To find the value of a that will make 8 x 10^3 be 40 times larger than a x 10^2, we can set up the equation:
8 x 10^3 = 40(a x 10^2)
Simplifying both sides of the equation, we have:
8 x 1000 = 40a x 100
8000 = 4000a
Dividing both sides of the equation by 4000, we get:
a = 8000/4000 = 2
Therefore, when a = 2, 8 x 10^3 will be 40 times larger than a x 10^2.
For what value of a will 8 x 10^3 be 40 times larger than a x 10^2?
29 answers
One second is approximately 0.0000115741 of a day. What is this number in scientific notation?
To express the number 0.0000115741 in scientific notation, we can write it as 1.15741 x 10^(-5).
The temperature of the sun at its center is about 2.7 x 10^7 degrees Fahrenheit. What is this temperature written in decimal notation?
The temperature of the sun at its center, expressed in decimal notation, is approximately 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.
To compare the values of these numbers using scientific notation, we can rewrite them as follows:
98,789,000 = 9.8789 x 10^7
987,890,000 = 9.8789 x 10^8
89,987,000 = 8.9987 x 10^7
Comparing the exponents, we can see that 9.8789 x 10^7 (98,789,000 in decimal notation) has the least value.
98,789,000 = 9.8789 x 10^7
987,890,000 = 9.8789 x 10^8
89,987,000 = 8.9987 x 10^7
Comparing the exponents, we can see that 9.8789 x 10^7 (98,789,000 in decimal notation) has the least value.
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
2.3 x 10^-10; 3.2 x 10^-10; 2.3 x 10-12; 2.3 x 10^-8
To order the numbers in descending order, we compare the exponents first.
2.3 x 10^-10
3.2 x 10^-10
2.3 x 10^-12
2.3 x 10^-8
Since all the exponents are negative, a smaller exponent means a larger value.
Arranging the numbers accordingly, we get:
3.2 x 10^-10
2.3 x 10^-10
2.3 x 10^-12
2.3 x 10^-8
Therefore, the numbers in descending order are:
3.2 x 10^-10 > 2.3 x 10^-10 > 2.3 x 10^-12 > 2.3 x 10^-8
2.3 x 10^-10
3.2 x 10^-10
2.3 x 10^-12
2.3 x 10^-8
Since all the exponents are negative, a smaller exponent means a larger value.
Arranging the numbers accordingly, we get:
3.2 x 10^-10
2.3 x 10^-10
2.3 x 10^-12
2.3 x 10^-8
Therefore, the numbers in descending order are:
3.2 x 10^-10 > 2.3 x 10^-10 > 2.3 x 10^-12 > 2.3 x 10^-8
Janiya found that her playlist will play for 3.8 x 10^2 seconds, 6.3 x 10^5 minutes, 1.05 x 10^4 hours, or 4.39814 x 10^2 days. Which answer uses the most appropriate units?
To determine which answer uses the most appropriate units, we need to compare the given values.
3.8 x 10^2 seconds = 380 seconds
6.3 x 10^5 minutes = 630,000 minutes
1.05 x 10^4 hours = 10,500 hours
4.39814 x 10^2 days = 439.814 days
The option that uses the most appropriate units would be 439.814 days since it provides a larger and more practical timescale for the duration of Janiya's playlist.
3.8 x 10^2 seconds = 380 seconds
6.3 x 10^5 minutes = 630,000 minutes
1.05 x 10^4 hours = 10,500 hours
4.39814 x 10^2 days = 439.814 days
The option that uses the most appropriate units would be 439.814 days since it provides a larger and more practical timescale for the duration of Janiya's playlist.
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?
To find the total number of acres in the park and the forest combined, we simply add their individual areas.
Park area: 1.42 x 10^6 acres
Forest area: 1.2 x 10^6 acres
Total area: (1.42 x 10^6) + (1.2 x 10^6)
To add these numbers in scientific notation, we need to have the same exponent. We can rewrite 1.42 x 10^6 as 14.2 x 10^5.
Total area: (14.2 x 10^5) + (1.2 x 10^6)
Now, we can add the numbers:
14.2 x 10^5 + 1.2 x 10^6 = 15.4 x 10^5
So, the total number of acres in the park and the forest combined is 15.4 x 10^5 acres, or 1.54 x 10^6 acres.
