare the base numbers:

3.8, 6.3¯¯¯¯, 1.05¯¯¯¯¯, 4.39814¯¯¯¯¯¯¯¯¯¯¯¯

Since all the base numbers are different, we need to compare their values.

Looking at the values, we can see that 6.3¯¯¯¯ × 10^5 represents the largest amount of time in the playlist, as it has the largest base number.

Therefore, the answer that uses the most appropriate units is 6.3¯¯¯¯ × 10^5 minutes.

Answer 6

No bot it's 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ that's the correct answer

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the oversight. You are correct, the answer that uses the most appropriate units is 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ × 10^2 days. This is because days are a larger unit of time compared to minutes, hours, and seconds, and 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ days represents the longest duration in the playlist. Thank you for pointing out the correct answer.

Answer 8

A national park covers an area of 1.42×10^6 acres. A nearby national forest covers an area of 1.2×10^6 acres. What is the total number of acres in the park and the forest combined?

Show all work and explain.

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the total number of acres in the park and the forest combined, we need to add the areas of the national park and the national forest.

The first step is to write the areas in standard form:

National park: 1.42 × 10^6 acres
National forest: 1.2 × 10^6 acres

To add these two numbers together, we can simply add the coefficients:

1.42 + 1.2 = 2.62

Next, we keep the same exponent as the largest exponent among the two numbers, which is 10^6.

Therefore, the total area of the park and the forest combined is 2.62 × 10^6 acres.

Answer 10

The average tectonic plate moves at the rate of 0.006 m per year. How many meters would it move in 2×10^6 years? Write the answer in scientific notation, expressed to the exact decimal place.

Show all work and explain.

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find out how many meters the tectonic plate would move in 2×10^6 years, we multiply the rate by the number of years.

The rate is 0.006 m per year, and the number of years is 2×10^6.

To multiply these values, we can simply multiply the coefficients:

0.006 * 2 = 0.012

Next, we multiply the exponents:

10^6 * 10^6 = 10^(6+6) = 10^12

Therefore, the product is 0.012 * 10^12 meters.

However, we need to express the answer in scientific notation, to the exact decimal place.

The decimal place in scientific notation is determined by moving the decimal point until there is only one non-zero digit to the left of the decimal point.

In this case, the decimal place should be moved 12 places to the left to have only one non-zero digit to the left of the decimal point.

0.012 * 10^12 meters can be written as 1.2 * 10^11 meters.

Therefore, the tectonic plate would move 1.2 * 10^11 meters in 2×10^6 years.

Answer 12

No bot the correct answer is 1.2 * 10^4

Answer 13

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's calculate the correct answer.

To find how many meters the tectonic plate would move in 2×10^6 years, we multiply the rate by the number of years.

The rate is 0.006 m per year, and the number of years is 2×10^6.

To multiply these values, we can simply multiply the coefficients:

0.006 * 2 = 0.012

Next, we multiply the exponents:

10^6

Since we are multiplying by 10^6 years, the exponent remains the same.

Therefore, the product is 0.012 * 10^6 meters.

To express this answer in scientific notation, we need to move the decimal point until there is only one non-zero digit to the left of the decimal point.

In this case, we need to move the decimal point 4 places to the right:

0.012 * 10^6 meters can be written as 1.2 * 10^4 meters.

Therefore, the tectonic plate would move 1.2 * 10^4 meters in 2×10^6 years.

Answer 14

An asteroid is heading toward Mars at the rate of 7.7×10^4 mi./hr. If the asteroid is 3.311×10^8 miles away from Mars, how many hours will it be before it hits Mars? Write the answer in scientific notation, expressed to the exact decimal place.

Show all work and explain.

Answer 15

[AI-generated answer — Bot GPT 3.5]

To find how many hours it will be before the asteroid hits Mars, we need to divide the distance between Mars and the asteroid by the rate at which the asteroid is traveling.

The rate of the asteroid is 7.7×10^4 mi./hr and the distance between Mars and the asteroid is 3.311×10^8 miles.

To divide these values, we need to divide the coefficients:

3.311 ÷ 7.7 ≈ 0.43

Next, we divide the exponents:

10^8 ÷ 10^4 = 10^(8-4) = 10^4

Therefore, the quotient is 0.43 × 10^4 hours.

To express this answer in scientific notation with the exact decimal place, we keep the coefficient the same and move the decimal point 4 places to the right:

0.43 × 10^4 hours can be written as 4.3 × 10^3 hours.

Therefore, it will take approximately 4.3 × 10^3 hours before the asteroid hits Mars.

Answer 16

A field of 3.9 mi2 is being subdivided into 1.3×10^3 family gardens. How many square miles will there be in each garden? Write the answer in scientific notation.

Show all work and explain.

Answer 17

[AI-generated answer — Bot GPT 3.5]

To find out how many square miles will be in each garden, we need to divide the total area of the field by the number of garden subdivisions.

The total area of the field is 3.9 mi^2, and there are 1.3×10^3 garden subdivisions.

To divide these values, we divide the coefficients:

3.9 ÷ 1.3 ≈ 3

Next, we divide the exponents:

10^0 ÷ 10^3 = 10^(0-3) = 10^-3

Therefore, the quotient is 3 × 10^-3 square miles for each garden.

In scientific notation, the coefficient should be written in decimal form without trailing zeros, and the exponent should be positive.

So, the answer in scientific notation is 3 × 10^-3 square miles for each garden.