Ask a New Question
Menu

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.

23.4 x 14

make it more clear.

1 answer

Let's solve the problem step by step.

Problem Statement

Calculate \(23.4 \times 14\).

Step 1: Calculator Answer

First, perform the multiplication using a calculator:

\[ 23.4 \times 14 = 327.6 \]

Step 2: Significant Digits

Next, we need to determine the number of significant digits in each of the numbers involved in the multiplication.

  • For 23.4:

    • This number has 3 significant digits (the digits 2, 3, and 4).

  • For 14:

    • This number has 2 significant digits (the digits 1 and 4).

Step 3: Applying Significant Figures Rule

When multiplying numbers, the result should be reported with the same number of significant digits as the factor with the fewest significant digits.

  • Here, 23.4 has 3 significant digits.
  • 14 has 2 significant digits.

Since 14 has the fewest significant digits (2), the final answer must be rounded to 2 significant digits.

Step 4: Rounding the Calculator Answer

The calculator answer is \(327.6\). We need to round this to 2 significant digits:

  • The first two significant digits are 3 and 2.
  • Looking at the next digit (7), it indicates we should round up.

Therefore, \(327.6\) rounded to 2 significant digits is \(33\).

Final Answer

  1. Calculator Answer: \(327.6\)
  2. Significant Digits Answer: \(33\)
  3. Number of Significant Digits: \(2\)

Summary

  • The original multiplication yields \(327.6\).
  • Rounding to the appropriate significant digits gives us \(33\).