To find the value of 'a', we need to set up an equation using the given information.
We know that 8×10^3 is 40 times larger than a×10^2.
This can be represented as:
8×10^3 = 40(a×10^2)
Using the distributive property, we can simplify the equation:
8×10^3 = 40a×10^2
Divide both sides of the equation by 40:
(8×10^3) / 40 = (40a×10^2) / 40
Simplifying further:
200 = a×10^2
Now, we need to divide both sides by 10^2 to isolate 'a':
200 / (10^2) = a
Simplifying:
200 / 100 = a
2 = a
Therefore, 'a' has a value of 2.
For what value of a will 8×10^3 be 40 times larger than a×10^2?
34 answers
One second is approximately 0.0000115741 of a day. What is this number in scientific notation?
To write the number 0.0000115741 in scientific notation, we need to express it as a number between 1 and 10, multiplied by a power of 10.
0.0000115741 can be written as 1.15741 multiplied by 10^-5.
Therefore, in scientific notation, 0.0000115741 is written as 1.15741 × 10^-5.
0.0000115741 can be written as 1.15741 multiplied by 10^-5.
Therefore, in scientific notation, 0.0000115741 is written as 1.15741 × 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?
To convert the temperature of the sun at its center, which is given as 2.7×10^7 degrees Fahrenheit, to decimal notation, we need to multiply the number by the corresponding power of 10.
2.7×10^7 can be written as 27,000,000 in decimal notation.
Therefore, the temperature of the sun at its center is 27,000,000 degrees Fahrenheit when written in decimal notation.
2.7×10^7 can be written as 27,000,000 in decimal notation.
Therefore, the temperature of the sun at its center is 27,000,000 degrees Fahrenheit when written in decimal notation.
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.
To compare the three numbers in scientific notation and determine which has the least value, we need to convert each number to scientific notation and compare their exponents.
98,789,000 = 9.8789 × 10^7
987,890,000 = 9.8789 × 10^8
89,987,000 = 8.9987 × 10^7
Comparing the exponents, we can see that 9.8789 × 10^7 (98,789,000) has the lowest exponent and therefore the least value among the three numbers.
So, 98,789,000 has the least value in scientific notation, expressed to the exact decimal place.
98,789,000 = 9.8789 × 10^7
987,890,000 = 9.8789 × 10^8
89,987,000 = 8.9987 × 10^7
Comparing the exponents, we can see that 9.8789 × 10^7 (98,789,000) has the lowest exponent and therefore the least value among the three numbers.
So, 98,789,000 has the least value in scientific notation, expressed to the exact decimal place.
Place the numbers in descending order. 2.3 × 10^−10; 3.2 × 10^−10; 2.3 × 10^−12; 2.3 × 10^−8
To place the numbers in descending order, we need to compare their exponents. Starting with the largest exponent:
3.2 × 10^-10
2.3 × 10^-10
2.3 × 10^-8
2.3 × 10^-12
Comparing the exponents, we find that:
2.3 × 10^-8 (the highest exponent) > 3.2 × 10^-10 > 2.3 × 10^-10 > 2.3 × 10^-12 (the lowest exponent)
Therefore, the numbers in descending order are:
2.3 × 10^-8
3.2 × 10^-10
2.3 × 10^-10
2.3 × 10^-12
3.2 × 10^-10
2.3 × 10^-10
2.3 × 10^-8
2.3 × 10^-12
Comparing the exponents, we find that:
2.3 × 10^-8 (the highest exponent) > 3.2 × 10^-10 > 2.3 × 10^-10 > 2.3 × 10^-12 (the lowest exponent)
Therefore, the numbers in descending order are:
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 1.05 ¯¯¯¯¯¯ ×104 hours 1 point modifying above 05 with bar times 10 superscript 4 baseline hours 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 6.3¯¯¯ ×105 minutes
The most appropriate unit to represent the length of Janiya's playlist is 3.8×107 seconds. This is because seconds are the smallest unit of time among the options given, and the value 3.8×107 represents the longest duration.
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?(1 point) Responses 15.5×10^6 15.5 times 10 superscript 6 baseline 2.62×10^6 2.62 times 10 superscript 6 baseline 2.62×10^12 2.62 times 10 superscript 12 baseline 1.54×10^6
To find the total number of acres in the park and the forest combined, we need to add the two values.
The park covers 1.42×10^6 acres and the forest covers 1.2×10^6 acres.
Adding these values gives us:
1.42×10^6 + 1.2×10^6 = 2.62×10^6
Therefore, the total number of acres in the park and the forest combined is 2.62×10^6.
The park covers 1.42×10^6 acres and the forest covers 1.2×10^6 acres.
