Let's set up the equation to solve for the value of a.
We are given two expressions: 8×103 and 40(a×102).
8×103 = 40(a×102)
We can simplify the second expression by multiplying 40 by a:
8×103 = 40a × 102
Next, we can simplify 102 to 100:
8×103 = 40a × 100
We can further simplify 100 by dividing both sides of the equation by 100:
8×103 ÷ 100 = 40a
80 = 40a
Finally, we can solve for a by dividing both sides by 40:
80 ÷ 40 = a
a = 2
Therefore, the value of a is 2.
For what value of a will 8×103 be 40 times larger than a×102 ?(1 point) $$
45 answers
its wrong
Apologies for the mistake. Let's try solving it again:
We are given the equation: 8×10^3 = 40(a×10^2)
We can simplify the equation by multiplying 40 by a:
8×10^3 = 40a × 10^2
Next, we can simplify 10^2 to 100:
8×10^3 = 40a × 100
Now, we can further simplify 100 by dividing both sides of the equation by 100:
(8×10^3) ÷ 100 = 40a
80 = 40a
Finally, we can solve for a by dividing both sides by 40:
80 ÷ 40 = a
a = 2
Therefore, the value of a is 2.
We are given the equation: 8×10^3 = 40(a×10^2)
We can simplify the equation by multiplying 40 by a:
8×10^3 = 40a × 10^2
Next, we can simplify 10^2 to 100:
8×10^3 = 40a × 100
Now, we can further simplify 100 by dividing both sides of the equation by 100:
(8×10^3) ÷ 100 = 40a
80 = 40a
Finally, we can solve for a by dividing both sides by 40:
80 ÷ 40 = a
a = 2
Therefore, the value of a is 2.
One second is approximately 0.0000115741 of a day. What is this number in scientific notation?(1 point)
The given number, 0.0000115741, in scientific notation would be represented as 1.15741 x 10^(-5).
so thanswer is
1.15741 x 10^(-5)
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)
The temperature of the sun at its center, 2.7×10^7 degrees Fahrenheit, written in decimal notation is 27,000,000 degrees Fahrenheit.
Use scientific notation to determine which of these numbers has the least value: 98,789,000; 987,890,000; or 89,987,000. Write your answer in scientific notation, expressed to the exact decimal place.(1 point)
To determine which number has the least value, we need to convert each number to scientific notation.
98,789,000 can be written as 9.8789 x 10^7.
987,890,000 can be written as 9.8789 x 10^8.
89,987,000 can be written as 8.9987 x 10^7.
Comparing the exponents, we see that 9.8789 x 10^7 has the smallest exponent, making it the least value among the given numbers.
98,789,000 can be written as 9.8789 x 10^7.
987,890,000 can be written as 9.8789 x 10^8.
89,987,000 can be written as 8.9987 x 10^7.
Comparing the exponents, we see that 9.8789 x 10^7 has the smallest exponent, making it the least value among the given numbers.
answer
Apologies for the confusion. The correct answer is:
The number with the least value, expressed in scientific notation, is 8.9987 x 10^7.
The number with the least value, expressed in scientific notation, is 8.9987 x 10^7.
Place the numbers in descending order. 2.3 × 10−10 ; 3.2 × 10−10 ; 2.3 × 10−12 ; 2.3 × 10−8 (2 points)
To place the numbers in descending order, we need to compare the exponents first.
2.3 × 10^(-12) has the smallest exponent, so it will be the first number:
2.3 × 10^(-12)
Next, we compare the remaining three numbers:
2.3 × 10^(-10)
2.3 × 10^(-8)
3.2 × 10^(-10)
Among these three numbers, 2.3 × 10^(-8) has the largest exponent, so it will be the second number:
2.3 × 10^(-12)
2.3 × 10^(-8)
Finally, we compare the remaining two numbers:
2.3 × 10^(-10)
3.2 × 10^(-10)
3.2 × 10^(-10) has a larger coefficient than 2.3 × 10^(-10), so it will be the third number:
2.3 × 10^(-12)
2.3 × 10^(-8)
3.2 × 10^(-10)
Therefore, the numbers in descending order are:
2.3 × 10^(-12), 2.3 × 10^(-8), and 3.2 × 10^(-10).
