At a certain lab, the average mass of one ant is measured to be 2, point, 9, times, 10, to the power minus 62.9×10
−6
kilograms. Use scientific notation to express the mass of 6060 ants.
Answer
Attempt 1 out of 2
Answer:
times, ______ ×10 ^________
kilograms
times, 2.9 × 10^-62.9 × 10^(-6) kg = 2.9 × 10^((-62.9 - 6)) kg = 2.9 × 10^-68.9 kg
The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method:
Cell G: 9, point, 2, 3, times, 10, to the power minus 39.23×10
−3
centimeters
Cell H: 4, point, 2, times, 10, to the power minus 44.2×10
−4
centimeters
How much larger is the diameter of cell G than the diameter of cell H? Express your answer using scientific notation.
Answer
Attempt 1 out of 2
Answer:
times, 10×10
centimeters
The diameter of cell G is 9.23 × 10^(-39.23 - 3) cm = 9.23 × 10^(-42.23) cm
The diameter of cell H is 4.2 × 10^(-44.2 - 4) cm = 4.2 × 10^(-48.2) cm
To find the difference in diameter, we divide the diameter of cell G by the diameter of cell H:
(9.23 × 10^(-42.23)) / (4.2 × 10^(-48.2))
To divide numbers in scientific notation, we subtract the exponents and divide the coefficients:
9.23 / 4.2 = 2.2
10^(-42.23 - (-48.2)) = 10^5.97 = 10^(6-0.03) = 10^6
Therefore, the diameter of cell G is 2.2 × 10^6 times larger than the diameter of cell H.
pls try again
To find the difference in diameter between cell G and cell H, we need to subtract the diameter of cell H from the diameter of cell G.
Diameter of cell G: 9.23 × 10^(-39.23) cm
Diameter of cell H: 4.2 × 10^(-44.2) cm
To subtract the diameters, we need to have the same exponent. We can achieve this by converting the diameter of cell H to the same exponent as the diameter of cell G.
4.2 × 10^(-44.2) cm = 0.042 × 10^(-39.23) cm
Now we can subtract the diameters:
Diameter of cell G - Diameter of cell H = (9.23 × 10^(-39.23)) - (0.042 × 10^(-39.23))
To compute the difference in scientific notation, we subtract the coefficients and keep the common exponent:
9.23 - 0.042 = 9.188
Therefore, the diameter of cell G is 9.188 times larger than the diameter of cell H. The difference can be expressed as:
9.188 × 10^(-39.23) cm
To express the mass of 6060 ants in scientific notation, we need to multiply the average mass of one ant by the number of ants.
The average mass of one ant is 2.9 × 10^-6 kilograms.
To find the mass of 6060 ants, we multiply the average mass of one ant by 6060:
(2.9 × 10^-6 kg) × (6060 ants)
Multiplying the numbers gives us:
(2.9 × 6060) × (10^-6 kg)
Calculating this gives us:
17574 × 10^-6 kg
In scientific notation, this is:
1.7574 × 10^-2 kg
Therefore, the mass of 6060 ants expressed in scientific notation is 1.7574 × 10^-2 kilograms.
To express the mass of 6060 ants using scientific notation, we can start by finding the mass of one ant in scientific notation.
The average mass of one ant is given as 2.9 × 10^(-6) kilograms. This means that the mass of one ant is 2.9 multiplied by 10 raised to the power of -6.
To find the total mass of 6060 ants, we need to multiply the mass of one ant by the number of ants.
(2.9 × 10^(-6)) × 6060 = (2.9 × 6060) × 10^(-6)
Now, let's calculate the product of 2.9 and 6060:
2.9 × 6060 = 17574
So, the total mass of 6060 ants is 17574 multiplied by 10 raised to the power of -6.
Therefore, the mass of 6060 ants in scientific notation is 1.7574 × 10^(-2) kilograms.