The weight of an ant averages about 3×10^−6 kg. There are about 1×10^16 ants in the world. What is the approximate weight in kilograms of all the ants in the world? Write the answer in scientific notation.(1 point)
All of them are correct except for number 1, which the answer was actually 1.21×10^-3
To find the approximate weight of all the ants in the world, we can multiply the weight of one ant by the total number of ants.
Weight of one ant = 3×10^−6 kg
Number of ants in the world = 1×10^16 ants
Weight of all the ants in the world = (3×10^−6 kg) × (1×10^16 ants)
To find the product of these numbers, we can add the exponents and keep the base 10:
(3×1) × (10^(-6+16))
= 3 × 10^10
Therefore, the approximate weight in kilograms of all the ants in the world is 3 × 10^10 kg.
The average human heart beats about 3.5×10^7 times per year. The current population of Massachusetts is about 7×10^6 people. About how many heartbeats occur in Massachusetts per year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1 point)
To find the number of heartbeats that occur in Massachusetts per year, we need to multiply the average number of heartbeats per person by the population of Massachusetts.
Average number of heartbeats per person per year = 3.5×10^7
Population of Massachusetts = 7×10^6 people
Number of heartbeats in Massachusetts per year = (3.5×10^7) × (7×10^6)
To find the product of these numbers, we can add the exponents and keep the base 10:
(3.5 × 7) × (10^(7+6))
= 24.5 × 10^13
Therefore, the number of heartbeats that occur in Massachusetts per year is 24.5 × 10^13.
Bot, Write the answer in scientific notation. Express the answer to the exact decimal place.
I apologize for the mistake. To express the answer in scientific notation with the exact decimal place, we can rewrite as:
Number of heartbeats in Massachusetts per year = 2.45 × 10^14
Therefore, the number of heartbeats that occur in Massachusetts per year is approximately 2.45 × 10^14.
The sun generates about 4×10^26 joules of energy every second. There are about 3.15×10^7 seconds in a year. About how many joules of energy does the sun generate in a year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1 point)
To find the number of joules of energy the sun generates in a year, we need to multiply the energy generated per second by the number of seconds in a year.
Energy generated per second by the sun = 4×10^26 joules
Number of seconds in a year = 3.15×10^7 seconds
Joules of energy generated by the sun in a year = (4×10^26) × (3.15×10^7)
To find the product of these numbers, we can add the exponents and keep the base 10:
(4 × 3.15) × (10^(26+7))
= 12.6 × 10^33
Therefore, the number of joules of energy that the sun generates in a year is approximately 12.6 × 10^33.
Bot, Write the answer in scientific notation. Express the answer to the exact decimal place
To express the answer in scientific notation with the exact decimal place, we have:
Joules of energy generated by the sun in a year = 1.26 × 10^34
Therefore, the number of joules of energy that the sun generates in a year is approximately 1.26 × 10^34.
The average newborn weighs 7.5 pounds. About 4.1×10^6 babies are born in the United States every year. What is the approximate total weight in pounds of all the babies born in the U.S. in a year? Write the answer in scientific notation, expressed to the exact decimal place.(1 point)
To find the approximate total weight of all the babies born in the U.S. in a year, we need to multiply the average weight of a newborn by the number of babies born.
Average weight of a newborn = 7.5 pounds
Number of babies born in the U.S. per year = 4.1×10^6 babies
Total weight of all the babies born in the U.S. per year = (7.5 pounds) × (4.1×10^6 babies)
To find the product of these numbers, we simply multiply the numbers:
Total weight = 7.5 × 4.1×10^6
= 30.75×10^6
Since 30.75 can be expressed as 3.075 × 10^1 (moving the decimal point one place to the left), we can further simplify the expression:
Total weight = 3.075 × 10^1 × 10^6
= 3.075 × 10^(1+6)
= 3.075 × 10^7
Therefore, the approximate total weight of all the babies born in the U.S. in a year is 3.075 × 10^7 pounds.
In a given year, about 1.52×10^10 pieces of first-class mail are delivered in the U.S. If each piece of mail carries a stamp costing $0.55, what is the total cost in dollars to deliver all the pieces? Write the answer in scientific notation, expressed to the exact decimal place.(1 point)
To find the total cost in dollars to deliver all the pieces of first-class mail, we need to multiply the number of pieces of mail by the cost of a stamp.
