Practice:
A decimal number is a number written in the decimal numeral system. This system uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The value of each digit depends on its position (place value) in the notation of the number. That is why the decimal system is called positional.
Decimal notation is the familiar form of writing: 42, 1234, 0.5, 3.14. Digits are written in a row, and each position has its own weight: units, tens, hundreds, thousands, and so on.
The number 527 means: 5 · 100 + 2 · 10 + 7 · 1 = 527. Each digit is multiplied by 10 raised to the power equal to its position number (starting from 0 on the right).
Decimal numbers have the same place values as natural numbers. Additionally, to the right of the decimal point, fractional place values appear: tenths, hundredths, thousandths, and so on.
For example, in the number 3.14: 3 is the integer part, 1 is tenths, 4 is hundredths.
A decimal number can be converted to binary, octal, hexadecimal, and other numeral systems. Main methods:
For example, 10 in binary = 1010, in octal = 12, in hexadecimal = A.
Examples of decimal numbers:
Conversion example: 42₁₀ = 101010₂ = 52₈ = 2A₁₆.
Decimal numbers are numbers written in the decimal numeral system using ten digits (0–9). This is the usual form of writing numbers for us. Fractions written with a decimal point are also called decimal: 3.14; 0.5; 2.718.
Decimal notation uses 10 digits (0–9), and binary notation uses only 2 (0 and 1). The same number looks different in different systems. For example, 10 in decimal = 1010 in binary.
You need to successively divide the number by 2 with remainder until the result becomes 0. The remainders written in reverse order give the binary representation. For example, 42 : 2 = 21 (rem. 0), 21 : 2 = 10 (rem. 1), 10 : 2 = 5 (rem. 0), 5 : 2 = 2 (rem. 1), 2 : 2 = 1 (rem. 0), 1 : 2 = 0 (rem. 1). Read remainders from bottom up: 101010.
A decimal fraction is a notation of a fractional number in the decimal numeral system using a decimal point. For example, 0.5; 3.14; 2.718. The integer part is separated from the fractional part by a point (in the Russian tradition — by a comma).
