there are nearly (pi) x (10^7) seconds in one year. find the percentage error in this approximation, where percentage error is defined as

abs value[ (assumed value - true value)/ true value] x 100%

to find the true value I did:

(365 days/yr) x (24 hours/1 day) x (60 minutes/hour) x (60 seconds/minute)

but this, when plugged in, didn't give me the correct answer...help!

To calculate the true value, you need to account for the fact that a year does not have exactly 365 days. Instead, it has approximately 365.25 days, accounting for leap years.

So, the true value should be:

(365.25 days/yr) x (24 hours/1 day) x (60 minutes/hour) x (60 seconds/minute)

Now let's calculate the true value:

True Value = (365.25 days/yr) x (24 hours/1 day) x (60 minutes/hour) x (60 seconds/minute)
= 31,536,000 seconds

Now we can calculate the percentage error using the formula provided:

Assumed Value = π x (10^7) seconds = 31,415,926.54 seconds

Percentage Error = |(Assumed Value - True Value) / True Value| x 100%
= |(31,415,926.54 - 31,536,000) / 31,536,000| x 100%
= |-120,073.46 / 31,536,000| x 100%
= 0.3814%

Therefore, the percentage error in this approximation is approximately 0.3814%.

To find the true value of the number of seconds in a year, you need to consider the exact number of seconds in a year.

The method you used, (365 days/yr) x (24 hours/1 day) x (60 minutes/hour) x (60 seconds/minute), is close, but not entirely accurate. This is because a year is not exactly 365 days long. It is actually about 365.25 days long (taking into account leap years).

To get a more precise value, you can calculate the number of seconds in a year as follows:

Number of seconds in a year = (365.25 days/year) x (24 hours/day) x (60 minutes/hour) x (60 seconds/minute)

Now, to find the percentage error, you can use the formula:

Percentage error = |(Assumed value - True value) / True value| x 100%

Let's calculate the values step by step:

True value = (365.25 days/year) x (24 hours/day) x (60 minutes/hour) x (60 seconds/minute)
Assumed value = π x (10^7) seconds

Using these values, we can calculate the percentage error:

Percentage error = |(Assumed value - True value) / True value| x 100%
= |(π x (10^7) - True value) / True value| x 100%

Substitute the appropriate values to find the percentage error.

Assume an average year of 235.24 days. That is 31,556,736 seconds instead of 31,415,920 .

Percentage error is the difference divided by the correct value, converted to %.

I get 0.45 %