Question

0.000175 meters (2 significant figures) 6.0964×10³ liters (1 significant figure) 5945 grams (3 significant figures) 41. write the number \fifty\ in numerical form giving one significant digit 42. write the number \fifty\ in numerical form giving two significant digits 43. write the number \fifty\ in numerical form giving four significant digits round 735.85 to the indicated number of significant figures: 44. 2 significant figures 45. 3 significant figures 46. 4 significant figures 47. 1 significant figure complete the following calculations, expressing your answer to the correct number of significant digits. 48. 24.57 + 5.678+5.3 49. 0.012 + 5.9 50. 59.34×5 51. 8.895 - 6.22 use dimensional - analysis to solve the following problems: 52. how many microliters are in 0.00528 liters? 53. what portion of a year is 3.97×10¹⁰ nanoseconds? 54. convert 0.75 hm³ to mm³

Explanation:

Step1: Solve problem 41

The number "fifty" in numerical form with one - significant digit is 50 (since 50 has 1 non - zero significant digit).

Step2: Solve problem 42

The number "fifty" in numerical form with two significant digits is 50. (Trailing zeros after a non - zero digit are significant when there is a decimal point or when the number is written in scientific notation. Here we can consider 50 as having 2 significant digits as it is an exact value in this context).

Step3: Solve problem 43

The number "fifty" in numerical form with four significant digits is 50.00.

Step4: Solve problem 44

To round 735.85 to 2 significant digits, we look at the third digit. Since 5 is the third digit and the number after it is 8 (which is greater than or equal to 5), we round up. So 735.85 rounds to 740.

Step5: Solve problem 45

To round 735.85 to 3 significant digits, we look at the fourth digit. Since 8 is greater than or equal to 5, we round up. So 735.85 rounds to 736.

Step6: Solve problem 46

To round 735.85 to 4 significant digits, we look at the fifth digit. Since 5 is equal to 5, we round up. So 735.85 rounds to 735.9.

Step7: Solve problem 47

To round 735.85 to 1 significant digit, we look at the second digit. Since 3 is less than 5, we round down. So 735.85 rounds to 700.

Step8: Solve problem 48

First, add 24.57+5.678 + 5.3 = 35.548. The least number of decimal places among the numbers being added is 1 (in 5.3). So, rounding to the correct number of significant digits (based on decimal places for addition), the answer is 35.5.

Step9: Solve problem 49

Add 0.012+5.9 = 5.912. The least number of decimal places among the numbers being added is 1 (in 5.9). So, rounding to the correct number of significant digits, the answer is 5.9.

Step10: Solve problem 50

Multiply 59.34×5 = 296.7. The number 5 has 1 significant digit. So, rounding to 1 significant digit, the answer is 300.

Step11: Solve problem 51

Subtract 8.895−6.22 = 2.675. The least number of decimal places among the numbers being subtracted is 2 (in 6.22). So, rounding to the correct number of significant digits, the answer is 2.68.

Step12: Solve problem 52

We know that 1 liter = 10^6 microliters. So, to find the number of microliters in 0.00528 liters, we multiply 0.00528×10^6 = 5280 μL.

Step13: Solve problem 53

First, convert 1 year to nanoseconds. 1 year = 365 days×24 h/day×3600 s/h×10^9 ns/s=3.1536×10^16 ns. Then, to find what portion of a year 3.97×10^15 ns is, we calculate (3.97×10^15)/(3.1536×10^16)=0.126.

Step14: Solve problem 54

We know that 1 km = 10^3 m and 1 m = 10^3 mm. So, 1 km^3=(10^3)^3 m^3 = 10^9 m^3 and 1 m^3=(10^3)^3 mm^3=10^9 mm^3. Then 0.75 km^3 = 0.75×10^9×10^9 mm^3=7.5×10^17 mm^3.

Answer:

1. 50
2. 50
3. 50.00
4. 740
5. 736
6. 735.9
7. 700
8. 35.5
9. 5.9
10. 300
11. 2.68
12. 5280 μL
13. 0.126
14. 7.5×10^17 mm^3