Question

Write the number in scientific notation. 0.006

Short answer

The scientific notation of 0.006 is \(6 \times 10^{-3}\).

Step-by-step solution

Identify the Decimal Place

Notice where the decimal point is currently located in the number 0.006. Here, it is located at the end of the number.

Move the Decimal Place

Move the decimal three places to the right, which makes the number 6. This action is equivalent to multiplying the original number by \(10^3\). When moving the decimal to the right, this introduces a negative exponent of 10 in the scientific notation.

Write in Scientific Notation

Now write the number in scientific notation, which is to place the newly found number (6) times 10 to the power of negative three (\(-10^3\)), thus 0.006 in scientific notation is \(6 \times 10^{-3}\).

Key concepts

Understanding Decimal Place

Decimal place is the position of a number to the right of the decimal point. Each move to the right decreases the value by a factor of ten. For instance, in 0.006, the number 6 is three decimal places to the right from the first non-zero digit. This is crucial for converting numbers into scientific notation since it helps you determine how many places to move the decimal point.

• The first decimal place is one-tenth (\(10^{-1}\)).
• The second decimal place is one-hundredth (\(10^{-2}\)).
• The third decimal place is one-thousandth (\(10^{-3}\)).

Recognizing these positions lets you transition from a standard decimal to a compact scientific notation form.

Grasping the Exponent

An exponent signals how many times to multiply a number by itself. In scientific notation, the exponent determines how far we move the decimal point. If the exponent is negative, it indicates a number smaller than one, moving the decimal point to the left. Conversely, a positive exponent points to a larger number, moving it to the right.
For example, in the scientific notation of 0.006, \(6 \times 10^{-3}\), the exponent \(-3\) signifies moving three places to reach the original decimal location. Understanding the role of the exponent is key to mastering scientific notation.

Multiplying by Powers of Ten

Multiplying by powers of ten is central to transforming a number into scientific notation. Each time you multiply by ten, you alter the position of the decimal place. This arithmetic rule comes in handy, especially when dealing with very large or very small numbers. To convert 0.006 to scientific notation, the number 6 is multiplied by \(10^{-3}\).

• A number multiplied by \(10^1\) shifts the decimal one position to the right, increasing its magnitude.
• Conversely, multiplying by \(10^{-1}\) shifts it to the left, decreasing its magnitude.

This mechanism forms the foundation of the exponent's role in scientific notation, simplifying complex arithmetic computations.