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Subtract 4.66×10−5−7.34×10−7 (1 point)

Responses

2.68×102
2.68 times 10 squared

−2.68×102
negative 2.68 times 10 squared

−4.5866×10−5
negative 4.5866 times 10 superscript negative 5 baseline

4.5866×10−5

9 answers

To subtract \( 4.66 \times 10^{-5} \) and \( 7.34 \times 10^{-7} \), we first need to express them with a common exponent.

The first number is \( 4.66 \times 10^{-5} \) and the second number can be written in the same exponent form:

  1. Convert \( 7.34 \times 10^{-7} \) to the \( 10^{-5} \) form: \[ 7.34 \times 10^{-7} = 0.0734 \times 10^{-5} \]

Now we can perform the subtraction: \[ 4.66 \times 10^{-5} - 0.0734 \times 10^{-5} = (4.66 - 0.0734) \times 10^{-5} = 4.5866 \times 10^{-5} \]

Thus, the final result is: \[ \boxed{4.5866 \times 10^{-5}} \]

The U.S. national debt was $2.9617×1013 in 2021 and $3.98×1011 in 1971. Find how much the debt increased in the 50-year period. (1 point)
Responses

$2.9219×1011
2.9219 dollars times 10 superscript 11 baseline

$3.0015×1013
3.0015 dollars times 10 superscript 13 baseline

$1.0183×1024
1.0183 dollars times 10 superscript 24 baseline

$2.9219×1013

To find out how much the U.S. national debt increased from 1971 to 2021, we need to perform the following calculation:

  1. Identify the values:

    • National debt in 2021: \( 2.9617 \times 10^{13} \)
    • National debt in 1971: \( 3.98 \times 10^{11} \)

  2. Convert both values to a common power of ten:

    • \( 3.98 \times 10^{11} \) can be expressed with a power of ten of \( 10^{13} \) by adjusting its coefficient: \[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]

  3. Perform the subtraction: \[ 2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13} \] \[ = 2.9219 \times 10^{13} \]

The increase in the national debt over the 50-year period is: \[ \boxed{2.9219 \times 10^{13}} \]

The size of a hydrogen atom is about 1.2×10−10 m across. The size of an oxygen atom is 0.000000000152 m across. What is the difference between the sizes of these atoms in scientific notation?(1 point)
Responses

2.72×10−10 m
2.72 times 10 superscript negative 10 baseline m

3.2×10−9 m
3.2 times 10 superscript negative 9 baseline m

3.2 ×10−10 m
3.2 times 10 superscript negative 10 baseline m

3.2×10−11 m

To find the difference between the sizes of a hydrogen atom (\(1.2 \times 10^{-10} , \text{m}\)) and an oxygen atom (\(0.000000000152 , \text{m}\)), we first convert the size of the oxygen atom into scientific notation.

  1. Convert the size of the oxygen atom: \[ 0.000000000152 , \text{m} = 1.52 \times 10^{-10} , \text{m} \]

  2. Now, find the difference between the sizes of the hydrogen and oxygen atoms:

    • Hydrogen atom size: \(1.2 \times 10^{-10} , \text{m}\)
    • Oxygen atom size: \(1.52 \times 10^{-10} , \text{m}\)

  3. Perform the subtraction: \[ 1.2 \times 10^{-10} , \text{m} - 1.52 \times 10^{-10} , \text{m} = (1.2 - 1.52) \times 10^{-10} \] \[ = -0.32 \times 10^{-10} \]

  4. Convert the result into proper scientific notation: \[ -0.32 \times 10^{-10} = -3.2 \times 10^{-11} , \text{m} \]

Thus, the difference between the sizes of the hydrogen and oxygen atoms is: \[ \boxed{-3.2 \times 10^{-11} , \text{m}} \]

(Note: If the question intends for the absolute difference or simply the difference irrespective of sign, just take \(3.2 \times 10^{-11} , \text{m}\).)

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?(1 point)
Responses

A platelet has a bigger diameter than a red blood cell by 9.83×10−6 m.
A platelet has a bigger diameter than a red blood cell by 9.83 times 10 superscript negative 6 baseline m.

A red blood cell has a bigger diameter than a platelet by 9.83×10−6 m.
A red blood cell has a bigger diameter than a platelet by 9.83 times 10 superscript negative 6 baseline m.

A red blood cell has a bigger diameter than a platelet by 5.17×10−6 m.
A red blood cell has a bigger diameter than a platelet by 5.17 times 10 superscript negative 6 baseline m.

A platelet has a bigger diameter than a red blood cell by 5.17×10−6 m.
A platelet has a bigger diameter than a red blood cell by 5.17 times 10 superscript negative 6 baseline m.

To determine which blood component has a bigger diameter and by how much, let's compare the diameters of the platelet and red blood cell.

  1. Diameters of the components:

    • Diameter of a platelet: \( 2.33 \times 10^{-6} , \text{m} \)
    • Diameter of a red blood cell: \( 0.0000075 , \text{m} \)

  2. Convert the diameter of the red blood cell to scientific notation: \[ 0.0000075 , \text{m} = 7.5 \times 10^{-6} , \text{m} \]

  3. Compare the two diameters:

    • Platelet: \( 2.33 \times 10^{-6} , \text{m} \)
    • Red blood cell: \( 7.5 \times 10^{-6} , \text{m} \)

Since \( 7.5 \times 10^{-6} , \text{m} \) (red blood cell) is greater than \( 2.33 \times 10^{-6} , \text{m} \) (platelet), the red blood cell has a bigger diameter.

  1. Calculate the difference in diameters: \[ 7.5 \times 10^{-6} , \text{m} - 2.33 \times 10^{-6} , \text{m} = (7.5 - 2.33) \times 10^{-6} \] \[ = 5.17 \times 10^{-6} , \text{m} \]

Therefore, a red blood cell has a bigger diameter than a platelet by approximately \( 5.17 \times 10^{-6} , \text{m} \).

So the correct response is: \[ \boxed{\text{A red blood cell has a bigger diameter than a platelet by } 5.17 \times 10^{-6} , \text{m.}} \]

China and India are the most populous countries in the world. China’s population is approximately 1.45×109 , while India’s population is approximately 1,400,000,000. How many more people live in China than in India?(1 point)
Responses

5×1010
5 times 10 superscript 10 baseline

5×109
5 times 10 superscript 9 baseline

5×108
5 times 10 superscript 8 baseline

5×107

To find out how many more people live in China than in India, we need to perform the subtraction of their populations.

  1. Convert the populations into scientific notation:

    • China's population: \( 1.45 \times 10^{9} \)
    • India’s population: \( 1,400,000,000 \) can be expressed as \( 1.4 \times 10^{9} \).

  2. Now perform the subtraction: \[ 1.45 \times 10^{9} - 1.4 \times 10^{9} = (1.45 - 1.4) \times 10^{9} \] \[ = 0.05 \times 10^{9} = 5.0 \times 10^{7} \]

Thus, the difference in population, indicating that China has approximately \( 5 \times 10^{7} \) more people than India. Therefore, the correct response is:

\[ \boxed{5 \times 10^{7}} \]