Kilometers = 1000 meters

hectometers = 100 meters

decameters = 10 meters

meters = 1 meter

decimeters = 1/10 of a meter

centimeters = 1/100 of a meter

millimeters = 1/1000 of a meter

Similar units can be designated for other base units by replacing meters with the desired base unit such as kilograms and milliliters. Conversions between metric units are easy since they are based upon powers of ten. To convert from kilometers to meters simply move the decimal point to the right three places. For example 3 kilometers is equal to 3000 meters. To convert from millimeters to decimeters one need only move the decimal place two spaces to the left. For example 345 millimeters equals 3.45 decimeters. The simple rule is:

To convert from metric unit A to metric unit B move the decimal point the number of places it takes to move from unit A to unit B on the list above. When moving down the list (i.e. from larger to smaller units) move the decimal point to the right, when moving up the list (i.e. from smaller to larger units) move it to the left.

A good thing to keep in mind, when converting from a larger unit like kilometers to a smaller unit like meters, the number of units will increase. Conversely, when converting from a smaller unit like millimeters to a larger unit like decimeters the number of units will decrease.

2) The English system of measurement is a little more awkward than the metric system. Some units for length, weight, and volume include:

Use the above relationships to convert within the English system. The method used to convert from one +sized unit to another depends on the conversions being made. This is what makes the English system so awkward.

3) To convert between the metric and English systems, the relationship between the units is needed. For example to convert from centimeters to inches we need to know:

1 inch = 2.54 centimeters

Suppose we want to convert 350 centimeters to inches. Set up the following table:

To convert centimeters into inches multiply 350 by 1/2.54. The table helps you remember where to put the 1 and 2.54 to create the correct conversion ratio.

The answer will be:

4) Converting from one scale to another is very similar to converting between the the metric and English systems.  It is convenient to use different scales in different situations. For example, on a map one centimeter may represent 35 kilometers. The relationship between centimeters and kilometers is:

1 centimeter = 35 kilometers

Suppose we want to know how many centimeters on the map represents 210 kilometers. Use the table below to convert between the two different scales.

To convert from kilometers to centimeters multiply 210 kilometers by 1/35. The table helps you remember where to put the 1 and 35 to create the correct conversion ratio. These numbers come from the given relationship and the arrows point to where they belong in the ratio. To perform the conversion multiply the numbers in the bottom two boxes to get the number in the third. In this case, we get:

5) Scientist often have to deal with really large and really small numbers such as 125,000,000,000,000 and 0.000000032. To make these numbers easier to deal with, they use scientific notation. Expressed in scientific notation the first number is and the second number is. Note that the large number has a positive exponent on the ten and the small number has a negative exponent.

To express 125,000,000,000,000 in scientific notation we move the decimal place so that it is immediately after the first digit of the number.

Since the decimal point was moved to the right 14 places we multiply 1.25 by . If the decimal place was moved to the left 14 places as would be the case for a very small number, then we would use a negative exponent. Here are some examples:

Consider the number 9,612,354,323. Moving the decimal point to the left 9 places gives 9.612354323. In scientific notation, we use only 9.61 and drop the rest of the digits. Thus, we get . For 0.000074135 the decimal point is moved right 5 places, in the negative direction, giving.