(g) Measurement and Significant Figures Perform the following ealeulations and round the answers to the correct number of significant figures (units of measurement have been omitted) $$ \begin{array}{llll} ext { (i) } \frac{2363 imes 5 a}{6250} & ext { (ii) } 5.41-0.398 & ext { (iii) } 3.38-0.31 & ext { (iv) } 4.18-58.16 imes(3.38- \ 3.01) \ ext { Solution: } \ ext { (i) The factor } 5.8 ext { has the fewest significant figures; therefore, the answer shoufid be }\end{array} $$

Question

(g) Measurement and Significant Figures Perform the following ealeulations and round the answers to the correct number of significant figures (units of measurement have been omitted) $$ \begin{array}{llll}	ext { (i) } \frac{2363 	imes 5 a}{6250} & 	ext { (ii) } 5.41-0.398 & 	ext { (iii) } 3.38-0.31 & 	ext { (iv) } 4.18-58.16 	imes(3.38- \ 3.01) \ 	ext { Solution: } \ 	ext { (i) The factor } 5.8 	ext { has the fewest significant figures; therefore, the answer shoufid be }\end{array} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$3.38-0.31$$
- step1: Subtract the numbers:
  $$3.07$$
Calculate or simplify the expression $$ 5.41 - 0.398 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5.41-0.398$$
- step1: Subtract the numbers:
  $$5.012$$
Calculate or simplify the expression $$ 4.18 - 58.16 * (3.38 - 3.01) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4.18-58.16\left(3.38-3.01\right)$$
- step1: Subtract the numbers:
  $$4.18-58.16\times 0.37$$
- step2: Multiply the numbers:
  $$4.18-21.5192$$
- step3: Subtract the numbers:
  $$-17.3392$$
Calculate or simplify the expression $$ (2363 * 5.8) / 6250 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(2363\times 5.8\right)}{6250}$$
- step1: Remove the parentheses:
  $$\frac{2363\times 5.8}{6250}$$
- step2: Multiply the numbers:
  $$\frac{13705.4}{6250}$$
- step3: Convert the expressions:
  $$\frac{\frac{68527}{5}}{6250}$$
- step4: Multiply by the reciprocal:
  $$\frac{68527}{5}\times \frac{1}{6250}$$
- step5: Multiply the fractions:
  $$\frac{68527}{5\times 6250}$$
- step6: Multiply:
  $$\frac{68527}{31250}$$
Let's solve each part of the problem step by step, ensuring we round to the correct number of significant figures.

### (i) Calculation of $$\frac{2363 \times 5.8}{6250}$$

1. **Calculate the numerator**: 
   $$
   2363 \times 5.8 = 13703.4
   $$
2. **Divide by the denominator**:
   $$
   \frac{13703.4}{6250} = 2.192864
   $$
3. **Significant Figures**: The number $$5.8$$ has 2 significant figures, which is the limiting factor. Therefore, we round $$2.192864$$ to **2 significant figures**:
   $$
   \text{Rounded result: } 2.2
   $$

### (ii) Calculation of $$5.41 - 0.398$$

1. **Perform the subtraction**:
   $$
   5.41 - 0.398 = 5.012
   $$
2. **Significant Figures**: The number $$5.41$$ has 3 significant figures, and $$0.398$$ has 3 significant figures. The result should be rounded to the least number of decimal places, which is 2:
   $$
   \text{Rounded result: } 5.01
   $$

### (iii) Calculation of $$3.38 - 0.31$$

1. **Perform the subtraction**:
   $$
   3.38 - 0.31 = 3.07
   $$
2. **Significant Figures**: Both numbers have 2 decimal places, so we keep 2 decimal places:
   $$
   \text{Rounded result: } 3.07
   $$

### (iv) Calculation of $$4.18 - 58.16 \times (3.38 - 3.01)$$

1. **Calculate the parentheses first**:
   $$
   3.38 - 3.01 = 0.37
   $$
2. **Multiply**:
   $$
   58.16 \times 0.37 = 21.5072
   $$
3. **Subtract from $$4.18$$**:
   $$
   4.18 - 21.5072 = -17.3272
   $$
4. **Significant Figures**: The number $$4.18$$ has 3 significant figures, and $$21.5072$$ has 5 significant figures. The result should be rounded to 2 decimal places (the least precise measurement):
   $$
   \text{Rounded result: } -17.33
   $$

### Summary of Results
- (i) $$2.2$$
- (ii) $$5.01$$
- (iii) $$3.07$$
- (iv) $$-17.33$$
- (i) 2.2 - (ii) 5.01 - (iii) 3.07 - (iv) -17.33

(g) Measurement and Significant Figures
Perform the following ealeulations and round the answers to the correct number of significant
figures (units of measurement have been omitted)

Upstudy AI Solution

Answer

Solution

(i) Calculation of

(ii) Calculation of

(iii) Calculation of

(iv) Calculation of

Summary of Results

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