VIDEO: Numbers of steps in mathematics

Step numbers - the math of numbers explained in simple terms

The number system that is used every day is a so-called place value system. This means that the value of a number results from the digits from which it is made up, as well as the position at which this digit is located. The value therefore depends on the place in the number where the digit is.

• An example: 3, better 003, means "three", the number 3 is at the bottom. Although made up of the same digits, 300 indicates a much higher number, as the number 3 is in the first place, the hundreds.
• This place value system is based on the number of levels 10, so the digits 1 to 9 and 0 are used.
• The levels of the number system can be represented as powers of ten, in ascending order 10⁰, 10¹, 10² Etc.
• Does one relate to negative in this ranking system Potencies with a, then decimal resp. Represent fractions with step numbers. The following applies: 10^-1 = 1/10, 10^-2= 1/100 etc.


Create a place value table - this is how it works for decimal numbers

Our number system is structured as a so-called place value system. The value of a ...

So you can represent numbers in step numbers

You can represent any number, however large or small, in this place value system on the basis of "10" in step numbers.

• All you have to do is enter the corresponding powers of ten or Assign the step numbers to the appropriate position in the number.
• Two examples should make this clear: You can divide the (large) number 100 580 (one hundred thousand five hundred eighty) into step numbers, namely 1 x 10⁵ for 100,000 (rule of thumb: 5 zeros) and 5 x 10² (for 500) and 8 x 10¹ (for 80).
• With step numbers you can (in short form) too Counting write that could fill whole blocks due to their number of zeros, for example is 10³⁴ a number that consists of 1 and 34 zeros and, by the way, does not have its own Names has more. Such numerical representations have in science, in the mathematics and in the Computer science big meaning. For example, the speed of light is 3 x 10⁸ m / s; written out you should have used a few zeros.
• The (small) number 0.00045 can also be represented in steps using the negative powers, namely 4 x 10^-4 and 5 x 10^-5 (Rule of thumb: the decimal point corresponds to the decimal place). This notation is also used in science and mathematics. Some fundamental constants, such as the mass of an electron, are very small (around 9 x 10^-31 kg). Here you would have needed 30 zeros after the decimal point to write this number.