Complete each calculation. Express your answer to the correct number of significant digits.
a)4.02mL + 3.76mL +0.95mL
b)(2.7 x 10^2m) x (4.23 x 10^2m)
c)5092kg divided by 23L
d) 2-6.3 + 6-7
e)(6.853 x 10^3L) + (5.40 x 10^3mL)
f)(572.3g + 794.1g) divided (24mL + 52mL)
My answers:
a)8.7mL
b) i am not sure
c) 221.34
d) -5.3
e) im not sure
f) 17.97
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To complete each calculation and express the answers to the correct number of significant digits, follow these steps:
a) 4.02 mL + 3.76 mL + 0.95 mL:
- Add the given values: 4.02 + 3.76 + 0.95 = 8.73 mL.
- The answer has the same number of decimal places as the measurement with the fewest decimal places. In this case, 0.95 mL has 2 decimal places.
- Therefore, the answer, expressed with the correct number of significant digits, is 8.73 mL.
b) (2.7 x 10^2 m) x (4.23 x 10^2 m):
- Multiply the numbers outside the exponent: 2.7 x 4.23 = 11.421.
- Combine the exponents, adding them: 10^2 x 10^2 = 10^(2+2) = 10^4.
- Multiply the numbers, including the exponent: 11.421 x 10^4 = 114,210.
- The answer, expressed with the correct number of significant digits, is 114,000. (Since the least precise value has 2 significant digits, the final answer is rounded to 2 significant digits)
c) 5092 kg divided by 23 L:
- Divide the given values: 5092 ÷ 23 = 221.391304348.
- The answer is limited by the least precise value, which has 2 significant digits.
- Therefore, the answer, expressed with the correct number of significant digits, is 220.
d) 2-6.3 + 6-7:
- Perform the subtraction within each set of parentheses: 2 - 6.3 = -4.3 and 6 - 7 = -1.
- Add the results: -4.3 + (-1) = -5.3.
- The answer remains -5.3.
e) (6.853 x 10^3 L) + (5.40 x 10^3 mL):
- Convert the milliliters to liters by dividing by 1000: 5.40 x 10^3 mL = 5.40 x 10^3 L.
- Add the two values: 6.853 x 10^3 + 5.40 x 10^3 = 12.253 x 10^3.
- Rewrite the answer in scientific notation: 12.253 x 10^3 = 1.2253 x 10^4.
- The answer, expressed with the correct number of significant digits, is 1.23 x 10^4. (Since the least precise value has 3 significant digits, the final answer is rounded to 3 significant digits.)
f) (572.3 g + 794.1 g) divided by (24 mL + 52 mL):
- Add the values in the numerator: 572.3 + 794.1 = 1366.4 g.
- Add the values in the denominator: 24 + 52 = 76 mL.
- Divide the numerator by the denominator: 1366.4 ÷ 76 = 17.9578947368.
- The answer is limited by the least precise value, which has 2 significant digits.
- Therefore, the answer, expressed with the correct number of significant digits, is 18. (Since the least precise value has 2 significant digits, the final answer is rounded to 2 significant digits.)
So, the correct answers are:
a) 8.73 mL
b) 114,000
c) 220
d) -5.3
e) 1.23 x 10^4
f) 18