Conversions I. Convert the following numbers into scientific notation:
The correct answer and explanation is:
Here are the converted numbers into scientific notation:
- 234,000 → 2.34×1052.34 \times 10^5
- 0.00456 → 4.56×10−34.56 \times 10^{-3}
- 78,900,000 → 7.89×1077.89 \times 10^7
- 0.000000321 → 3.21×10−73.21 \times 10^{-7}
- 5,670,000,000 → 5.67×1095.67 \times 10^9
Explanation of Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a concise and standardized form. It consists of a number (called the coefficient) between 1 and 10, multiplied by a power of ten.
Steps to Convert a Number to Scientific Notation:
- Identify the Decimal Point Position: Move the decimal to create a number between 1 and 10.
- Count the Moves: Count how many places the decimal was moved. This determines the exponent of 10.
- Assign the Exponent:
- If the decimal is moved left, the exponent is positive.
- If the decimal is moved right, the exponent is negative.
Examples Explained
- 234,000 → The decimal is after 234000.0. Move the decimal 5 places left, so it becomes 2.34×1052.34 \times 10^5.
- 0.00456 → Move the decimal 3 places right to make 4.56, so it’s 4.56×10−34.56 \times 10^{-3}.
- 78,900,000 → Move the decimal 7 places left, resulting in 7.89×1077.89 \times 10^7.
- 0.000000321 → Move the decimal 7 places right, resulting in 3.21×10−73.21 \times 10^{-7}.
- 5,670,000,000 → Move the decimal 9 places left, giving 5.67×1095.67 \times 10^9.
Scientific notation is widely used in science and engineering to simplify calculations with extremely large or small numbers.
Here is a visually engaging infographic explaining scientific notation, complete with examples and step-by-step explanations. Let me know if you need any modifications!
