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Chapter 10: Problem 608

Convert each number to decimal form. $$3.75 \times 10^{-1}$$

Short Answer

Expert verified
0.375

Step by step solution

01

Understand the Scientific Notation

The given number is in scientific notation. Scientific notation represents numbers as a product of a coefficient and a power of 10. Here, the coefficient is 3.75 and the exponent is -1.
02

Interpret the Exponent

The exponent of -1 means the decimal point in the coefficient (3.75) needs to be moved one place to the left. This is because a negative exponent indicates division by 10 raised to the absolute value of the exponent.
03

Move the Decimal Point

Move the decimal point in 3.75 one place to the left to convert to decimal form. Moving one place to the left changes 3.75 to 0.375.
04

Write the Decimal Form

After moving the decimal point, the number in decimal form is 0.375.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

decimal form
Decimal form is the way we commonly write numbers in everyday life. It's a way to express numbers without using fractions or scientific notation. For example, instead of writing 3.75 as \(3.75 \times 10^{-1}\), we simply write it as 0.375. Decimal form is easy to read and understand, especially when dealing with small or large numbers. It makes arithmetic operations like addition, subtraction, multiplication, and division more straightforward.
negative exponent
When dealing with scientific notation, you often encounter negative exponents. A negative exponent indicates that the number is very small, involving division rather than multiplication. For instance, \(10^{-1}\) means dividing by 10, resulting in the need to move the decimal point to the left. With our example of \(3.75 \times 10^{-1}\), the -1 tells us we are dividing by 10 or moving the decimal point one place to the left.
moving decimal point
Understanding how to move the decimal point is crucial when converting from scientific notation to decimal form. In our exercise, we have the number \(3.75 \times 10^{-1}\). The -1 exponent means we need to move the decimal point one place to the left. As a result, 3.75 becomes 0.375. This process is straightforward:
  • Identify the exponent.
  • If the exponent is negative, move the decimal point to the left.
  • If the exponent is positive, move the decimal point to the right.
So, always check the exponent and move the decimal accordingly.

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