Content

• Steps
• Method 1 of 2: Converting kilometers to miles
• Method 2 of 2: Using the Fibonacci Sequence to Convert Miles to Kilometers

There are many converters on the Internet that automatically convert kilometers (km) to miles; however, teachers often require that calculations be presented on paper. This article shows the algebraic method for converting km to miles, that is, a simple expression is given in which you need to substitute the corresponding number. In this expression, the units "km" will be abbreviated, but the units "miles" will remain (which is correct since km is converted to miles).

Steps

Method 1 of 2: Converting kilometers to miles

1. 1 Find the km value you want to convert to miles and plug it into the expression below.
   
   

   ____ km

   *

   100000 cm    1 km

   *

   1 inch    2,54 cm

   *

   1 mile 63360 inch

   =

   ? mile

2. 2 Use the calculator to calculate the final result in miles. Note that the expression presented includes all the steps for reducing units of measure (this is useful for understanding the process and for presenting calculations on paper).
3. 3 If you do not need to submit calculations on paper, use the expression below to convert km to miles.
   
   

   ____ km	*	1 mile 1,609344 km	=	? mile

Method 2 of 2: Using the Fibonacci Sequence to Convert Miles to Kilometers

1. 1 The Fibonacci sequence is a numerical sequence in which each subsequent number is equal to the sum of the previous two numbers. This sequence is used to convert a given value in miles to a value in kilometers. The Fibonacci sequence is an infinite series of numbers; the first two numbers are 0 and 1, and each subsequent number is equal to the sum of the two previous numbers.
   • Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
   • To calculate each subsequent number, you need to add the previous two: 89 + 144 = 233.
2. 2 The Fibonacci sequence almost (but not quite) perfectly matches the relationship between kilometers and miles. If any number in the Fibonacci sequence is considered as a value in miles, then the next number in the sequence is the same value in kilometers. In other words, three miles equals (roughly) five kilometers and eight miles equals 13 kilometers (and so on). This system is not perfect (actually 8 miles = 12.875 km), but very suitable for a quick and approximate conversion.
3. 3 To convert a value (number) that is not in the Fibonacci sequence, expand it by the sum of the Fibonacci numbers. Then find the numbers following these numbers in the sequence and add them up to calculate the value in kilometers.
   • For example, you need to convert 100 miles to kilometers. The number 100 can be decomposed into the sum of the Fibonacci numbers 89 + 8 + 3. In the sequence, 89 comes 144, 8 comes 13, and 3 comes 5. Add these numbers: 144 + 13 + 5 = 162. So 100 miles are approximately equal to 162 km.
   • Actually 100 miles = 160.934 km.