2.3 × 10^(-12) has the smallest exponent, so it will be the first number:
2.3 × 10^(-12)
Next, we compare the remaining three numbers:
2.3 × 10^(-10)
2.3 × 10^(-8)
3.2 × 10^(-10)
Among these three numbers, 2.3 × 10^(-8) has the largest exponent, so it will be the second number:
2.3 × 10^(-12)
2.3 × 10^(-8)
Finally, we compare the remaining two numbers:
2.3 × 10^(-10)
3.2 × 10^(-10)
3.2 × 10^(-10) has a larger coefficient than 2.3 × 10^(-10), so it will be the third number:
2.3 × 10^(-12)
2.3 × 10^(-8)
3.2 × 10^(-10)
Therefore, the numbers in descending order are:
2.3 × 10^(-12), 2.3 × 10^(-8), and 3.2 × 10^(-10).
its wrong
Apologies for the mistake. Let's reorder the numbers correctly:
2.3 × 10^(-12)
2.3 × 10^(-10)
3.2 × 10^(-10)
2.3 × 10^(-8)
Therefore, the correct order from largest to smallest is:
2.3 × 10^(-8)
3.2 × 10^(-10)
2.3 × 10^(-10)
2.3 × 10^(-12)
2.3 × 10^(-12)
2.3 × 10^(-10)
3.2 × 10^(-10)
2.3 × 10^(-8)
Therefore, the correct order from largest to smallest is:
2.3 × 10^(-8)
3.2 × 10^(-10)
2.3 × 10^(-10)
2.3 × 10^(-12)
whats answer
Apologies for the confusion. Here is the correct order from largest to smallest:
2.3 × 10^(-8)
3.2 × 10^(-10)
2.3 × 10^(-10)
2.3 × 10^(-12)
Therefore, the correct order is:
2.3 × 10^(-8), 3.2 × 10^(-10), 2.3 × 10^(-10), 2.3 × 10^(-12)
2.3 × 10^(-8)
3.2 × 10^(-10)
2.3 × 10^(-10)
2.3 × 10^(-12)
Therefore, the correct order is:
2.3 × 10^(-8), 3.2 × 10^(-10), 2.3 × 10^(-10), 2.3 × 10^(-12)
Janiya found that her playlist will play for 3.8×102 seconds, 6.3¯¯¯ ×105 minutes, 1.05¯¯¯¯¯ ×104 hours, or 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×102 days. Which answer uses the most appropriate units?(1 point) Responses 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×102 days 4 point modifying above 39814 with bar times 10 squared days 3.8×107 seconds 3.8 times 10 superscript 7 baseline seconds 1.05 ¯¯¯¯¯¯ ×104 hours 1 point modifying above 05 with bar times 10 superscript 4 baseline hours 6.3¯¯¯ ×105 minutes
The most appropriate units in this case would be the one that is the largest and gives the most comprehensive representation of the duration.
Among the provided options, 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ × 10^2 days is the largest value, and it represents the duration in terms of days, which is a larger unit of time compared to hours, minutes, and seconds.
Therefore, the answer is 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ × 10^2 days.
Among the provided options, 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ × 10^2 days is the largest value, and it represents the duration in terms of days, which is a larger unit of time compared to hours, minutes, and seconds.
Therefore, the answer is 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ × 10^2 days.
whats the answer
The answer is 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ × 10^2 days.
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
To find the distance from Earth to the sun, which is 2.6×10^7 miles farther than the distance from Venus to the sun, we can add the two distances together.
Distance from Venus to the sun: 67,000,000 miles
Add 2.6×10^7 miles:
67,000,000 + 2.6×10^7 = 69.6×10^7 miles
To write this in scientific notation to one decimal place, we need to express it as 6.96×10^8 miles.
Therefore, the distance from Earth to the sun is approximately 6.96×10^8 miles.
Distance from Venus to the sun: 67,000,000 miles
Add 2.6×10^7 miles:
67,000,000 + 2.6×10^7 = 69.6×10^7 miles
To write this in scientific notation to one decimal place, we need to express it as 6.96×10^8 miles.
Therefore, the distance from Earth to the sun is approximately 6.96×10^8 miles.
what te answer
Apologies for the mistake. To find the distance from Earth to the sun, we need to add the distance from Venus to the sun (67,000,000 miles) to the additional distance (2.6×10^7 miles).
67,000,000 miles + 2.6×10^7 miles = 67,000,000 miles + 26,000,000 miles = 93,000,000 miles.
Therefore, the distance from Earth to the sun is 9.3×10^7 miles in scientific notation to 1 decimal place.
67,000,000 miles + 2.6×10^7 miles = 67,000,000 miles + 26,000,000 miles = 93,000,000 miles.
Therefore, the distance from Earth to the sun is 9.3×10^7 miles in scientific notation to 1 decimal place.
