what is 31 billion in scientific notation?
The correct answer and explanation is:
Correct Answer:
31 billion in scientific notation is: 3.1×1010\boxed{3.1 \times 10^{10}}
Explanation (Approx. 300 Words):
Scientific notation is a way to express very large or very small numbers in a compact form. It is commonly used in science, engineering, and mathematics to make numbers easier to read, compare, and compute.
Scientific notation has the form: a×10na \times 10^n
Where:
- aa is a number greater than or equal to 1 but less than 10 (called the coefficient)
- nn is an integer (positive for large numbers and negative for small numbers)
Step-by-Step: Converting 31 Billion
- Understand what “31 billion” means:
- “Billion” in the U.S. system means 1,000,000,000 or 10⁹.
- So, 31 billion = 31,000,000,00031,000,000,000
- Move the decimal point:
- In 31,000,000,000, the decimal point is at the end (after the last zero).
- To convert it into scientific notation, move the decimal point 10 places to the left to get a number between 1 and 10.
- 31,000,000,000=3.1×101031,000,000,000 = 3.1 \times 10^{10}
- Verify:
- Multiply: 3.1×1010=3.1×10,000,000,000=31,000,000,0003.1 \times 10^{10} = 3.1 \times 10,000,000,000 = 31,000,000,000
- So, the conversion is accurate.
Why Use Scientific Notation?
- Simplifies large numbers: Writing “31,000,000,000” is cumbersome and prone to errors.
- Helpful in calculations: Especially when dealing with powers of ten, like in physics or chemistry.
- Easy to compare magnitudes: You can quickly compare sizes of values based on their exponent.
In conclusion, the number 31 billion in scientific notation is: 3.1×1010\boxed{3.1 \times 10^{10}}