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

Question

0.0945 x 1.47

make it more clear.

Answer 1

To calculate \( 0.0945 \times 1.47 \) while considering significant digits, follow these steps:

Step 1: Perform the Calculation

Using a calculator: \[ 0.0945 \times 1.47 = 0.139215 \]

Step 2: Determine the Significant Digits

Number of Significant Digits in Each Number

1. For 0.0945:

   • There are four significant digits (9, 4, 5, and the leading zeros are not counted).

2. For 1.47:

   • There are three significant digits (1, 4, and 7).

Step 3: Determine the Result's Significant Digits

When multiplying numbers, the final answer should be rounded to the same number of significant digits as the factor with the least significant digits.

• The number with the least significant digits is 1.47 (3 significant digits).

Step 4: Round the Calculator Answer

The calculator result is \( 0.139215 \). Since we need to round this to 3 significant digits, we look at the first three digits, \( 139 \), and the fourth digit, which is \( 2 \).

• Rounding \( 0.139 \) (when considering 3 significant digits):
  • \( 0.139215 \) rounds to 0.139 (since the fourth digit \( 2 \) does not round the last significant digit up).

Final Answer

Calculator Answer: \( 0.139215 \)

Significant Digits Answer: 0.139

Number of Significant Digits: 3

Summary:

• Calculated: \( 0.139215 \)
• Rounded (to 3 significant digits): \( 0.139 \)
• Significant Digits in Final Result: 3