Type in the power of ten that completes this number sentence.
200,000,000 = 10
The Correct Answer and Explanation is :
The correct answer is:
200,000,000 = 2 × 10⁸.
Explanation:
To understand how we get this, we need to express 200,000,000 as a number in scientific notation.
Scientific notation is a way to write very large or very small numbers more easily. It involves two parts:
- A number between 1 and 10 (the coefficient).
- A power of 10 (the exponent).
The number 200,000,000 can be written as:
- 2 × 100,000,000.
Now, let’s express 100,000,000 as a power of 10. Notice that:
- 100,000,000 is the same as 1 followed by eight zeros (1,000,000,000).
- This is equal to 10⁸, because 10 raised to the power of 8 gives us 100,000,000.
Therefore:
- 200,000,000 = 2 × 10⁸.
So, the power of ten that completes the sentence “200,000,000 = 10” is 10⁸.
Why we use powers of 10:
The reason for using powers of 10 is to make it easier to work with large numbers. In standard notation, writing out large numbers with all their digits can be cumbersome and prone to mistakes. By using scientific notation, we condense large numbers into a more manageable form.
- Scientific notation helps us quickly see the scale of a number.
- It also allows us to perform calculations involving very large or very small numbers without having to handle many digits.
In this case, 200,000,000 is a large number, and by using the power of 10 (10⁸), it becomes easier to understand and work with mathematically.