Write the number 340,000 in scientific notation.
The Correct Answer and Explanation is:
The number 340,000 can be written in scientific notation as:
3.4 × 10⁵
Explanation:
Scientific notation is a way of expressing very large or very small numbers more compactly, using powers of 10. The general format of scientific notation is:
a × 10ⁿ
Where:
- a is a number between 1 and 10 (including 1 but less than 10).
- n is an integer that represents the power of 10.
To convert the number 340,000 into scientific notation, follow these steps:
- Move the decimal point:
The first step is to locate the decimal point in the original number. For 340,000, the decimal point is at the end of the number, after the last zero: 340,000.. - Position the decimal point:
Next, you want to move the decimal point so that it is placed after the first non-zero digit. In this case, the first non-zero digit is 3, so you move the decimal point after the 3, creating the number 3.4. - Count the number of places the decimal point moved:
The decimal point was moved 5 places to the left: from 340,000 to 3.4. This means the exponent of 10 will be 5 (since the decimal point moved five places to the left). - Write the scientific notation:
Now that we have the number 3.4, and the decimal point was moved 5 places, the scientific notation for 340,000 is 3.4 × 10⁵.
In summary:
- The coefficient (the number between 1 and 10) is 3.4.
- The exponent (the power of 10) is 5 because the decimal point was moved 5 places to the left.
Thus, 340,000 in scientific notation is 3.4 × 10⁵.