The weight of an ant averages about 3×10−6 kg. There are about 1×1016 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)
kg
To find the number of joules of energy the sun generates in a year, we can multiply the amount of energy generated per second (4×10^26 joules/second) by the total number of seconds in a year (3.15×10^7 seconds).
The calculation would be:
Energy generated by the sun in a year = (4×10^26 joules/second) * (3.15×10^7 seconds)
To multiply the numbers in scientific notation, we add the exponents and multiply the coefficients:
(4 * 3.15) * (10^(26 + 7)) = 12.6 * 10^33
So, the approximate number of joules of energy that the sun generates in a year is 1.26 × 10^34 joules.
To find the weight of all the ants in the world, we can multiply the weight of one ant (3×10−6 kg) by the total number of ants in the world (1×1016 ants).
The calculation would be:
Weight of all ants = (3×10−6 kg) * (1×1016 ants)
To multiply the numbers in scientific notation, we add the exponents and multiply the coefficients:
(3 * 1) * (10^(-6 + 16)) = 3 * 10^10
So, the approximate weight in kilograms of all the ants in the world is 3 × 10^10 kg.
To find the number of heartbeats that occur in Massachusetts per year, we can multiply the average number of heartbeats per year (3.5×107) by the current population of Massachusetts (7×106 people).
The calculation would be:
Number of heartbeats in Massachusetts per year = (3.5×107 beats/year) * (7×106 people)
To multiply the numbers in scientific notation, we add the exponents and multiply the coefficients:
(3.5 * 7) * (10^(7 + 6)) = 24.5 * 10^13
So, the approximate number of heartbeats that occur in Massachusetts per year is 2.45 × 10^14 beats per year.
To find the total cost in dollars to deliver all the pieces of mail, we can multiply the number of pieces of mail (1.52×10^10) by the cost of a stamp ($0.55).
The calculation would be:
Total cost to deliver all the pieces of mail = (1.52×10^10 pieces) * ($0.55/stamp)
To multiply the numbers in scientific notation, we multiply the coefficients and keep the exponent the same:
(1.52 * 0.55) * (10^10) = 0.836 * 10^10
So, the approximate total cost to deliver all the pieces of mail is $8.36 × 10^9.
3.075 x 10^7
To multiply 5.5×10^4 by 2.2×10^-8, we multiply the coefficients and add the exponents:
(5.5 * 2.2) * (10^(4 + (-8))) = 12.1 * 10^(-4)
So, the answer is 1.21 × 10^(-3).
When multiplying two numbers in scientific notation, we multiply the coefficients and add the exponents of the powers of 10.
To find the total volume of 1.5×10^6 sugar cubes, we multiply the volume of one sugar cube (4.9 ml) by the total number of sugar cubes (1.5×10^6).
The calculation would be:
Total volume of sugar cubes = (4.9 ml) * (1.5×10^6 sugar cubes)
To multiply the numbers in scientific notation, we multiply the coefficients and keep the exponent the same:
(4.9 * 1.5) * (10^0 * 10^6) = 7.35 * 10^6
So, the total volume of 1.5×10^6 sugar cubes is 7.35 × 10^6 ml.
To multiply 0.75 by 2.8×10^ -5, we multiply the coefficients and add the exponents:
0.75 * 2.8 * 10^(-5) = 2.1 * 10^(-5)
So, the result is 2.1 × 10^(-5).
The average human heart beats about 3.5×107 times per year. The current population of Massachusetts is about 7×106 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)
The sun generates about 4×1026 joules of energy every second. There are about 3.15×107 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) joules
The average newborn weighs 7.5 pounds. About 4.1×106 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) pounds
In a given year, about 1.52×1010 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) $
What is 5.5×104 multiplied by 2.2×10−8? Write the answer in scientific notation.(1 point)
Responses
1.21×10−4 1.21 * 10 superscript negative 4
1.21×10−3 1.21 * 10 negative cubed
12.1×10−4 12.1 * 10 superscript negative 4 1.21×10−5
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.
Add the coefficients and multiply the exponents of the powers of 10.
Add the coefficients and add the exponents of the powers of 10.
Multiply the coefficients and add the exponents of the powers of 10.
A sugar cube has a volume of about 4.9 ml. What is the total volume in milliliters of 1.5×106 sugar cubes?(1 point)
Responses
7.35×106 ml 7.35 times 10 superscript 6 baseline ml 0.735×107 ml 0.735 times 10 superscript 7 baseline ml 7.35×105 ml 7.35 times 10 superscript 5 baseline ml 7.35×107 ml
Multiply 0.75 by 2.8×10^ −5 .(1 point)
Responses 2.1×10^ −4 2 point 1 times 10 to the negative 4 power 2.1×10^ −5 2 point 1 times 10 to the negative 5 power 2.1×10^ −7 2 point 1 times 10 to the negative 7 power 2.1×10^ −6
Multiply 0.75 by 2.8×10−5 .(1 point) Responses 2.1×10−5 2 point 1 times 10 to the negative 5 power 2.1×10−4 2 point 1 times 10 to the negative 4 power 2.1×10−6 2 point 1 times 10 to the negative 6 power 2.1×10−7 2 point 1 times 10 to the negative 7 power
To multiply 0.75 by 2.8×10^(-5), we multiply the coefficients and add the exponents:
0.75 * 2.8 * 10^(-5) = 2.1 * 10^(-5)
So, the result is 2.1 × 10^(-5).
To find the total weight of all the babies born in the U.S. in a year, we can multiply the average weight of a newborn (7.5 pounds) by the number of babies born in the U.S. in a year (4.1×10^6 babies).
The calculation would be:
Total weight of babies born in the U.S. in a year = (7.5 pounds) * (4.1×10^6 babies)
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:
(7.5 * 4.1) * (10^0 * 10^6) = 30.75 * 10^6
So, the approximate total weight of all the babies born in the U.S. in a year is 30.75 × 10^6 pounds.