31 billion in scientific notation
The Correct Answer and Explanation is :
To express 31 billion in scientific notation, you would write it as:
(3.1 \times 10^{10})
Explanation:
Scientific notation is a way of expressing very large or very small numbers in a compact form. It is particularly useful in scientific, engineering, and mathematical contexts, where dealing with such numbers is common.
- Understanding the Basics:
Scientific notation is based on powers of ten. A number is expressed as the product of a coefficient (a number between 1 and 10) and 10 raised to an exponent. The exponent indicates how many places the decimal point has moved. - Converting to Scientific Notation:
To convert 31 billion to scientific notation, you first need to understand what 31 billion means in numeric form.
- 31 billion is written numerically as 31,000,000,000. To convert this to scientific notation:
- Identify where the decimal point is. In whole numbers, it is usually at the end of the number. Thus, we can think of 31 billion as (31.0).
- Next, move the decimal point to create a number between 1 and 10. Moving the decimal point one place to the left gives you (3.1).
- Count how many places you moved the decimal point: you moved it 10 places. This is reflected in the exponent, so you express it as (10^{10}).
- Final Result:
Combining these parts gives you (3.1 \times 10^{10}).
Using scientific notation simplifies calculations and makes it easier to understand the scale of large numbers. It is especially beneficial in scientific calculations where precision is required and helps prevent errors in communication and computation.
Applications:
Scientific notation is widely used in various fields such as physics, chemistry, and economics, allowing for easier comparisons and calculations involving large datasets, astronomical distances, or quantities like the number of atoms in a sample.