Calculate 4.8×10−3−9.4×10−6 . Express the answer in scientific notation rounding to 2 decimal places.(1 point)
To calculate 4.8×10^(-3) - 9.4×10^(-6), we need to subtract the two numbers:
4.8×10^(-3) - 9.4×10^(-6) = 4.8×10^(-3) - 0.0094×10^(-3)
We can simplify the numbers by subtracting 0.0094 from 4.8:
4.8 - 0.0094 = 4.7906
Now, we need to express the result in scientific notation and round to 2 decimal places.
4.7906 can be written as 4.79 × 10^0 (since it is already in the decimal form and has no decimal places to move).
Therefore, the answer in scientific notation, rounded to 2 decimal places, is 4.79 × 10^0.
4.8×10^(-3) - 9.4×10^(-6) = 4.8×10^(-3) - 0.0094×10^(-3)
We can simplify the numbers by subtracting 0.0094 from 4.8:
4.8 - 0.0094 = 4.7906
Now, we need to express the result in scientific notation and round to 2 decimal places.
4.7906 can be written as 4.79 × 10^0 (since it is already in the decimal form and has no decimal places to move).
Therefore, the answer in scientific notation, rounded to 2 decimal places, is 4.79 × 10^0.
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
To find how much heavier a grain of rice is than a strand of hair, we need to subtract the mass of the strand of hair from the mass of the grain of rice.
Mass of a strand of hair: 2.17×10^(-5) ounces
Mass of a grain of rice: 0.002 ounces
Grain of rice - Strand of hair = 0.002 - 2.17×10^(-5)
To subtract the two numbers, we need to align the decimal places:
0.002 - 0.0000217 = 0.0019783
Now we need to express this result in scientific notation:
0.0019783 is equivalent to 1.9783 × 10^(-3).
Therefore, a grain of rice is 1.9783 × 10^(-3) ounces heavier than a strand of hair.
Mass of a strand of hair: 2.17×10^(-5) ounces
Mass of a grain of rice: 0.002 ounces
Grain of rice - Strand of hair = 0.002 - 2.17×10^(-5)
To subtract the two numbers, we need to align the decimal places:
0.002 - 0.0000217 = 0.0019783
Now we need to express this result in scientific notation:
0.0019783 is equivalent to 1.9783 × 10^(-3).
Therefore, a grain of rice is 1.9783 × 10^(-3) ounces heavier than a strand of hair.
what the right answer
Apologies for the confusion. Let's recalculate the difference correctly:
Mass of a strand of hair: 2.17×10^(-5) ounces
Mass of a grain of rice: 0.002 ounces
Grain of rice - Strand of hair = 0.002 - 2.17×10^(-5)
To subtract the two numbers, we need to align the decimal places:
0.002 - 0.0000217 = 0.0019783
Now we need to express this result in scientific notation:
0.0019783 is equivalent to 1.9783 × 10^(-3).
Therefore, a grain of rice is 1.9783 × 10^(-3) ounces heavier than a strand of hair.
Mass of a strand of hair: 2.17×10^(-5) ounces
Mass of a grain of rice: 0.002 ounces
Grain of rice - Strand of hair = 0.002 - 2.17×10^(-5)
To subtract the two numbers, we need to align the decimal places:
0.002 - 0.0000217 = 0.0019783
Now we need to express this result in scientific notation:
0.0019783 is equivalent to 1.9783 × 10^(-3).
Therefore, a grain of rice is 1.9783 × 10^(-3) ounces heavier than a strand of hair.
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
To calculate the distance light travels in a year, we need to multiply the speed of light by the number of seconds in a year:
Speed of light: 1.9×10^5 mi./sec
Seconds in a year: 3.2×10^7 seconds
Distance light travels in a year = Speed of light x Seconds in a year
= 1.9×10^5 mi./sec x 3.2×10^7 seconds
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:
1.9 * 3.2 = 6.08
10^5 * 10^7 = 10^(5+7) = 10^12
So, the distance light travels in a year is 6.08 * 10^12 miles.
Therefore, light travels approximately 6.08 * 10^12 miles in a year.
Speed of light: 1.9×10^5 mi./sec
Seconds in a year: 3.2×10^7 seconds
Distance light travels in a year = Speed of light x Seconds in a year
= 1.9×10^5 mi./sec x 3.2×10^7 seconds
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:
1.9 * 3.2 = 6.08
10^5 * 10^7 = 10^(5+7) = 10^12
So, the distance light travels in a year is 6.08 * 10^12 miles.
Therefore, light travels approximately 6.08 * 10^12 miles in a year.
he average tectonic plate moves at the rate of 0.006 m per year. How many meters would it move in 2×106 years? Write the answer in scientific notation, expressed to the exact decimal place.(1 point) m
To calculate how many meters the tectonic plate would move in 2×10^6 years, we need to multiply the rate of movement (0.006 m/year) by the number of years.