Adding these values gives us:
1.42×10^6 + 1.2×10^6 = 2.62×10^6
Therefore, the total number of acres in the park and the forest combined is 2.62×10^6.
The distance from Venus to the sun is about 67,000,000 miles. The distance from Earth to the sun is about 2.6×10^7 farther. What is the distance from Earth to the sun? Write your answer in scientific notation to 1 decimal place.(1 point) ×10^7 miles
To find the distance from Earth to the sun, we need to subtract the distance from Venus to the sun, which is 67,000,000 miles, from the total distance between Venus and the sun plus the additional distance between Earth and the sun.
Total distance from Venus to the sun = 67,000,000 miles
Additional distance from Earth to the sun = 2.6×10^7 miles
To find the distance from Earth to the sun, we subtract the distance from Venus to the sun from the total distance:
Distance from Earth to the sun = (Total distance from Venus to the sun) - (Additional distance from Earth to the sun)
Distance from Earth to the sun = 67,000,000 miles - 2.6×10^7 miles
To subtract these values, we need to express them in scientific notation with the same exponent:
Distance from Earth to the sun = 67×10^6 miles - 2.6×10^7 miles
Now, subtract the values:
Distance from Earth to the sun = (67 - 2.6) × 10^6 miles
Distance from Earth to the sun = 64.4 × 10^6 miles
Writing the distance in scientific notation with 1 decimal place, we get:
Distance from Earth to the sun = 6.4 × 10^7 miles
Therefore, the distance from Earth to the sun is approximately 6.4×10^7 miles.
Total distance from Venus to the sun = 67,000,000 miles
Additional distance from Earth to the sun = 2.6×10^7 miles
To find the distance from Earth to the sun, we subtract the distance from Venus to the sun from the total distance:
Distance from Earth to the sun = (Total distance from Venus to the sun) - (Additional distance from Earth to the sun)
Distance from Earth to the sun = 67,000,000 miles - 2.6×10^7 miles
To subtract these values, we need to express them in scientific notation with the same exponent:
Distance from Earth to the sun = 67×10^6 miles - 2.6×10^7 miles
Now, subtract the values:
Distance from Earth to the sun = (67 - 2.6) × 10^6 miles
Distance from Earth to the sun = 64.4 × 10^6 miles
Writing the distance in scientific notation with 1 decimal place, we get:
Distance from Earth to the sun = 6.4 × 10^7 miles
Therefore, the distance from Earth to the sun is approximately 6.4×10^7 miles.
Calculate 4.8×10−3−9.4×10−6. Express the answer in scientific notation rounding to 2 decimal places.
To subtract the given values in scientific notation, we need to make sure both values have the same exponent.
4.8×10^-3 - 9.4×10^-6
Since 9.4×10^-6 is smaller, we can rewrite it as 0.0094×10^-3.
Now, we can subtract the two values:
4.8×10^-3 - 0.0094×10^-3 = (4.8 - 0.0094) × 10^-3
Simplifying the subtraction:
4.7906 × 10^-3
Rounded to 2 decimal places, the answer is:
4.79 × 10^-3
4.8×10^-3 - 9.4×10^-6
Since 9.4×10^-6 is smaller, we can rewrite it as 0.0094×10^-3.
Now, we can subtract the two values:
4.8×10^-3 - 0.0094×10^-3 = (4.8 - 0.0094) × 10^-3
Simplifying the subtraction:
4.7906 × 10^-3
Rounded to 2 decimal places, the answer is:
4.79 × 10^-3
Sorry i messed up
Calculate 4.8×10^−3−9.4×10^−6. Express the answer in scientific notation rounding to 2 decimal places.
Calculate 4.8×10^−3−9.4×10^−6. Express the answer in scientific notation rounding to 2 decimal places.
To subtract the given values in scientific notation, we need to make sure both values have the same exponent.
4.8×10^-3 - 9.4×10^-6
Since 9.4×10^-6 is smaller, we can rewrite it as 0.0094×10^-3.
Now, we can subtract the two values:
4.8×10^-3 - 0.0094×10^-3 = (4.8 - 0.0094) × 10^-3
Simplifying the subtraction:
4.7906 × 10^-3
Rounded to 2 decimal places, the answer is:
4.79 × 10^-3
4.8×10^-3 - 9.4×10^-6
Since 9.4×10^-6 is smaller, we can rewrite it as 0.0094×10^-3.
Now, we can subtract the two values:
4.8×10^-3 - 0.0094×10^-3 = (4.8 - 0.0094) × 10^-3
Simplifying the subtraction:
4.7906 × 10^-3
Rounded to 2 decimal places, the answer is:
4.79 × 10^-3
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 calculate how much heavier a grain of rice is than a strand of hair, we need to subtract the mass of the hair from the mass of the rice.
