## Comparing Numbers. . .fromDifferent Periods of Time

Comparing Numbers - Representing Different Periods of Time . . .

Comparing "Numbers" without using a Number Line:

Direct Comparison , without using a number line, has many practical

advantages because it does not require a physical drawing.

Although a number line provides a visual model which is easy to understand, it is not feasible to use it in most situations. The following limitations make a number line cumbersome and time consuming to use:

• There is not enough space to physically plot more than a few numbers on the same line graph (number line).
• Plotting extremely small numbers, or extremely large numbers, or numbers with completely different orders of magnitude, or numbers which are almost equal may each require dramatically different labeling of scale marks. In addition, each situation may require completely different intervals marked on the number line.

Direct Comparison eliminates the problems listed above. Direct comparison does not require a physical drawing.

Real Numbers are sequential. By comparing place values, any two numbers can be compared directly - once the numbers are written in the same standard notation.

How to Compare Numbers Using Direct Comparison - click description

To accurately compare numbers from different time periods , you must recompute them as if they occurred in the same time period .

This may be easier said than done. However, it is possible in many cases.

Here are two common examples: (1) The interest rates charged (or paid) by banks can be computed on an annual basis, no matter how the banks calculate compounding. (2)The purchasing power of money can be estimated in different time periods using the consumer price index.

Example : Which has the greatest purchasing power : \$100 in the year 1965 , or \$500 in the year 2008 ?

In the United States, \$1 in 1965 has the same purchasing power as \$6.74 in 2008 (Bureau of Labor Statistics: http://www.bls.gov/data/inflation_calculator.htm ) .

To calculate what the equivalent purchasing power of \$100 in 1965 would be in 2008 :

(\$100)(6.74) = \$674

Both numbers can now be compared in terms of 2008 purchasing power :

\$100 in 1965 = \$674 in 2008

\$500 in 2008 = \$74.18 in 1965

The comparison shown above demonstrates that the purchasing power of \$500 in 2008 is less than the purchasing power of \$100 in 1965.

\$500 in 2008 < \$100 in 1965

Or, stated another way, the comparison shown above demonstrates that the purchasing power of \$100 in 1965 is greater than the purchasing power of \$500 in 2008.

\$100 in 1965 > \$500 in 2008