Use scientific notation to determine which of these numbers is greater: 34,835,760 or 43,835,760. Write your answer in scientific notation, expressed to the exact decimal place.

Answer 1

To compare the numbers 34,835,760 and 43,835,760 using scientific notation, we first convert each number to scientific notation.

1. For 34,835,760: \[ 34,835,760 = 3.4835760 \times 10^7 \] (since we move the decimal point 7 places to the left).

2. For 43,835,760: \[ 43,835,760 = 4.3835760 \times 10^7 \] (again moving the decimal point 7 places to the left).

Now we can compare the two numbers:

• \(3.4835760 \times 10^7\)
• \(4.3835760 \times 10^7\)

Since both numbers have the same exponent \(10^7\), we only need to compare the coefficients:

• \(3.4835760\) (for 34,835,760)
• \(4.3835760\) (for 43,835,760)

Since \(4.3835760 > 3.4835760\), we find that \(43,835,760 > 34,835,760\).

Thus, the number \(43,835,760\) is greater than \(34,835,760\).

In scientific notation, the greater number is:

\[ \boxed{4.3835760 \times 10^7} \]

Answer 2

can you double check

Answer 3

Absolutely! Let's double-check the calculations and comparisons step by step.

1. Convert the numbers to scientific notation:

   • For 34,835,760:

     • Move the decimal point 7 places left: \[ 34,835,760 = 3.4835760 \times 10^7 \]

   • For 43,835,760:

     • Move the decimal point 7 places left: \[ 43,835,760 = 4.3835760 \times 10^7 \]

2. Compare the two scientific notations:

   We have:

   • \(3.4835760 \times 10^7\)
   • \(4.3835760 \times 10^7\)

   Both numbers have the same exponent \(10^7\). We only need to compare the coefficients:

   • \(3.4835760\) (from 34,835,760)
   • \(4.3835760\) (from 43,835,760)

Since \(4.3835760 > 3.4835760\), it confirms that: \[ 43,835,760 > 34,835,760 \]

3. Conclusion: Thus, the greater number is indeed: \[ \boxed{4.3835760 \times 10^7} \]

Everything checks out correctly! Thank you for your patience!