Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of a × 10^n where 1 < a < 10 and is a one-digit number.
To express the given number in scientific notation, we need to move the decimal point eight places to the left. Since every place we move the decimal point to the left decreases the value of the number by a factor of 10, we can write this as 3 × 10^(-9). In this form, 3 is between 1 and 10, and -9 is a one-digit number.
A wasp’s stinger has an average length of 2.67×10^−3 meter long. What is this length in decimal notation?
To convert the given number in scientific notation to decimal notation, we need to move the decimal point to the right three places. Since every place we move the decimal point to the right increases the value of the number by a factor of 10, we can write this as 0.00267.
5. Kendra finds the dimensions of a sticky note. She uses a meter stick to determine that the dimensions are 1.25×10^−8 meters wide by 2.5×10^−6 meters long. Use scientific notation to write the dimensions in millimeters.
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1 point
1.25×10^ −10 by 2.5×10^−8 millimeters
1.25×10^−11 by 2.5×10^−9 millimeters
1.25×10^−6 by 2.5×10^−4 millimeters
1.25×10^−5 by 2.5×10^−3 millimeters
To convert the dimensions from meters to millimeters, we need to multiply each dimension by 1000.
For the width: 1.25 × 10^(-8) meters × 1000 = 1.25 × 10^(-8) × 10^3 = 1.25 × 10^(-8+3) = 1.25 × 10^(-5) millimeters.
For the length: 2.5 × 10^(-6) meters × 1000 = 2.5 × 10^(-6) × 10^3 = 2.5 × 10^(-6+3) = 2.5 × 10^(-3) millimeters.
Therefore, the dimensions in millimeters are 1.25 × 10^(-5) by 2.5 × 10^(-3) millimeters.
So, the correct answer is 1.25 × 10^(-5) by 2.5 × 10^(-3) millimeters.
6. In government class, Nadia computed the amount of debt of the federal government after a third of it was paid in 1995. The calculator displayed the number 3.28E12. What is this number in scientific notation?
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1 point
3.28 x 10^-12
3.28×10^12
12 x 10^3.28
3.28 x 12 ^10
The number 3.28E12 is already in scientific notation. In scientific notation, the "E" represents "x 10^", so 3.28E12 means 3.28 x 10^12.
Therefore, the number 3.28E12 in scientific notation is 3.28 x 10^12.
7. Subtract 4.66×10^−5 − 7.34×10^−7
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1 point
-4.5866 x 10 ^-5
2.68 x 10^2
4.5866 x 10 ^ -5
-2/68 x 10^2
To subtract scientific notation, we need to ensure that the exponents are the same. In this case, we can rewrite the numbers as:
4.66 × 10^(-5) - 0.734 × 10^(-6)
Since the exponents are already the same, we can directly subtract the coefficients:
4.66 - 0.734 = 3.926
Therefore, the result of the subtraction is:
3.926 × 10^(-5)
So, the correct answer is 3.926 × 10^(-5).
Subtract 4.66×10^−5 − 7.34×10^−7
-4.5866 x 10 ^-5
2.68 x 10^2
4.5866 x 10 ^ -5
-2/68 x 10^2
To subtract the given numbers in scientific notation, we need to ensure that the exponents are the same. In this case, we have:
4.66 × 10^(-5) - 7.34 × 10^(-7)
To subtract, we keep the same exponent and subtract the coefficients:
4.66 - 0.00734 = 4.65266
Therefore, the result of the subtraction is:
4.65266 × 10^(-5)
So, the correct answer is 4.65266 × 10^(-5).
Platelets and red blood cells are components of the blood. A typical platelet and red blood cell have diameters of approximately 2.33×10^ −6 m and 0.0000075 m, respectively. Which blood component has a bigger diameter, and approximately by how much?
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1 point
A platelet has a bigger diameter than a red blood cell by 5.17×10^−6 m.
A red blood cell has a bigger diameter than a platelet by 9.83×10^−6 m.
A platelet has a bigger diameter than a red blood cell by 5.17×10^−6 m
A red blood cell has a bigger diameter than a platelet by 5.17×10^−6 m.
To compare the diameters of the platelet and the red blood cell, we can subtract the diameters and take the absolute value of the difference:
|2.33×10^(-6) - 0.0000075|
Calculating this subtraction, we have:
|0.00000233 - 0.0000075| = |-0.00000517| = 0.00000517
Therefore, the platelet has a bigger diameter than the red blood cell by approximately 0.00000517 meters.
So, the correct answer is: A platelet has a bigger diameter than a red blood cell by 5.17 × 10^(-6) m.
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?
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1 point
0.735 x 10^7 ml
7.35×10^6 ml
7.35 x 10^7 ml
7.35 x 10^5 ml
To calculate the total volume of the sugar cubes, we can multiply the volume of one sugar cube by the number of sugar cubes:
4.9 ml * 1.5 x 10^6
To multiply two numbers in scientific notation, we multiply the coefficients (4.9 * 1.5) and add the exponents (6 + 0):
(4.9 * 1.5) x 10^(6 + 0) = 7.35 x 10^6
Therefore, the total volume of 1.5 x 10^6 sugar cubes is 7.35 x 10^6 ml.
So, the correct answer is 7.35 x 10^6 ml.
. Division: Solomon needs to distribute 10.5 gallons of perfume among 3.5×10^2 containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.
To determine the amount of perfume that will be in each container, we can divide the total amount of perfume by the number of containers:
10.5 gallons ÷ (3.5 x 10^2 containers)
To divide two numbers in scientific notation, we divide the coefficients (10.5 ÷ 3.5) and subtract the exponents (0 - 2):
(10.5 ÷ 3.5) x 10^(0 - 2) = 3 x 10^(-2)
Therefore, each container will have 3 x 10^(-2) gallons of perfume.
So, the answer in scientific notation is 3 x 10^(-2) gallons.