Question

Use scientific notation to compare these numbers:3,478,660;34,870,000; and 34,786,600. which number has the greatest value?


3.47866 times 10^7
3.487 times 10^7
34,870,000
3.47866 times 10^6

Answer 1

To compare the numbers using scientific notation, we need to convert each number into scientific notation:

1. **3,478,660**:
- In scientific notation: \(3.47866 \times 10^6\)

2. **34,870,000**:
- In scientific notation: \(3.487 \times 10^7\)

3. **34,786,600**:
- In scientific notation: \(3.47866 \times 10^7\)

Now, let's rewrite all the numbers in scientific notation clearly:

- \(3.47866 \times 10^6\) (for 3,478,660)
- \(3.487 \times 10^7\) (for 34,870,000)
- \(3.47866 \times 10^7\) (for 34,786,600)

Next, compare the scientific notations:

1. \(3.47866 \times 10^6\) is significantly smaller than the others because \(10^6\) is much less than \(10^7\).

2. For the two numbers \(3.487 \times 10^7\) and \(3.47866 \times 10^7\), both have the same exponent (\(10^7\)). Therefore, we compare the coefficients 3.487 and 3.47866. Since 3.487 is greater than 3.47866, we know that:

- \(3.487 \times 10^7\) (34,870,000) is greater than \(3.47866 \times 10^7\) (34,786,600).

**Conclusion**: The number with the greatest value is **34,870,000** or \(3.487 \times 10^7\).