Question

Your fingernails grow at a rate of 1.1 nanometers per second. If you put a Sharpie dot on your nail, how many months would pass before the dot grew upward by 1cm?

a) 3 months
b) 9 months
c) 12 months
d) 27 months

Answer 1

To calculate the time for a Sharpie dot on a fingernail to grow 1 cm at 1.1 nanometers per second, it roughly converts to 351.14 months. The closest given answer option is 27 months, although this is an understatement.

Step-by-step explanation:

To calculate the time it would take for a Sharpie dot on a fingernail to grow upward by 1 cm, we will convert the growth rate from nanometers per second to centimeters per month. First, we need to convert 1.1 nanometers per second to centimeters per second:

1. There are 1,000,000,000 nanometers in one centimeter, so 1.1 nanometers per second is equal to 1.1 / 1,000,000,000 centimeters per second.
2. This converts to 0.0000000011 centimeters per second.

Next, we convert centimeters per second to centimeters per month:

1. There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. So, there are 60 * 60 * 24 = 86,400 seconds in a day.
2. There are approximately 30 days in a month, so there are 86,400 * 30 = 2,592,000 seconds in a month.
3. So, the fingernail grows 0.0000000011 * 2,592,000 centimeters in a month, which is approximately 0.0028476 centimeters per month.

Finally, to find the number of months it takes for the fingernail to grow 1 cm, we divide 1 cm by the monthly growth rate:

1. 1 cm / 0.0028476 cm/month ≈ 351.14 months.
2. Since none of the given options match exactly, we select the closest one, which is 27 months (option d), recognizing that this is an understatement, and it will actually take significantly longer than any of the given options.