Convert decimeters to kilometers

The decimeter is the first submultiple of the meter: the English article defines it as "a unit of length in the International System of Units, equal to one tenth of a metre, ten centimetres, one hundred millimetres, and 3.937 inches"[1]. The value comes from the SI prefix deci-, which stands for one tenth[2].

The decimeter describes lengths measured at close range, and the same article names three settings where it is the working unit: the liter is defined as one cubic decimeter, the path length in a polarimeter is given in decimeters, and ship's draft markings are shown in decimeters in most of the world[1].

The kilometer measures distances on land. The prefix kilo- stands for a thousand, so a kilometer is a thousand meters[2], and the English article calls it the preferred unit for distances between places in most of the world, with the United States, the United Kingdom and Liberia using the statute mile for that purpose[3].

Four steps of ten separate the decimeter from the kilometer, and the steps between them are the meter, the decameter and the hectometer. The two in the middle have their own symbols, dam and hm[2].

The result can be written in two ways. The decimal form can be typed into a spreadsheet and used in further arithmetic. The form with whole kilometers and the remainder in meters describes a stretch of road the way people say it out loud.

A decimeter is 0.0001 kilometers. Ten decimeters give 0.001 km, and a hundred decimeters give 0.01 km.

Every conversion in this direction comes down to dividing the number of decimeters by ten thousand. A thousand decimeters is 0.1 km, or a hundred meters. Five thousand decimeters give 0.5 km. Ten thousand decimeters give a full kilometer.

Below ten thousand the result starts with a zero and a decimal point. A value of 77.8 dm is 0.00778 km. A value of 1552 dm is 0.1552 km. A value of 5995 dm is 0.5995 km.

The same result can be given in whole kilometers with the remainder in meters. A value of 15,028 dm is 1.5028 km, which is 1 km and 502.8 m.

The converter above works both ways and shows the result while you type. Below 0.01 kilometers it repeats the result under the field on a line labeled Scientific notation, which turns an answer with three zeros after the point into 1 × 10⁻⁴ km.

The conversion rests on a fixed relation: ten thousand decimeters make up one kilometer. To turn decimeters into kilometers you divide their number by ten thousand.

The full formula: kilometers = decimeters ÷ 10,000. The other way round: decimeters = kilometers × 10,000.

Three examples of different size come out of that formula. A value of 400 dm divided by ten thousand gives 0.04 km. A value of 748 dm gives 0.0748 km. A value of 90,000 dm gives 9 km.

In writing, the division changes only the position of the decimal point. The digits stay as they are and the point moves four places to the left. 71 dm becomes 0.0071 km, and 43,000 dm becomes 4.3 km. You fill the missing places before the first digit with zeros.

The result can also be written as a common fraction, because the divisor never changes. A value of 301 dm is 301/10,000 km, and in decimal form 0.0301 km.

The other way round the operation is reversed: you multiply by ten thousand and the point moves four places to the right. That is what the kilometers to decimeters converter does. If your value is written in centimeters, use the centimeters to decimeters converter, and for the step from meters use the meters to kilometers converter.