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

To perform the subtraction \( 4.66 \times 10^{-5} - 7.34 \times 10^{-7} \), we need to express both numbers with the same exponent for easier calculation.

First, convert \( 7.34 \times 10^{-7} \) to a form that has the same exponent as \( 4.66 \times 10^{-5} \):

\[ 7.34 \times 10^{-7} = 0.0734 \times 10^{-5} \]

Now we can rewrite the subtraction:

\[ 4.66 \times 10^{-5} - 0.0734 \times 10^{-5} = (4.66 - 0.0734) \times 10^{-5} \]

Calculating the subtraction:

\[ 4.66 - 0.0734 = 4.5866 \]

Thus, we have:

\[ 4.66 \times 10^{-5} - 7.34 \times 10^{-7} = 4.5866 \times 10^{-5} \]

The correct answer is:

4.5866×10⁻⁵

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

$2.9219×1013
2.9219 dollars times 10 superscript 13 baseline

$1.0183×1024
1.0183 dollars times 10 superscript 24 baseline

$2.9219×1011
2.9219 dollars times 10 superscript 11 baseline

$3.0015×1013

To find the increase in the U.S. national debt over the 50-year period from 1971 to 2021, we need to subtract the 1971 debt from the 2021 debt.

Given:

• Debt in 2021 = \( 2.9617 \times 10^{13} \)
• Debt in 1971 = \( 3.98 \times 10^{11} \)

First, we need to express both amounts in similar scientific notation, so we can easily subtract them. We can convert \( 3.98 \times 10^{11} \) to a form that has the same exponent as \( 2.9617 \times 10^{13} \):

\[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]

Now we can rewrite the subtraction:

\[ 2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13} \]

Calculating the subtraction:

\[ 2.9617 - 0.0398 = 2.9219 \]

Thus, the increase in debt is:

\[ 2.9219 \times 10^{13} \]

So the correct answer is:

$2.9219×10^{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

3.2×10−11 m
3.2 times 10 superscript negative 11 baseline m

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

3.2×10−9 m

To find the difference between the sizes of a hydrogen atom and an oxygen atom in scientific notation, we first express both measurements in a similar format.

The sizes given are:

• Size of a hydrogen atom: \( 1.2 \times 10^{-10} , \text{m} \)
• Size of an oxygen atom: \( 0.000000000152 , \text{m} \)

Next, convert the size of the oxygen atom into scientific notation:

\[ 0.000000000152 = 1.52 \times 10^{-10} , \text{m} \]

Now we can calculate the difference in size between the hydrogen and oxygen atoms:

\[ 1.2 \times 10^{-10} - 1.52 \times 10^{-10} \]

To perform the subtraction, we can write this as:

\[ (1.2 - 1.52) \times 10^{-10} \]

Calculating the subtraction:

\[ 1.2 - 1.52 = -0.32 \]

Now, combining this with the scientific notation:

\[ -0.32 \times 10^{-10} \]

To express it correctly in scientific notation, we need to write \(-0.32\) as \( -3.2 \times 10^{-1} \), so:

\[ -0.32 \times 10^{-10} = -3.2 \times 10^{-1} \times 10^{-10} = -3.2 \times 10^{-11} \]

Thus, the absolute difference between the sizes of the hydrogen and oxygen atoms (ignoring the sign) is:

\[ 3.2 \times 10^{-11} , \text{m} \]

The correct answer is:

3.2×10⁻¹¹ m