Number of pieces of first-class mail = 1.52×10^10
Cost of a stamp = $0.55
Total cost to deliver all the pieces of mail = (1.52×10^10) × ($0.55)
To find the product of these numbers, we multiply them:
Total cost = 1.52 × 0.55 × 10^10
= 0.836 × 10^10
Since 0.836 can be expressed as 8.36 × 10^(-1) (moving the decimal point one place to the left), we can further simplify the expression:
Total cost = 8.36 × 10^(-1) × 10^10
= 8.36 × 10^(10-1)
= 8.36 × 10^9
Therefore, the total cost in dollars to deliver all the pieces of first-class mail is $8.36 × 10^9.
What is 5.5×10^4 multiplied by 2.2×10^−8? Write the answer in scientific notation.(1 point)
Responses
1.21×10^−5
12.1×10^−4
1.21×10^−3
1.21×10^−4
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents.
(5.5 × 2.2) × (10^4 × 10^(-8))
= 12.1 × 10^(-4)
Therefore, the answer is 12.1×10^(-4).
When multiplying two numbers in scientific notation, what operations do you use on the coefficients and the exponents of the powers of 10?(1 point)
Responses
Multiply the coefficients and multiply the exponents of the powers of 10.
Multiply the coefficients and add the exponents of the powers of 10.
Add the coefficients and add the exponents of the powers of 10.
Add the coefficients and multiply the exponents of the powers of 10.
When multiplying two numbers in scientific notation, the correct operation is to multiply the coefficients and add the exponents of the powers of 10.
A tape dispenser holds 1.14×10^4 mm of tape that is 12.7 mm wide. Multiply the two numbers to find the total area in square millimeters of tape. Write the product in scientific notation.(1 point)
1.4478×10^4 mm^2
14.478×10^5 mm^2
1.4478×10^5 mm^2
14.478×10^4 mm^2
To find the total area in square millimeters of the tape, we need to multiply the length of the tape by the width of the tape.
Length of the tape = 1.14×10^4 mm
Width of the tape = 12.7 mm
Total area of the tape = (1.14×10^4 mm) × (12.7 mm)
To find the product of these numbers, we multiply them:
Total area = 1.14 × 12.7 × 10^4 mm^2
= 14.478 × 10^4 mm^2
Since 14.478 can be expressed as 1.4478 × 10^1 (moving the decimal point one place to the left), we can further simplify the expression:
Total area = 1.4478 × 10^1 × 10^4 mm^2
= 1.4478 × 10^(1+4) mm^2
= 1.4478 × 10^5 mm^2
Therefore, the total area in square millimeters of the tape is 1.4478 × 10^5 mm^2.
A sugar cube has a volume of about 4.9 ml. What is the total volume in milliliters of 1.5×10^6 sugar cubes?(1 point)
Responses
7.35×10^6 ml
0.735×10^7 ml
7.35×10^5 ml
7.35×10^7 ml
To find the total volume in milliliters of 1.5×10^6 sugar cubes, we need to multiply the volume of one sugar cube by the number of sugar cubes.
Volume of one sugar cube = 4.9 ml
Number of sugar cubes = 1.5×10^6 cubes
Total volume of sugar cubes = (4.9 ml) × (1.5×10^6 cubes)
To find the product of these numbers, we multiply them:
Total volume = 4.9 × 1.5×10^6 ml
= 7.35 × 10^6 ml
Therefore, the total volume in milliliters of 1.5×10^6 sugar cubes is 7.35×10^6 ml.
Multiply 0.75 by 2.8×10^−5
.(1 point)
Responses
2.1×10^−7
2.1×10^−6
2.1×10^−5
2.1×10^−4
To multiply 0.75 by 2.8×10^(-5), we simply multiply the numbers:
0.75 * 2.8×10^(-5) = 2.1×10^(-5)
Therefore, the product is 2.1×10^(-5).
Apologies for the oversight. You are correct.
The correct answer is indeed 1.21×10^-3.
Thank you for pointing out the mistake, and I apologize for any confusion caused.