what is Decimal Expansions
Decimal expansion refers to the representation of a number in the decimal system, which uses base 10. In this system, any number can be expressed as a sum of multiples of powers of 10. The decimal expansion of a number consists of digits from 0 to 9, where each digit represents a certain power of 10.
For example, the decimal expansion of the number 123.45 can be split into three parts: the integer part (123), the decimal separator (.), and the fractional part (45). The integer part represents 100s, 10s, and 1s, while the fractional part represents tenths and hundredths.
Decimal expansions allow for precise representation of real numbers, including rational and irrational numbers. They are widely used in everyday calculations and measurements.
what is 925 using decimal expansions
The decimal expansion of the number 925 is simply 925.
The decimal expansion of the number 2,701
The decimal expansion of the number 2,701 is 2701.
Decimal expansion refers to the representation of a number in the decimal (base 10) number system. It is a way to express numbers using decimal digits (0-9) along with a decimal point.
In a decimal expansion, the digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts. The value of each digit is determined by its position relative to the decimal point, with the digit closest to the decimal point having the smallest value.
For example, in the decimal expansion of the number 123.45, the digit 1 represents 100, the digit 2 represents 10, the digit 3 represents 1, the digit 4 represents 0.1, and the digit 5 represents 0.01.
Decimal expansions can be infinite or finite. In finite decimal expansions, the digits after the decimal point have a specific pattern and eventually end. For example, the decimal expansion of the number 0.125 terminates after the digit 5.
In infinite decimal expansions, the digits after the decimal point continue indefinitely without a pattern. For example, the decimal expansion of the number 1/3 is 0.3333... with the digit 3 repeating infinitely.
Decimal expansions are commonly used for everyday calculations, and they allow for precise representations of numbers in many practical applications.
Decimal expansions refer to the representation of a number using decimal notation. It is a way of expressing a number as a series of digits, with a decimal point separating the whole number part from the fractional part. For example, the decimal expansion of the number 3.14 is "3" (whole number part) and "14" (fractional part).
To find the decimal expansion of a number, you need to understand the place value system used in decimal notation. In the decimal system, each digit's value depends on its position relative to the decimal point. The digit to the left of the decimal point represents units, the next digit represents tenths, the next hundredths, and so on.
To construct the decimal expansion, you can use long division or similar methods. Divide the number by increasing powers of 10, starting from 1, and record the quotient as the corresponding digit. Keep repeating the process until you obtain the desired level of precision.
For example, to find the decimal expansion of 7/8, divide 7 by 8 using long division:
0.875 (quotient)
------------
8 | 7.000 (dividend)
- 6. (subtract)
----
10 (bring down a zero)
-8
---
20 (bring down another zero)
- 16
---
40 (no more decimal places)
Therefore, the decimal expansion of 7/8 is 0.875.
Note that some numbers may have repeating or non-terminating decimal expansions, such as 1/3 (0.33333...) or π (3.14159...). In such cases, the digits repeat infinitely, and you can denote the repeating part by using a bar over the repeating digits.