Digit terms

Lecture




Any natural multivalued number can be represented as a sum of bit terms.

For example, the number 64 consists of 6 dozen and 4 units.

64 = 6 dozen + 4 units = 6 • 10 + 4 = 60 + 4

The numbers 60 and 4 are called bit terms .


The representation of a number in the form:

425 = 400 + 20 + 5

is called the decomposition of a number into bit terms or the sum of bit terms.

Examples

356 = 3 hundreds + 5 dozen + 6 units = 3 • 100 + 5 • 10 + 6 = 300 + 50 + 6

8,092 = 8 thousand + 0 hundreds + 9 dozen + 2 units = 8 • 1 000 + 0 • 100 + 9 • 10 + 2 = 8 000 + 90 + 2

Numbers 1, 10, 100, 1000, etc. - are called bit units . So, 1 is the unit of the unit of units; 10 - tens digit unit; 100 - unit of hundreds of discharge, etc.

Often in tasks it is required not only to decompose a number into bit terms, but also to determine the number of all units of a discharge. In this case, we advise you to make a detailed analysis of the number.

An example of a detailed analysis of a multivalued number 2 038 479 (two million thirty eight thousand four hundred seventy nine).

  1. First, decompose the number by the sum of the bit terms.

    2 038 479 = 2 • 1 000 000 + 0 • 100 000 + 3 • 10 000 + 8 • 1 000 + 4 • 100 + 7 • 10 + 9 = 2 000 000 + 30 000 + 8 000 + 400 + 70 + 9
  • This number consists of:
    • two million units (2 • 1 000 000);
    • three tens of thousands (3 • 10 000);
    • eight units of thousands (8 • 1000);
    • four hundred (4 • 100);
    • seven dozen (7 • 10);
    • nine units (9).
  1. Determine how many in the number 2 038 479 total units using the table.
How many units are there? To determine the number of units, we write the whole number, including the very discharge of units. 2,038,479
How many dozens are there in total? To determine the number of tens, we write the entire number without the discharge of units (that is, the discharge to the tens). 203 847 _
How many are in the number of hundreds? To determine the number of hundreds, we write the whole number without the digits of tens and units (that is, the digits to hundreds). 203 84 _ _
How many units are thousands? To determine the number of thousands of units, we record the whole number without the digits of hundreds, tens and units (that is, the digits of the preunits of thousands). 2,038 _ _ _
How many in the number of tens of thousands? To determine the number of tens of thousands, we record the whole number without the digits of the units of thousands, hundreds, tens and units (that is, the digits of up to tens of thousands). 2 03 _ _ _ _
How many in the number of hundreds of thousands? To determine the number of hundreds of thousands, we record the entire number without the discharges of tens of thousands, units of thousands, hundreds, tens, and units (that is, discharges up to hundreds of thousands). 20 _ _ _ _ _
How many units in the number of millions? To determine the number of units of millions, we record the entire number without the digits of hundreds of thousands, tens of thousands, units of thousands, hundreds, tens and units (i.e., digits up to units of millions) 2 _ _ _ _ _ _
  • This number contains:
    • 2 units of class million (third class)
    • 38 units of class thousand (second class)
    • 479 units of class of units (first class)

We advise you to pay special attention to this topic, as the ability to decompose numbers into bit terms will help you when speaking and solving examples with multi-digit numbers.

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Arithmetic

Terms: Arithmetic