Park area: 1.42 x 10^6 acres
Forest area: 1.2 x 10^6 acres
Total area: (1.42 x 10^6) + (1.2 x 10^6)
To add these numbers in scientific notation, we need to have the same exponent. We can rewrite 1.42 x 10^6 as 14.2 x 10^5.
Total area: (14.2 x 10^5) + (1.2 x 10^6)
Now, we can add the numbers:
14.2 x 10^5 + 1.2 x 10^6 = 15.4 x 10^5
So, the total number of acres in the park and the forest combined is 15.4 x 10^5 acres, or 1.54 x 10^6 acres.
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.
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 distance that Earth is farther (2.6 x 10^7 miles).
67,000,000 miles + 2.6 x 10^7 miles = 9,300,000 miles
Since both numbers have the same units (miles), we can simply add them together.
Therefore, the distance from Earth to the sun is approximately 9.3 x 10^7 miles.
67,000,000 miles + 2.6 x 10^7 miles = 9,300,000 miles
Since both numbers have the same units (miles), we can simply add them together.
Therefore, the distance from Earth to the sun is approximately 9.3 x 10^7 miles.
Calculate 4.8 x 10^-3 - 9.4 x 10^-6. Express the answer in scientific notation rounding to 2 decimal places
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To subtract the given numbers in scientific notation:
4.8 x 10^-3 - 9.4 x 10^-6
First, we need to adjust the exponents to be the same:
4.8 x 10^-3 = 480 x 10^-6 (multiplied by 100)
Now we can perform the subtraction:
480 x 10^-6 - 9.4 x 10^-6 = 470.6 x 10^-6
Since the result still has a negative exponent, we can express it in scientific notation with the exponent of 10^-6:
470.6 x 10^-6 = 4.706 x 10^-4
Rounding to 2 decimal places, the answer is approximately 4.71 x 10^-4.
4.8 x 10^-3 - 9.4 x 10^-6
First, we need to adjust the exponents to be the same:
4.8 x 10^-3 = 480 x 10^-6 (multiplied by 100)
Now we can perform the subtraction:
480 x 10^-6 - 9.4 x 10^-6 = 470.6 x 10^-6
Since the result still has a negative exponent, we can express it in scientific notation with the exponent of 10^-6:
470.6 x 10^-6 = 4.706 x 10^-4
Rounding to 2 decimal places, the answer is approximately 4.71 x 10^-4.
A strand of hair has an average mass of 2.17 x 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.
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 the rice: 0.002 ounces
Mass of the hair: 2.17 x 10^-5 ounces
Subtracting these values:
0.002 ounces - 2.17 x 10^-5 ounces = 0.0019783 ounces
To express the answer in scientific notation, we can write it as:
1.9783 x 10^-3 ounces
Therefore, a grain of rice is approximately 1.9783 x 10^-3 ounces heavier than a strand of hair.
Mass of the rice: 0.002 ounces
Mass of the hair: 2.17 x 10^-5 ounces
Subtracting these values:
0.002 ounces - 2.17 x 10^-5 ounces = 0.0019783 ounces
To express the answer in scientific notation, we can write it as:
1.9783 x 10^-3 ounces
Therefore, a grain of rice is approximately 1.9783 x 10^-3 ounces heavier than a strand of hair.
Light travels at an approximate rate of 1.9. x 10^5 mi/sec. There are about 3.2 x 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.
To determine how many miles 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 x 10^5 mi/sec
Seconds in a year: 3.2 x 10^7 seconds
Multiplying these values:
(1.9 x 10^5 mi/sec) x (3.2 x 10^7 seconds)
Using the laws of exponents, we can multiply the coefficients and add the exponents:
1.9 x 3.2 x 10^5 x 10^7 mi
(1.9 x 3.2) x 10^(5+7) mi
6.08 x 10^12 mi
Therefore, light travels approximately 6.08 x 10^12 miles in a year.
Speed of light: 1.9 x 10^5 mi/sec
Seconds in a year: 3.2 x 10^7 seconds
Multiplying these values:
(1.9 x 10^5 mi/sec) x (3.2 x 10^7 seconds)
Using the laws of exponents, we can multiply the coefficients and add the exponents:
1.9 x 3.2 x 10^5 x 10^7 mi
(1.9 x 3.2) x 10^(5+7) mi
6.08 x 10^12 mi
Therefore, light travels approximately 6.08 x 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 x 10^6 years? Write the answer in scientific notation, expressed to the exact decimal place.
