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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

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To compare the numbers \( 34,835,760 \) and \( 43,835,760 \) using scientific notation, we first express both numbers in that form:

  1. For \( 34,835,760 \): \[ 34,835,760 = 3.4835760 \times 10^7 \]

  2. For \( 43,835,760 \): \[ 43,835,760 = 4.3835760 \times 10^7 \]

Now, both numbers are expressed in terms of \( 10^7 \). Next, we can compare their coefficients:

  • The coefficient of \( 34,835,760 \) is \( 3.4835760 \).
  • The coefficient of \( 43,835,760 \) is \( 4.3835760 \).

Since \( 4.3835760 \) is greater than \( 3.4835760 \), we conclude that:

\[ 43,835,760 > 34,835,760 \]

Thus, in scientific notation, we write:

\[ 4.3835760 \times 10^7 > 3.4835760 \times 10^7 \]

Therefore, \( 43,835,760 \) is greater than \( 34,835,760 \).

so 43,835,760?

Yes, that's correct! The number \( 43,835,760 \) is greater than \( 34,835,760 \). In scientific notation, \( 43,835,760 \) can be expressed as \( 4.3835760 \times 10^7 \). So, the greater number is indeed \( 43,835,760 \).

it says write your answer in scientific notation

Apologies for any confusion! The greater number \( 43,835,760 \) written in scientific notation is:

\[ 4.3835760 \times 10^7 \]

This is the correct representation in scientific notation. Thank you for your patience!

Use scientific notation to determine which of these numbers has the least value: 123,893, 31,892, or 12,786. Write your answer in scientific notation, expressed to the exact decimal place

Let's convert each of the given numbers \( 123,893 \), \( 31,892 \), and \( 12,786 \) into scientific notation:

  1. For \( 123,893 \): \[ 123,893 = 1.23893 \times 10^5 \]

  2. For \( 31,892 \): \[ 31,892 = 3.1892 \times 10^4 \]

  3. For \( 12,786 \): \[ 12,786 = 1.2786 \times 10^4 \]

Now we can compare the scientific notations of the numbers, expressed in terms of \( 10^4 \):

  • \( 123,893 \) in scientific notation is \( 1.23893 \times 10^5 \).
  • \( 31,892 \) in scientific notation is \( 3.1892 \times 10^4 \).
  • \( 12,786 \) in scientific notation is \( 1.2786 \times 10^4 \).

Since \( 10^5 \) (from \( 123,893 \)) is greater than both \( 10^4 \) terms, we focus on the two numbers in the \( 10^4 \) range:

  • Comparing \( 3.1892 \) and \( 1.2786 \):
    • \( 1.2786 < 3.1892 \)

Thus, the least value among the three numbers is \( 12,786 \).

In scientific notation, the least value is:

\[ 1.2786 \times 10^4 \]

So, the answer is \( 1.2786 \times 10^4 \).

Use scientific notation to determine which of these numbers has the greatest value: 654,987,034; 645,897,430; or 546,789,340. Write your answer in scientific notation, expressed to the exact decimal place

Let's convert each of the given numbers \( 654,987,034 \), \( 645,897,430 \), and \( 546,789,340 \) into scientific notation:

  1. For \( 654,987,034 \): \[ 654,987,034 = 6.54987034 \times 10^8 \]

  2. For \( 645,897,430 \): \[ 645,897,430 = 6.45897430 \times 10^8 \]

  3. For \( 546,789,340 \): \[ 546,789,340 = 5.46789340 \times 10^8 \]

Now we can compare the scientific notations. Since all of them are expressed in terms of \( 10^8 \), we can focus on their coefficients:

  • \( 6.54987034 \) (from \( 654,987,034 \))
  • \( 6.45897430 \) (from \( 645,897,430 \))
  • \( 5.46789340 \) (from \( 546,789,340 \))

Among these coefficients:

  1. \( 6.54987034 \)
  2. \( 6.45897430 \)
  3. \( 5.46789340 \)

The greatest coefficient is \( 6.54987034 \).

Thus, the number with the greatest value is \( 654,987,034 \), and in scientific notation, it is expressed as:

\[ 6.54987034 \times 10^8 \]

So, the answer is \( 6.54987034 \times 10^8 \).

Compare 0.0000635 and 0.000456. Write < , > , or = in the blank.(1 point)
0.0000635_____0.000456

To compare the numbers \(0.0000635\) and \(0.000456\), we can rewrite them in scientific notation:

  1. \(0.0000635\) can be expressed as: \[ 6.35 \times 10^{-5} \]

  2. \(0.000456\) can be expressed as: \[ 4.56 \times 10^{-4} \]

Now, let's compare the two numbers:

  • The first number \(6.35 \times 10^{-5}\) is in the range of \(10^{-5}\).
  • The second number \(4.56 \times 10^{-4}\) is in the range of \(10^{-4}\).

Since \(10^{-5}\) is less than \(10^{-4}\), it follows that \(0.0000635\) is less than \(0.000456\).

Thus, we have: \[ 0.0000635 < 0.000456 \]

The answer for the blank is: \[ < \]