How do i calculate these and express the answers in significant digits?
2.865 x 10^4m x 1.47 x 10^3
8.071 cm^2/ 4.216
1.142 x 10^-8 mm^2 / 8.5 x 10^-4 mm
i tried the first one and got 4212. but i don't know if it's right
I don't understand the questions since some have units and others don't.
For first one, I have
2.865E4 x 1.47E3 = 4.21155E7. The first number has 4 s.f. and second has 3 s.f. The rule in multiplying is that the final answer may have no more s.f. than any of the numbers multiplied. Therefore, you are allowed 3 s.f. in the answer so you would round to 4.21E7. I don't know what unit that 1.47E3 has.If it isn't m that may complicate the problem a little.
To calculate and express the answers in significant digits, you need to follow a few steps:
Step 1: Perform the calculation without considering significant digits.
Step 2: Determine the number of significant digits in each value.
Step 3: Round the final result to match the value with the fewest significant digits.
Let's go through each calculation step-by-step:
1. Calculation: (2.865 x 10^4 m) x (1.47 x 10^3)
Result: 4.21455 x 10^7 m^2
To determine the number of significant digits:
- The value 2.865 has four significant digits.
- The value 1.47 has three significant digits.
Since the value with the fewest significant digits is 1.47, you should round your final answer to three significant digits. The result is 4.21 x 10^7 m^2.
2. Calculation: 8.071 cm^2 / 4.216
Result: 1.91253933406 cm^2
To determine the number of significant digits:
- The value 8.071 has four significant digits.
- The value 4.216 has four significant digits.
Since both values have the same number of significant digits, you should round your final answer accordingly. The result is 1.913 cm^2.
3. Calculation: (1.142 x 10^-8 mm^2) / (8.5 x 10^-4 mm)
Result: 0.0000134117647 mm
To determine the number of significant digits:
- The value 1.142 has four significant digits.
- The value 8.5 has two significant digits.
Since the value with the fewest significant digits is 8.5, you should round your final answer to two significant digits. The result is 0.000013 mm.
Please note that the rounding of values should always align with the value having the fewest significant digits, as this ensures the final answer is presented accurately.