Question

Write each number in scientific notation. 0.00421

Short answer

4.21 × 10^{-3}

Step-by-step solution

- Identify the Decimal Point Position

Observe the number 0.00421 and identify the position of the decimal point. It is located after the third zero following the decimal point, before the digit 4.

- Move the Decimal Point to Just After the First Non-Zero Digit

To convert the number to scientific notation, move the decimal point to just after the first non-zero digit, which is 4. This changes 0.00421 to 4.21.

- Count the Number of Places the Decimal Point was Moved

Count how many places the decimal point has been moved to the right to change 0.00421 to 4.21. In this case, it was moved 3 places.

- Express the Number as a Product of the Decimal and a Power of 10

The number of places the decimal point was moved becomes the exponent of 10, but since the decimal was moved to the right, the exponent will be negative. The final scientific notation for 0.00421 is \(4.21 \times 10^{-3}\).

Key concepts

headline of the respective core concept

Scientific notation is a way to represent very large or very small numbers succinctly.
It involves expressing numbers as a product of a decimal and a power of 10.
In this exercise, we'll focus on some key concepts to help you understand and use scientific notation effectively.

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The decimal point is a crucial part of understanding scientific notation.
It's the dot that separates the whole number part from the fractional part in a decimal number.
For example, in the number 0.00421, the decimal point is just before the digit 00421.
Identifying where the decimal point is located is the first step in converting a standard number into scientific notation.
Here is how you do it:

• Locate the decimal point in the given number.
• Determine the position relative to the digits.

This sets the stage for the next steps in scientific notation.

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A non-zero digit is any digit from 1 to 9.
It's important because scientific notation requires the decimal point to be placed after the first non-zero digit.
In the number 0.00421, the first non-zero digit is 4.
To convert to scientific notation, move the decimal point so it appears right after this digit.
This changes the number to 4.21.
Then, other steps will deal with how many places the decimal was moved.

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The power of 10 is what makes scientific notation powerful.
It's written as a small number (exponent) above 10 when expressing numbers.
For example, in the scientific notation form of 0.00421, which is 4.21 × 10^-3, the -3 is the power of 10.
This tells you how many places the decimal point was moved.
When the decimal is moved to the right, the exponent is negative (indicating a very small number).
If moved to the left, the exponent would be positive (indicating a larger number).
Handling powers of 10 effectively is crucial for mastering scientific notation.