Question

Subtract Numbers in Scientific Notation Quick Check
3 of 53 of 5 Items
Question
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

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
3.2 times 10 superscript negative 9 baseline m

2.72×10−10
m

Answer 1

To find the difference between the sizes of the hydrogen and oxygen atoms, we first need to represent both numbers in scientific notation.

The size of a hydrogen atom is given as:
\[ 1.2 \times 10^{-10} \, m \]

The size of an oxygen atom is given in standard decimal notation:
\[ 0.000000000152 \, m \]
This can be converted to scientific notation:
\[ 0.000000000152 = 1.52 \times 10^{-10} \, m \]

Now, we can subtract the size of the oxygen atom from the size of the hydrogen atom:
\[
(1.2 \times 10^{-10}) - (1.52 \times 10^{-10}) = (1.2 - 1.52) \times 10^{-10}
\]
\[
= -0.32 \times 10^{-10}
\]

To express this in proper scientific notation, we convert \(-0.32\) to \(-3.2\) by shifting the decimal point one place to the right, which means we need to adjust the exponent:
\[
-0.32 \times 10^{-10} = -3.2 \times 10^{-11}
\]

The difference in sizes of the hydrogen and oxygen atoms is:
\[
-3.2 \times 10^{-11} \, m
\]

However, if the problem asks for the absolute difference (ignoring the sign), the answer would be:
\[
3.2 \times 10^{-11} \, m
\]

So, the correct response is:
**3.2×10−11 m**