The temperature of the sun at its center is about 2.7×10^7 degrees Fahrenheit. What is this temperature written in decimal notation?(1 point)
The temperature of the sun at its center 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.(1 point)
To determine which number has the least value using scientific notation, we need to convert each number to scientific notation.
98,789,000 = 9.8789 x 10^7
987,890,000 = 9.8789 x 10^8
89,987,000 = 8.9987 x 10^7
Based on their scientific notation representation, the number 9.8789 x 10^7 (98,789,000) has the least value.
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 compare the exponents first. The larger the negative exponent, the smaller the value.
2.3 × 10^-12 (smallest)
2.3 × 10^-10
2.3 × 10^-8
3.2 × 10^-10 (largest)
So, the numbers in descending order are:
2.3 × 10^-12
2.3 × 10^-10
3.2 × 10^-10
2.3 × 10^-8
Janiya found that her playlist will play for 3.8×10^2 seconds, 6.3¯¯¯ ×10^5 minutes, 1.05¯¯¯¯¯ ×10^4 hours, or 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days. Which answer uses the most appropriate units?(1 point)
To determine which answer uses the most appropriate units, we need to compare the units and see which one is commonly used for measuring the duration of a playlist.
Answer 1: 3.8×10^2 seconds - This is measured in seconds, which is a common unit for measuring time but not commonly used for the duration of a playlist.
Answer 2: 6.3¯¯¯ ×10^5 minutes - This is measured in minutes, which is commonly used for measuring the duration of a playlist.
Answer 3: 1.05¯¯¯¯¯ ×10^4 hours - This is measured in hours, which is also commonly used for measuring the duration of a playlist.
Answer 4: 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×10^2 days - This is measured in days, which is not typically used for measuring the duration of a playlist.
Based on common usage, Answer 2 (6.3¯¯¯ ×10^5 minutes) and Answer 3 (1.05¯¯¯¯¯ ×10^4 hours) both use appropriate units for measuring the duration of a playlist.
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
To find the total number of acres in the park and the forest combined, we simply need to add the areas of the park and the forest.
Area of the national park: 1.42×10^6 acres
Area of the national forest: 1.2×10^6 acres
Adding these two areas together:
1.42×10^6 + 1.2×10^6 = 2.62×10^6 acres
Therefore, the total number of acres in the park and the forest combined is 2.62×10^6 acres.
The distance from Venus to the sun is about 67,000,000 miles. The distance from Earth to the sun is about 2.6×10^7 farther. What is the distance from Earth to the sun? Write your answer in scientific notation to 1 decimal place.(1 point)
To find the distance from Earth to the sun, we need to subtract the distance from Venus to the sun from the given distance of 67,000,000 miles.
67,000,000 miles - 2.6×10^7 miles = 4.4 × 10^7 miles
Therefore, the distance from Earth to the sun is approximately 4.4 × 10^7 miles.
Calculate 4.8×10^−3−9.4×10^−6 . Express the answer in scientific notation rounding to 2 decimal places.(1 point)
To subtract the given numbers in scientific notation, we need to ensure that the exponents are the same.
4.8×10^(-3) - 9.4×10^(-6)
To make the exponents the same, we can rewrite 9.4×10^(-6) as 0.0094 × 10^(-3).
Now we can subtract:
4.8×10^(-3) - 0.0094×10^(-3) = (4.8 - 0.0094) × 10^(-3)
Simplifying the subtraction:
4.7906 × 10^(-3)
Rounding to two decimal places, we get:
4.79 × 10^(-3)
Therefore, the answer is 4.79 × 10^(-3) in scientific notation, rounded to two decimal places.
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)
To find how much heavier a grain of rice is compared to a strand of hair, we need to subtract the mass of the hair from the mass of the rice.
