Question

Answer the following problem using the correct number of sig figs1.123/6.0+2.001+5.6/5.3 (9.9)=

Answer 1

The given problem needs to be solved while carefully applying the rules for significant figures for each mathematical operation. After calculating each part step by step, the final answer to the expression 1.123/6.0 + 2.001 + (5.6/5.3) × 9.9, with proper significant figures, is 13.19.

Step-by-step explanation:

To solve the given problem while adhering to significant figures, we must first perform each operation separately and then combine the results at the end, ensuring that we carry as many digits as possible through to the final calculation before rounding. In your question, the expression given is 1.123/6.0 + 2.001 + (5.6/5.3) × 9.9. Here's how we evaluate each part while considering significant figures:

• For the division 1.123/6.0, we have four significant figures in the numerator and two significant figures in the denominator. The rule for division is that the result should have the same number of significant figures as the operand with the least number of significant figures. After performing the calculation, we round the result to two significant figures.
• The addition 2.001 + (result from the previous step) requires attention to decimal places. Since 2.001 has four significant figures, we can carry the result to four decimal places.
• For the division 5.6/5.3, we have two significant figures in both the numerator and the denominator, so we keep two significant figures in the result.
• The multiplication (result from the previous division) × 9.9 must be rounded to two significant figures because 9.9 has two significant figures..
• Finally, we add the individual results together, taking care to round the final answer according to the least number of decimal places.

Now, let's compute the results step by step:

1. 1.123/6.0 = 0.1872 (should be rounded to two significant figures: 0.19)
2. 2.001 + 0.19 = 2.191 (still retains four significant figures because of 2.001)
3. 5.6/5.3 = 1.05660377358... (rounded to two significant figures: 1.1)
4. 1.1 × 9.9 = 10.89 (should be rounded to two significant figures: 11)
5. Finally, add 2.191 + 11 = 13.191 (rounded to the least number of decimal places, we get 13.19)

The correct answer to the given expression with the proper number of significant figures is therefore 13.19.