Question

Write the number in decimal notation.Temperature of the Core of the Sun: \(1.5 \times 10^{7}\) degrees Celsius

Short answer

The number \(1.5 \times 10^{7}\) degrees Celsius in decimal notation is 15000000 degrees Celsius.

Step-by-step solution

Identify the number in Scientific Notation

The given number is \(1.5 \times 10^{7}\). Here 1.5 is the coefficient and 7 is the exponent.

Interpret the Exponent

The exponent of 7 on the 10 in the scientific notation represents that it is the amount by which the decimal point has to be moved. A positive exponent indicates the movement to the right.

Convert to Decimal Notation

To convert to decimal notation, start at the decimal point in the number, and then move it 7 positions to the right. When there are no more digits to the right, fill these positions with zeroes. The number in decimal notation is 15000000.

Key concepts

Decimal Notation

Decimal notation is a simple way to express numbers using a base-10 system. It employs digits from 0 to 9 to represent any number. When using decimal notation, numbers can be written in their standard form without exponents or other modifications.
For example, the number "1.5" in decimal notation consists of three parts:

• The digit "1" represents one whole number.
• The digit "5" represents five-tenths.
• The position after the decimal point determines the fraction part, which in this case is one-tenth place.

When converting from scientific notation like \(1.5 \times 10^{7}\), you move the decimal point rightwards as indicated by the exponent to convert it to standard decimal notation.
This results in 15,000,000, representing how the initial small-looking number is quite large when translated into its full form.

Exponent Interpretation

Understanding exponents is essential when working with numbers in scientific notation. An exponent tells you how many times you should multiply the base number by itself. In the scientific notation \(1.5 \times 10^{7}\), the number "7" is the exponent of the base "10."
Here are some critical points about exponent interpretation:

• Positive exponents, like "7," mean you move the decimal point to the right, effectively multiplying the number by 10 for every move.
• Negative exponents would tell you to move the decimal to the left, dividing the number by 10 rather than multiplying.
• The exponent essentially signifies the scale of the number, indicating its size relative to a base number, frequently 10 in scientific contexts.

For example, moving the decimal point 7 places right expands \(1.5\) from a smaller decimal number to 15,000,000 in its expanded decimal form. This growth occurs due to each move increasing the figure by a factor of 10.

Mathematical Conversion

Converting numbers between notations is crucial in mathematics for clarity and application, especially when dealing with scientific data like temperatures of astronomical objects.
Here's a step-by-step guide on converting between scientific to decimal notation:

• Firstly, identify the coefficient and the exponent in the scientific notation. In \(1.5 \times 10^{7}\), "1.5" is the coefficient, "7" is the exponent.
• The exponent tells you how many places to move the decimal point. Positive means right, negative means left.
• Move the decimal point accordingly (in this case, 7 positions to the right for positive 7).
• If spaces are left unoccupied by digits, fill them with zeros until you complete the shift.

This conversion allows for an easy understanding of vast or tiny numbers, ensuring they are presented in a comprehensible, recognizable decimal format. Knowing how to perform these conversions equips you with the ability to interpret real-world data effectively, conveying information understandably.