Mass of hair = 2.17×10^-5 ounces
Mass of rice = 0.002 ounces
To find the difference in mass, we subtract the mass of the hair from the mass of the rice:
Difference in mass = Mass of rice - Mass of hair
Difference in mass = 0.002 ounces - 2.17×10^-5 ounces
To subtract these values, we need to express them in the same units. Both values are already in ounces, so we can proceed to the subtraction:
Difference in mass = (0.002 - 2.17×10^-5) ounces
Simplifying the subtraction gives us:
Difference in mass = 0.0019783 ounces
The answer, expressed in scientific notation, is:
Difference in mass = 1.9783×10^-3 ounces
Mass of hair = 2.17×10^-5 ounces
Mass of rice = 0.002 ounces
To find the difference in mass, we subtract the mass of the hair from the mass of the rice:
Difference in mass = Mass of rice - Mass of hair
Difference in mass = 0.002 ounces - 2.17×10^-5 ounces
To subtract these values, we need to express them in the same units. Both values are already in ounces, so we can proceed to the subtraction:
Difference in mass = (0.002 - 2.17×10^-5) ounces
Simplifying the subtraction gives us:
Difference in mass = 0.0019783 ounces
The answer, expressed in scientific notation, is:
Difference in mass = 1.9783×10^-3 ounces
Light travels at an approximate rate of 1.9×10^5 mi./sec. There are about 3.2×10^7 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
To calculate the distance light travels in a year, we need to multiply its speed 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
To find the distance, we multiply the speed by the time:
Distance = Speed × Time
Distance = 1.9×10^5 mi./sec × 3.2×10^7 seconds
Multiplying these values gives us:
Distance = (1.9 × 3.2) × (10^5 × 10^7) mi.
Simplifying further:
Distance = 6.08 × 10^12 mi.
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
To find the distance, we multiply the speed by the time:
Distance = Speed × Time
Distance = 1.9×10^5 mi./sec × 3.2×10^7 seconds
Multiplying these values gives us:
Distance = (1.9 × 3.2) × (10^5 × 10^7) mi.
Simplifying further:
Distance = 6.08 × 10^12 mi.
Therefore, light travels approximately 6.08×10^12 miles in a year.
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.
To calculate the total distance the tectonic plate would move in 2×10^6 years, we need to multiply its average speed by the number of years.
Average speed of the plate = 0.006 m/year
Number of years = 2×10^6 years
To find the distance, we multiply the speed by the time:
Distance = Speed × Time
Distance = 0.006 m/year × 2×10^6 years
Multiplying these values gives us:
Distance = 0.012×10^6 m
To write the answer in scientific notation, we need to convert the decimal part to a single digit and adjust the exponent accordingly:
Distance = 1.2×10^4 m
Therefore, the tectonic plate would move approximately 1.2×10^4 meters in 2×10^6 years.
Average speed of the plate = 0.006 m/year
Number of years = 2×10^6 years
To find the distance, we multiply the speed by the time:
Distance = Speed × Time
Distance = 0.006 m/year × 2×10^6 years
Multiplying these values gives us:
Distance = 0.012×10^6 m
To write the answer in scientific notation, we need to convert the decimal part to a single digit and adjust the exponent accordingly:
Distance = 1.2×10^4 m
Therefore, the tectonic plate would move approximately 1.2×10^4 meters in 2×10^6 years.
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.(1 point) hours
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.
Distance = 3.311×10^8 miles
Speed = 7.7×10^4 mi./hr
To find the time, we divide the distance by the speed:
Time = Distance / Speed
Time = (3.311×10^8 miles) / (7.7×10^4 mi./hr)
Dividing these values gives us:
Time = (3.311 / 7.7) × (10^8 / 10^4) hr
Simplifying the division:
Time = 0.42909091 × 10^4 hr
To write the answer in scientific notation, we need to convert the decimal part to a single digit and adjust the exponent accordingly:
Time = 4.3 × 10^3 hr
Therefore, it will take approximately 4.3×10^3 hours for the asteroid to hit Mars.
Distance = 3.311×10^8 miles
Speed = 7.7×10^4 mi./hr
To find the time, we divide the distance by the speed:
Time = Distance / Speed
Time = (3.311×10^8 miles) / (7.7×10^4 mi./hr)
Dividing these values gives us:
Time = (3.311 / 7.7) × (10^8 / 10^4) hr
Simplifying the division:
Time = 0.42909091 × 10^4 hr
To write the answer in scientific notation, we need to convert the decimal part to a single digit and adjust the exponent accordingly:
Time = 4.3 × 10^3 hr
Therefore, it will take approximately 4.3×10^3 hours for the asteroid to hit Mars.
