To carry out the subtraction of \(8.0 - 1.99\) while considering significant digits, we will follow these steps:
Step 1: Align the numbers
Align the numbers by their decimal point:
8.0
- 1.99
Step 2: Subtract the values
Now perform the subtraction:
\[ 8.0 - 1.99 = 6.01 \]
Step 3: Identify significant digits
When it comes to significant digits in the context of subtraction:
- The number 8.0 has 2 significant digits (the "8" and the "0" after the decimal point).
- The number 1.99 has 3 significant digits (the "1", "9", and "9").
Step 4: Determine the limiting factor
When performing addition or subtraction, the result should be rounded to the least number of decimal places based on the numbers involved in the operation. In this case, the number with the least decimal places is 8.0, which has 1 decimal place.
Step 5: Round the result
Now we round the result \(6.01\) to 1 decimal place:
- The first decimal place of \(6.01\) is \(0\).
- The second decimal place is \(1\), which means we do not round up.
Thus, rounding \(6.01\) to 1 decimal place gives us:
\[ 6.0 \]
Step 6: Final answer
- Calculator answer: \(6.01\)
- Significant digits answer: \(6.0\)
- Number of significant digits in the final result: 2 significant digits (the "6" and the "0" after the decimal point).
Summary
- Final Answer: 6.0 (with 2 significant digits)
- Intermediate Calculation: 6.01 before rounding.