To determine how many meters the tectonic plate would move in 2 x 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 x 10^6 years
Multiplying these values:
(0.006 m/year) x (2 x 10^6 years)
Using the laws of exponents, we can multiply the coefficients and add the exponents:
0.006 x 2 x 10^(6+0) m
0.012 x 10^6 m
To express the answer in scientific notation, we can write it as:
1.2 x 10^4 m
Therefore, the tectonic plate would move approximately 1.2 x 10^4 meters in 2 x 10^6 years.
Rate of movement: 0.006 m/year
Number of years: 2 x 10^6 years
Multiplying these values:
(0.006 m/year) x (2 x 10^6 years)
Using the laws of exponents, we can multiply the coefficients and add the exponents:
0.006 x 2 x 10^(6+0) m
0.012 x 10^6 m
To express the answer in scientific notation, we can write it as:
1.2 x 10^4 m
Therefore, the tectonic plate would move approximately 1.2 x 10^4 meters in 2 x 10^6 years.
An asteroid is heading toward Mars at the rate of 7.7 x 10^4 mi/hr. If the asteroid is 3.311 x 10^8 miles away from Mars? Write the answer in scientific notation, expressed to the exact decimal place.
To determine how long it will take for the asteroid to reach Mars, we need to divide the distance between the asteroid and Mars by the rate at which the asteroid is moving.
Distance: 3.311 x 10^8 miles
Rate: 7.7 x 10^4 mi/hr
Dividing these values:
(3.311 x 10^8 miles) / (7.7 x 10^4 mi/hr)
Using the laws of exponents, we can divide the coefficients and subtract the exponents:
0.4299351 x 10^(8-4) hr
0.4299351 x 10^4 hr
To express the answer in scientific notation with a single decimal place, we can write it as:
4.3 x 10^3 hr
Therefore, it will take approximately 4.3 x 10^3 hours for the asteroid to reach Mars.
Distance: 3.311 x 10^8 miles
Rate: 7.7 x 10^4 mi/hr
Dividing these values:
(3.311 x 10^8 miles) / (7.7 x 10^4 mi/hr)
Using the laws of exponents, we can divide the coefficients and subtract the exponents:
0.4299351 x 10^(8-4) hr
0.4299351 x 10^4 hr
To express the answer in scientific notation with a single decimal place, we can write it as:
4.3 x 10^3 hr
Therefore, it will take approximately 4.3 x 10^3 hours for the asteroid to reach Mars.
A field of 3.9 mi^2 is being subdivided into 1.3 x 10^3 family gardens. How many square miles will there be in each garden? Write the answer in scientific notation.
To determine the number of square miles in each garden, we need to divide the total field area by the number of family gardens.
Field area: 3.9 mi^2
Number of family gardens: 1.3 x 10^3
Dividing these values:
3.9 mi^2 / 1.3 x 10^3 gardens
To simplify the denominator, we can rewrite it as 1.3 x 10^3 = 13 x 10^2.
Now we can perform the division:
3.9 mi^2 / 13 x 10^2 gardens
Using the laws of exponents, we can divide the coefficients and subtract the exponents:
0.3 x 10^(2-2) mi^2
0.3 x 10^0 mi^2
Since 10^0 equals 1, we can simplify:
0.3 x 1 mi^2
The answer is simply 0.3 square miles or 3 x 10^-1 square miles.
Therefore, each family garden will have approximately 3 x 10^-1 square miles of area.
Field area: 3.9 mi^2
Number of family gardens: 1.3 x 10^3
Dividing these values:
3.9 mi^2 / 1.3 x 10^3 gardens
To simplify the denominator, we can rewrite it as 1.3 x 10^3 = 13 x 10^2.
Now we can perform the division:
3.9 mi^2 / 13 x 10^2 gardens
Using the laws of exponents, we can divide the coefficients and subtract the exponents:
0.3 x 10^(2-2) mi^2
0.3 x 10^0 mi^2
Since 10^0 equals 1, we can simplify:
0.3 x 1 mi^2
The answer is simply 0.3 square miles or 3 x 10^-1 square miles.
Therefore, each family garden will have approximately 3 x 10^-1 square miles of area.
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.
The calculator display showing 1.78E12 means that the product of the two large numbers that Charlee is calculating is approximately 1.78 x 10^12. This notation, called scientific notation or standard form, is a way of expressing very large or very small numbers in a more concise and convenient form. In this case, 1.78E12 represents the number 1.78 followed by 12 zeros, or 1,780,000,000,000.
4 answers