Answer :
Sure! Let's solve each part of this problem using the rules for significant figures step-by-step:
### (a) [tex]\( 7.6 \times 21.9 \)[/tex]
1. Identify significant figures:
- [tex]\(7.6\)[/tex] has 2 significant figures.
- [tex]\(21.9\)[/tex] has 3 significant figures.
2. Perform the multiplication: [tex]\(7.6 \times 21.9 = 166.44\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 2.
4. Result: [tex]\(166.44\)[/tex] rounded to 2 significant figures is [tex]\(170\)[/tex].
### (b) [tex]\( 5.0009 \times 0.06 \)[/tex]
1. Identify significant figures:
- [tex]\(5.0009\)[/tex] has 5 significant figures.
- [tex]\(0.06\)[/tex] has 1 significant figure.
2. Perform the multiplication: [tex]\(5.0009 \times 0.06 = 0.300054\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 1.
4. Result: [tex]\(0.300054\)[/tex] rounded to 1 significant figure is [tex]\(0.3\)[/tex].
### (c) [tex]\( 39.3 \times 0.804 \)[/tex]
1. Identify significant figures:
- [tex]\(39.3\)[/tex] has 3 significant figures.
- [tex]\(0.804\)[/tex] has 3 significant figures.
2. Perform the multiplication: [tex]\(39.3 \times 0.804 = 31.5972\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 3.
4. Result: [tex]\(31.5972\)[/tex] rounded to 3 significant figures is [tex]\(31.6\)[/tex].
### (d) [tex]\( 101.2 + 18.702 \)[/tex]
1. Identify decimal places:
- [tex]\(101.2\)[/tex] has 1 decimal place.
- [tex]\(18.702\)[/tex] has 3 decimal places.
2. Perform the addition: [tex]\(101.2 + 18.702 = 119.902\)[/tex].
3. Apply the significant figures rule: Use the smallest number of decimal places from the inputs, which is 1 decimal place.
4. Result: [tex]\(119.902\)[/tex] rounded to 1 decimal place is [tex]\(119.9\)[/tex].
### (e) [tex]\( 1.58 \times 0.03 \)[/tex]
1. Identify significant figures:
- [tex]\(1.58\)[/tex] has 3 significant figures.
- [tex]\(0.03\)[/tex] has 1 significant figure.
2. Perform the multiplication: [tex]\(1.58 \times 0.03 = 0.0474\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 1.
4. Result: [tex]\(0.0474\)[/tex] rounded to 1 significant figure is [tex]\(0.05\)[/tex].
### (f) [tex]\( 1.4 + 2.53 \)[/tex]
1. Identify decimal places:
- [tex]\(1.4\)[/tex] has 1 decimal place.
- [tex]\(2.53\)[/tex] has 2 decimal places.
2. Perform the addition: [tex]\(1.4 + 2.53 = 3.93\)[/tex].
3. Apply the significant figures rule: Use the smallest number of decimal places from the inputs, which is 1 decimal place.
4. Result: [tex]\(3.93\)[/tex] rounded to 1 decimal place is [tex]\(3.9\)[/tex].
### (g) [tex]\( 934.9 \div 0.00455 \)[/tex]
1. Identify significant figures:
- [tex]\(934.9\)[/tex] has 4 significant figures.
- [tex]\(0.00455\)[/tex] has 3 significant figures.
2. Perform the division: [tex]\(934.9 \div 0.00455 = 205472.527\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 3.
4. Result: [tex]\(205472.527\)[/tex] rounded to 3 significant figures is [tex]\(2.05 \times 10^{5}\)[/tex].
I hope this helps! If you have more questions, feel free to ask!
### (a) [tex]\( 7.6 \times 21.9 \)[/tex]
1. Identify significant figures:
- [tex]\(7.6\)[/tex] has 2 significant figures.
- [tex]\(21.9\)[/tex] has 3 significant figures.
2. Perform the multiplication: [tex]\(7.6 \times 21.9 = 166.44\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 2.
4. Result: [tex]\(166.44\)[/tex] rounded to 2 significant figures is [tex]\(170\)[/tex].
### (b) [tex]\( 5.0009 \times 0.06 \)[/tex]
1. Identify significant figures:
- [tex]\(5.0009\)[/tex] has 5 significant figures.
- [tex]\(0.06\)[/tex] has 1 significant figure.
2. Perform the multiplication: [tex]\(5.0009 \times 0.06 = 0.300054\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 1.
4. Result: [tex]\(0.300054\)[/tex] rounded to 1 significant figure is [tex]\(0.3\)[/tex].
### (c) [tex]\( 39.3 \times 0.804 \)[/tex]
1. Identify significant figures:
- [tex]\(39.3\)[/tex] has 3 significant figures.
- [tex]\(0.804\)[/tex] has 3 significant figures.
2. Perform the multiplication: [tex]\(39.3 \times 0.804 = 31.5972\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 3.
4. Result: [tex]\(31.5972\)[/tex] rounded to 3 significant figures is [tex]\(31.6\)[/tex].
### (d) [tex]\( 101.2 + 18.702 \)[/tex]
1. Identify decimal places:
- [tex]\(101.2\)[/tex] has 1 decimal place.
- [tex]\(18.702\)[/tex] has 3 decimal places.
2. Perform the addition: [tex]\(101.2 + 18.702 = 119.902\)[/tex].
3. Apply the significant figures rule: Use the smallest number of decimal places from the inputs, which is 1 decimal place.
4. Result: [tex]\(119.902\)[/tex] rounded to 1 decimal place is [tex]\(119.9\)[/tex].
### (e) [tex]\( 1.58 \times 0.03 \)[/tex]
1. Identify significant figures:
- [tex]\(1.58\)[/tex] has 3 significant figures.
- [tex]\(0.03\)[/tex] has 1 significant figure.
2. Perform the multiplication: [tex]\(1.58 \times 0.03 = 0.0474\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 1.
4. Result: [tex]\(0.0474\)[/tex] rounded to 1 significant figure is [tex]\(0.05\)[/tex].
### (f) [tex]\( 1.4 + 2.53 \)[/tex]
1. Identify decimal places:
- [tex]\(1.4\)[/tex] has 1 decimal place.
- [tex]\(2.53\)[/tex] has 2 decimal places.
2. Perform the addition: [tex]\(1.4 + 2.53 = 3.93\)[/tex].
3. Apply the significant figures rule: Use the smallest number of decimal places from the inputs, which is 1 decimal place.
4. Result: [tex]\(3.93\)[/tex] rounded to 1 decimal place is [tex]\(3.9\)[/tex].
### (g) [tex]\( 934.9 \div 0.00455 \)[/tex]
1. Identify significant figures:
- [tex]\(934.9\)[/tex] has 4 significant figures.
- [tex]\(0.00455\)[/tex] has 3 significant figures.
2. Perform the division: [tex]\(934.9 \div 0.00455 = 205472.527\)[/tex].
3. Apply the significant figures rule: Use the smallest number of significant figures from the inputs, which is 3.
4. Result: [tex]\(205472.527\)[/tex] rounded to 3 significant figures is [tex]\(2.05 \times 10^{5}\)[/tex].
I hope this helps! If you have more questions, feel free to ask!