Question

the distance between the two hydrogen atoms in a molecule of water is 0.000000000172 m. express this distance in scientific notation. possible points: 1
○ 17.2 × 10⁹ m
○ 1.72 × 10⁻¹⁰ m
○ 1.72 ×10⁻⁹ m
○ 1.72 × 10¹⁰ m

Explanation:

Step1: Recall scientific notation rules

Scientific notation is in the form \( a \times 10^{n} \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer. For a number less than 1, we move the decimal point to the right until we get a number between 1 and 10, and \( n \) is negative (equal to the number of places we moved the decimal).

The given number is \( 0.000000000172 \) m. Let's move the decimal point to the right.

Step2: Move the decimal point

Start with \( 0.000000000172 \). Move the decimal point 10 places to the right to get \( 1.72 \). Since we moved the decimal 10 places to the right, the exponent \( n \) is \( - 10 \).

So in scientific notation, it is \( 1.72\times10^{- 10}\) m.

Now let's check the options:

• \( 17.2\times10^{9}\) m: \( 17.2\) is not between 1 and 10, and the exponent sign is wrong.
• \( 1.72\times10^{-10}\) m: Matches our calculation.
• \( 1.72\times10^{-9}\) m: The number of decimal places moved is incorrect (should be 10, not 9).
• \( 1.72\times10^{10}\) m: The exponent sign is wrong (number is less than 1, so exponent should be negative).

Answer:

B. \( 1.72 \times 10^{-10}\) m