## Convert Units of Measurement. . .comparing numberswhich representdifferent units of measurement

Comparing Numbers which represent different units of measurement . . .

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

Compare the numbers 6 miles per hour and 3 meters per second .

(1) Convert both numbers to the same units of measurement, and then (2) compare the numbers.

(1) Convert both numbers to the same units of measurement. (For purposes of this example, miles per hour will be converted to meters per second.)

1 mile = 1609.344 meters

1 hour = 3600 seconds

(2) Compare the numbers 2.7 meters per second (which is the equivalent of 6 miles per hour) and 3 meters per second . (A number line is not necessary, but is shown to highlight the results of the unit conversion.)

Number Line

The number line shows that 2.7 is less than 3 .

2.7 < 3

The number line shows that 3 is greater than 2.7 .

3 > 2.7