what is 13.8 billion expressed as 10 to the power of something
The Correct Answer and Explanation is:
Answer:
13.8 billion expressed as a power of 10 is:
1.38 × 10¹⁰
Explanation
To express 13.8 billion as a power of 10, we need to understand both the numeric value of 13.8 billion and the concept of scientific notation.
Step 1: What is 13.8 billion as a number?
The term billion in the U.S. system (short scale) means 1,000,000,000, or 10⁹. Therefore:
13.8 billion = 13.8 × 1,000,000,000 = 13,800,000,000
Step 2: Expressing in scientific notation
Scientific notation is a way of writing very large (or very small) numbers compactly, in the form:
a × 10ⁿ,
where:
- a is a number between 1 and 10 (called the coefficient),
- n is an integer (positive for large numbers, negative for small ones).
Now, to express 13,800,000,000 in this format, we move the decimal point to the left until there is only one non-zero digit to its left. In this case, moving the decimal point 10 places gives:
13,800,000,000 → 1.38 × 10¹⁰
Step 3: Why 10 places?
Starting with 13.8 billion:
- Write as 13,800,000,000
- Count how many places you move the decimal point (from after the last zero) to make the number between 1 and 10:
Move decimal left 10 places:
13,800,000,000 → 1.38
That’s why the exponent is 10.
Conclusion:
So, 13.8 billion = 1.38 × 10¹⁰.
This notation is especially useful in science and engineering for handling very large values like the estimated age of the universe (which is about 13.8 billion years).
