2.267×0.0921 on a logarithm diagram in a tarbular form

Answer 1

To calculate \(2.267 \times 0.0921\) using logarithms, follow these steps:

1. Find the logarithms of each number.

   Using logarithm tables or a calculator:

   • \(\log_{10}(2.267) \approx 0.3565\)
   • \(\log_{10}(0.0921) \approx -1.0345\)

2. Add the logarithms.

   \[ \log_{10}(2.267 \times 0.0921) = \log_{10}(2.267) + \log_{10}(0.0921) \]

   \[ = 0.3565 - 1.0345 = -0.678 \]

3. Convert the logarithm back to standard form.

   To find the result: \[ 2.267 \times 0.0921 = 10^{-0.678} \] You can calculate \(10^{-0.678}\) using a calculator: \[ 10^{-0.678} \approx 0.208 \]

Tabular Form

Here's how you can represent this in a tabular form:

| Step | Value | |------------------------------------|--------------| | Value 1 | 2.267 | | Logarithm of Value 1 | \( \log_{10}(2.267) \approx 0.3565 \) | | Value 2 | 0.0921 | | Logarithm of Value 2 | \( \log_{10}(0.0921) \approx -1.0345 \) | | Sum of Logarithms | \( -0.678 \) | | Result \( (2.267 \times 0.0921) \)| \( 10^{-0.678} \approx 0.208 \) |

So, the multiplication of \(2.267\) and \(0.0921\) is approximately \(0.208\).