Understanding the Equivalent Decimal Form of Forty-Nine Thousand

The equivalent decimal form of forty-nine thousand is 49,000. This representation is crucial in various contexts, from mathematical calculations to real-world applications in science and engineering. Let's explore the concept further and see how to represent this number in different forms, particularly focusing on its decimal and scientific notations.

Decimal Representation

When we simply state a number as 'forty-nine thousand,' we are referring to the decimal number 49,000. This representation is straightforward and widely used. The number system we use is base-10, meaning that each digit represents a power of 10. In the case of 49,000, this can be broken down as:

Data Breakdown

49,000 (base-10): 4 × 104 9 × 103

Tenths, Hundredths, and Thousandths

The decimal places after the decimal point indicate fractions of a whole number. For instance, tenths (1/10), hundredths (1/100), and thousandths (1/1000) are represented by the digits immediately following the decimal point.

In the case of the number 0.049, the digit '4' is in the hundredths place, the digit '9' is in the thousandths place, and there is no digit in the tenths place. Therefore, 0.049 represents forty-nine thousandths of a whole number.

Converting to Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It takes the form of a coefficient multiplied by a power of 10.

Converting the Given Options

Let's convert the given options to scientific notation to better understand their significance:

A) .49 .49 × 105 B) .0049 .0049 × 107 C) .049 .049 × 106 D) 4.9 × 104 49,000

From the above options, A, B, and C do not represent 49,000. Option D is the correct representation because 4.9 × 104 equals 49,000, which matches our original number. This is the standard form for expressing the number in scientific notation.

Key Concepts in Scientific Notation

In scientific notation, a number must be represented as a coefficient (a number between 1 and 10) multiplied by a power of 10. This coefficients are significant because they provide the actual value of the number, while the power of 10 indicates the scale.

Examples of Scientific Notation

32 3.2 × 101 0.00034 3.4 × 10-4

In the case of 49,000, the coefficient is 4.9 and the power is 104, making the scientific notation 4.9 × 104.

Conclusion

Understanding the equivalent decimal form and scientific notation of a number like forty-nine thousand is essential for accurate mathematical and scientific communication. Whether you're dealing with large numbers in finance, research, or any other field, knowing how to represent and convert numbers into different forms can significantly enhance your overall comprehension.