Converting to SI units w/ significant digits & scientific notation

[delgeezee]

Hi.
I'm asked to convert 2 year into the SI Unit seconds:

Known:
1 Hr = 3600 s
1 Day = 86400 s

So using a calculator...
1 yr = 365*86,400 = 31,536,000

I want to express the answer in scientific notation:

Because the lesser number on has 3 significant digits, the scientific notation will also be expressed w/ 3 significant digits. Correct?

The coefficient in scientific notation must be greater then 1 and less then 10. Correct?

My answer:
$3.15 * 10^{7}$
Book's answer:
$3.16 * 10^{7}$

Why does the book's answer have it rounded up?

 

[Chestermiller]

They must have used 365.25 days for the length of a year.

Chet

 

[delgeezee]

They must have used 365.25 days for the length of a year.

Chet

Thank you for the reply. At first I thought you were joking & the book made no mention. I had no idea 365.25 is the average number of days in a year.

 

[gneill]

Thank you for the reply. At first I thought you were joking & the book made no mention. I had no idea 365.25 is the average number of days in a year.

You might say it's a bit of a leap

 

[asteriatic]

Your answer is correct, as it follows the rules for significant digits and scientific notation. The book's answer may have been rounded up to the nearest significant digit, which is also acceptable. The important thing is that both answers are within the acceptable range and convey the same information. The slight difference in the coefficient does not significantly change the value of the measurement. It is always important to follow the rules for significant digits and scientific notation when converting units to maintain accuracy and consistency in scientific measurements.