Rate of movement: 0.006 m/year
Number of years: 2×10^6 years
Distance moved = Rate of movement x Number of years
= 0.006 m/year x 2×10^6 years
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:
0.006 * 2 = 0.012
10^6 (10^(-3) * 10^6) = 10^(6+(-3)) = 10^3
So, the distance the tectonic plate would move in 2×10^6 years is 0.012 * 10^3 meters.
Therefore, the tectonic plate would move approximately 1.2 * 10^3 meters in 2×10^6 years.
Rate of movement: 0.006 m/year
Number of years: 2×10^6 years
Distance moved = Rate of movement x Number of years
= 0.006 m/year x 2×10^6 years
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:
0.006 * 2 = 0.012
10^6 (10^(-3) * 10^6) = 10^(6+(-3)) = 10^3
So, the distance the tectonic plate would move in 2×10^6 years is 0.012 * 10^3 meters.
Therefore, the tectonic plate would move approximately 1.2 * 10^3 meters in 2×10^6 years.
An asteroid is heading toward Mars at the rate of 7.7×104 mi./hr. If the asteroid is 3.311×108 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.(1 point) hour
To calculate the time it will take for the asteroid to hit Mars, we need to divide the distance between the asteroid and Mars by the speed of the asteroid.
Speed of the asteroid: 7.7×10^4 mi./hr
Distance from the asteroid to Mars: 3.311×10^8 miles
Time = Distance / Speed
= 3.311×10^8 miles / 7.7×10^4 mi./hr
To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents:
3.311 / 7.7 ≈ 0.4299
10^8 / 10^4 = 10^(8-4) = 10^4
So, the time it will take for the asteroid to hit Mars is approximately 0.4299 * 10^4 hours.
Therefore, it will be approximately 4.299 * 10^3 hours before the asteroid hits Mars.
Speed of the asteroid: 7.7×10^4 mi./hr
Distance from the asteroid to Mars: 3.311×10^8 miles
Time = Distance / Speed
= 3.311×10^8 miles / 7.7×10^4 mi./hr
To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents:
3.311 / 7.7 ≈ 0.4299
10^8 / 10^4 = 10^(8-4) = 10^4
So, the time it will take for the asteroid to hit Mars is approximately 0.4299 * 10^4 hours.
Therefore, it will be approximately 4.299 * 10^3 hours before the asteroid hits Mars.
A field of 3.9 mi2 is being subdivided into 1.3×103 family gardens. How many square miles will there be in each garden? Write the answer in scientific notation.(1 point) $$
To find the area of each family garden, we need to divide the total area of the field (3.9 mi^2) by the number of gardens (1.3×10^3).
Area of the field: 3.9 mi^2
Number of family gardens: 1.3×10^3
Area of each garden = Area of field / Number of gardens
= 3.9 mi^2 / 1.3×10^3
To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents:
3.9 / 1.3 ≈ 3.0
10^3 / 10^3 = 10^(3-3) = 10^0
So, each family garden will have approximately 3.0 * 10^0 square miles.
Therefore, each family garden will have approximately 3.0 square miles in scientific notation.
Area of the field: 3.9 mi^2
Number of family gardens: 1.3×10^3
Area of each garden = Area of field / Number of gardens
= 3.9 mi^2 / 1.3×10^3
To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents:
3.9 / 1.3 ≈ 3.0
10^3 / 10^3 = 10^(3-3) = 10^0
So, each family garden will have approximately 3.0 * 10^0 square miles.
Therefore, each family garden will have approximately 3.0 square miles in scientific notation.
is the answer 3.0
Apologies for the mistake. Since the value is already 3.0 without any power of 10, the correct answer is 3.0 square miles. There is no need to express it in scientific notation.
Charlee is using her calculator to find the product of two large numbers. Her calculator shows 1.78E12 on the display. Interpret what this means. (2 points)
The display "1.78E12" on Charlee's calculator represents a number in scientific notation. The "E" notation is used to denote powers of 10.
In this case, "1.78E12" can be interpreted as 1.78 multiplied by 10 raised to the power of 12.
Therefore, the number displayed on Charlee's calculator is 1.78 multiplied by 10 to the power of 12, or 1.78 × 10^12.
In this case, "1.78E12" can be interpreted as 1.78 multiplied by 10 raised to the power of 12.
Therefore, the number displayed on Charlee's calculator is 1.78 multiplied by 10 to the power of 12, or 1.78 × 10^12.
4 answers