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.
To find the size of each garden, we need to divide the total area of the field by the number of gardens.
Total area of the field = 3.9 mi^2
Number of gardens = 1.3×10^3
To find the size of each garden, we divide the total area by the number of gardens:
Size of each garden = Total area / Number of gardens
Size of each garden = 3.9 mi^2 / 1.3×10^3
Dividing these values gives us:
Size of each garden = 3.9 / (1.3×10^3) mi^2
Simplifying the division:
Size of each garden = 0.003 mi^2 / (10^3)
To write the answer in scientific notation, we need to convert the decimal part to a single digit and adjust the exponent accordingly:
Size of each garden = 3 × 10^-3 mi^2
Therefore, there will be approximately 3×10^-3 square miles in each garden.
Total area of the field = 3.9 mi^2
Number of gardens = 1.3×10^3
To find the size of each garden, we divide the total area by the number of gardens:
Size of each garden = Total area / Number of gardens
Size of each garden = 3.9 mi^2 / 1.3×10^3
Dividing these values gives us:
Size of each garden = 3.9 / (1.3×10^3) mi^2
Simplifying the division:
Size of each garden = 0.003 mi^2 / (10^3)
To write the answer in scientific notation, we need to convert the decimal part to a single digit and adjust the exponent accordingly:
Size of each garden = 3 × 10^-3 mi^2
Therefore, there will be approximately 3×10^-3 square miles in each garden.
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 expression "1.78E12" on Charlee's calculator is in scientific notation. In scientific notation, the letter "E" represents "times 10 to the power of." So, "1.78E12" means 1.78 multiplied by 10^12.
Therefore, the value displayed on Charlee's calculator is 1.78 times 10 to the power of 12, which is 1.78 followed by 12 zeros:
1.78E12 = 1,780,000,000,000.
Therefore, the value displayed on Charlee's calculator is 1.78 times 10 to the power of 12, which is 1.78 followed by 12 zeros:
1.78E12 = 1,780,000,000,000.
ok bot give me all the answers to the questions i just asked in a list
Certainly! Here are all the answers you requested:
1. For what value of a will 8×10^3 be 40 times larger than a×10^2?
- The value of 'a' is 2.
2. One second is approximately 0.0000115741 of a day. What is this number in scientific notation?
- The number in scientific notation is 1.15741 × 10^-5.
3. The temperature of the sun at its center is about 2.7×10^7 degrees Fahrenheit. What is this temperature written in decimal notation?
- The temperature in decimal notation is 27,000,000 degrees Fahrenheit.
4. Use scientific notation to determine which of these numbers has the least value: 98,789,000; 987,890,000; or 89,987,000.
- The number with the least value is 98,789,000.
5. The distance from Venus to the sun is about 67,000,000 miles. The distance from Earth to the sun is about 2.6×10^7 farther. What is the distance from Earth to the sun? Write your answer in scientific notation to 1 decimal place.
- The distance from Earth to the sun is 6.4 × 10^7 miles.
6. Calculate 4.8×10^−3−9.4×10^−6. Express the answer in scientific notation rounding to 2 decimal places.
- The answer is 4.79 × 10^-3.
7. 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.
- A grain of rice is 1.9783 × 10^-3 ounces heavier than a strand of hair.
8. 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.
- It would move 1.2 × 10^4 meters in 2 × 10^6 years.
9. 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
1. For what value of a will 8×10^3 be 40 times larger than a×10^2?
- The value of 'a' is 2.
2. One second is approximately 0.0000115741 of a day. What is this number in scientific notation?
- The number in scientific notation is 1.15741 × 10^-5.
3. The temperature of the sun at its center is about 2.7×10^7 degrees Fahrenheit. What is this temperature written in decimal notation?
- The temperature in decimal notation is 27,000,000 degrees Fahrenheit.
4. Use scientific notation to determine which of these numbers has the least value: 98,789,000; 987,890,000; or 89,987,000.
- The number with the least value is 98,789,000.
5. The distance from Venus to the sun is about 67,000,000 miles. The distance from Earth to the sun is about 2.6×10^7 farther. What is the distance from Earth to the sun? Write your answer in scientific notation to 1 decimal place.
- The distance from Earth to the sun is 6.4 × 10^7 miles.
6. Calculate 4.8×10^−3−9.4×10^−6. Express the answer in scientific notation rounding to 2 decimal places.
- The answer is 4.79 × 10^-3.
7. 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.
- A grain of rice is 1.9783 × 10^-3 ounces heavier than a strand of hair.
8. 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.
- It would move 1.2 × 10^4 meters in 2 × 10^6 years.
9. 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
Umm I asked 15 questions where's the rest of them?