Question

Use the following information to complete parts I, II, and III. 1 hour = 3,600 seconds 1 year = 31,556,952 seconds Part : Use scientific notation to estimate the number of hours in one year. Part II: Use scientific notation to calculate the exact number of hours in one year. Part Ill: In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences in your answers. WRITER 107

Answer 1

I, We can estimate the number of hours in a year comparing the orders of magnitude of both (in seconds).

An hour has 3.6 * 10^3 seconds, and a year has approximately 3.2 * 10^7, so we can approximate the number of hours in a year as:

$\frac{3.2\cdot10^7}{3.6\cdot10^3}\approx0.9\cdot10^{(7-3)}=0.9\cdot10^4=9\cdot10^3$

II. We can calculate the exact value using all the numbers and calculating:

$\frac{31,556,952}{3,600}=8,765=8.765\cdot10^3$

III. In the first part we can approximate the value doing a manual or mental calculation with the digits (3.2/3.6) and substracting the exponents of the power of 10.

In the second case, we calculate the quotient with all the information and then transform the result into scientific notation.

The difference is in the precision of the digits when we do a mental estimation versus a complete calculation. But, we can be in the order of magnitude with not so much error because the most significant part is in the power of 10 and it is easier to calculate even manually.