Mass of the hair: 2.17×10^(-5) ounces
Mass of the rice: 0.002 ounces
Subtracting the mass of the hair from the mass of the rice:
0.002 ounces - 2.17×10^(-5) ounces
To subtract these values, we need to convert the mass of the hair to the same decimal place as the mass of the rice:
2.17×10^(-5) ounces = 0.0000217 ounces
Now, we can subtract:
0.002 ounces - 0.0000217 ounces = 0.0019783 ounces
Rounding to the appropriate number of significant figures, the mass difference is approximately 0.00198 ounces.
Converted to scientific notation:
0.00198 ounces = 1.98×10^(-3) ounces
Therefore, a grain of rice is approximately 1.98×10^(-3) ounces heavier than a strand of hair.
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 point)
To calculate the total distance light travels in a year, we need to multiply the rate of light by the number of seconds in a year:
Rate of light: 1.9×10^5 mi./sec
Number of seconds in a year: 3.2×10^7 seconds
Distance light travels in a year:
(1.9×10^5 mi./sec) × (3.2×10^7 seconds)
Next, we can use the laws of exponents to multiply the numbers in scientific notation:
(1.9 × 3.2) × (10^5 × 10^7) mi.
Simplifying the multiplication:
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.(1 point)
To find the total distance that the tectonic plate moves in 2×10^6 years, we need to multiply the rate of movement by the number of years:
Rate of movement: 0.006 m per year
Number of years: 2×10^6 years
Distance moved in 2×10^6 years:
(0.006 m per year) × (2×10^6 years)
Next, we can use the laws of exponents to multiply the numbers in scientific notation:
(0.006 × 2) × (10^6 × 10^6) m
Simplifying the multiplication:
0.012 × 10^12 m
Since 0.012 is already expressed in decimal notation, we don't need to convert it.
Therefore, the tectonic plate would move approximately 0.012 × 10^12 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)
To find the time it will take for the asteroid to hit Mars, we need to divide the distance between the asteroid and Mars by the rate at which the asteroid is moving:
Distance from Mars: 3.311×10^8 miles
Rate of movement: 7.7×10^4 mi./hr
Time to hit Mars:
(3.311×10^8 miles) / (7.7×10^4 mi./hr)
Next, we can use the laws of exponents to divide the numbers in scientific notation:
(3.311 ÷ 7.7) × (10^8 ÷ 10^4) hr
Simplifying the division:
0.4298701 × 10^4 hr
Rounded to the appropriate number of decimal places, we get:
0.4299 × 10^4 hr
Therefore, it will take approximately 0.4299 × 10^4 hours (or 4.299 × 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.(1 point)
To find the number of square miles in each garden, we need to divide the total area of the field by the number of family gardens:
Total area of the field: 3.9 mi^2
Number of family gardens: 1.3×10^3
Square miles per garden:
(3.9 mi^2) / (1.3×10^3)
Next, we can divide the numbers in scientific notation:
3.9 / 1.3 = 3
We can also divide the exponents:
10^0 ÷ 10^3 = 10^(-3)
Therefore, there will be approximately 3 × 10^(-3) (or 0.003) square miles in each family garden.
A field of 3.9 mi^2 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.(1 point
To find the number of square miles in each garden, we need to divide the total area of the field by the number of family gardens:
Total area of the field: 3.9 mi^2
Number of family gardens: 1.3×10^3
Square miles per garden:
3.9 mi^2 / 1.3×10^3
To divide these numbers, we divide 3.9 by 1.3:
3.9 / 1.3 = 3
To divide the exponents, we subtract exponent of 10:
10^0 ÷ 10^3 = 10^(-3)
Combining these results, there will be approximately 3 × 10^(-3) square miles in each family 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 value 1.78E12 displayed on Charlee's calculator is in scientific notation. In scientific notation, the letter "E" represents "times 10 raised to the power of." Therefore, 1.78E12 can be interpreted as 1.78 multiplied by 10 raised to the power of 12. In decimal notation, this is written as 1,780,000,000,000.
So, the display on Charlee's calculator shows the product of the two large numbers as 1,780,000,000,000.