Subtract Numbers in Scientific Notation Quick Check

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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

1 answer

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