Answer :
Sure! Let's work through the questions step-by-step:
### Question 1:
Convert the following large number into scientific notation with 4 significant figures:
```
25600000000000000000000000000000000000
```
#### Solution:
The number `25600000000000000000000000000000000000` in scientific notation with 4 significant figures is:
[tex]\[ 2.560 \times 10^{37} \][/tex]
### Question 2:
Convert each of the following into decimal form:
```
1. 1.56 \times 10^4
2. 156 \times 10^5
3. 3.6 \times 10^{-2} + 36 \times 10^{-1}
4. 736.9 \times 10^5
5. 73 / 9 \times 10^8
6. 0.0059 \times 10^5
7. 0.00059 \times 10^{-1}
```
#### Solution:
1. [tex]\( 1.56 \times 10^4 = 15,600 \)[/tex]
2. [tex]\( 156 \times 10^5 = 15,600,000 \)[/tex]
3. [tex]\( 3.6 \times 10^{-2} + 36 \times 10^{-1} = 0.036 + 3.6 = 3.636 \)[/tex]
4. [tex]\( 736.9 \times 10^5 = 73,690,000 \)[/tex]
5. [tex]\( \frac{73}{9} \times 10^8 \approx 811,111,111.11 \)[/tex]
6. [tex]\( 0.0059 \times 10^5 = 590 \)[/tex]
7. [tex]\( 0.00059 \times 10^{-1} = 0.000059 \)[/tex]
### Question 3:
Calculate the following and give the answer in correct scientific notation:
```
a) 2.34 \times 10^{65}
b) 313.0 + 9.2 \times 10^{66} - 1.2 \times 10^3
```
#### Solution:
1. [tex]\( 2.34 \times 10^{65} = 2.34 \times 10^{65} \)[/tex] (already in scientific notation)
2. [tex]\( 313.0 + 9.2 \times 10^{66} - 1.2 \times 10^3 \approx 9.2 \times 10^{66} \)[/tex]
### Question 4:
Calculate the following and give the answer in correct scientific notation:
```
a) 8.95 \times 10^{76} / 1.25 \times 10^{56}
b) (4.5 \times 10^{29})(2.45 \times 10^{100})
```
#### Solution:
1. [tex]\( \frac{8.95 \times 10^{76}}{1.25 \times 10^{56}} = 7.16 \times 10^{20} \)[/tex]
2. [tex]\( (4.5 \times 10^{29})(2.45 \times 10^{100}) = 1.1025 \times 10^{130} \)[/tex]
### Question 5:
Give the number of significant figures in each of the following:
```
a) 1.05 g
b) 0.0003040 mm
c) 29000 ± 10 ft
d) 0.90 \times 10^{45} L
e) The number of eggs (12) that make up a dozen
```
#### Solution:
1. [tex]\( 1.05 \)[/tex] has 3 significant figures.
2. [tex]\( 0.0003040 \)[/tex] has 4 significant figures.
3. [tex]\( 29000 \)[/tex] has 3 significant figures (due to the uncertainty ± 10).
4. [tex]\( 0.90 \times 10^{45} \)[/tex] has 2 significant figures.
5. [tex]\( 12 \)[/tex] is an exact number and has an infinite number of significant figures.
### Question 6:
Determine the answer for each of the following using the correct number of significant figures:
```
a) 17.34 + 4.900 + 23.1
b) 9.80 - 4.762
c) 3.9 \times 6.05 \times 420
d) 14.1 / 5 = r
```
#### Solution:
1. [tex]\( 17.34 + 4.900 + 23.1 = 45.34 \)[/tex]
2. [tex]\( 9.80 - 4.762 = 5.038 \)[/tex]
3. [tex]\( 3.9 \times 6.05 \times 420 = 9900 \)[/tex]
4. [tex]\( 14.1 / 5 = 2.82 \)[/tex]
### Question 7:
Round each of the following to 3 significant figures:
```
1. 77.0653
2. 0.00023350
3. 2.895 \times 10^{21}
4. 6,300,178.2
5. 10.2030
```
#### Solution:
1. 77.0653 rounded to 3 significant figures is [tex]\( 77.1 \)[/tex]
2. 0.00023350 rounded to 3 significant figures is [tex]\( 0.000234 \)[/tex]
3. [tex]\( 2.895 \times 10^{21} \)[/tex] remains [tex]\( 2.90 \times 10^{21} \)[/tex] when rounded to 3 significant figures
4. 6,300,178.2 rounded to 3 significant figures is [tex]\( 6,300,000 \)[/tex]
5. 10.2030 rounded to 3 significant figures is [tex]\( 10.2 \)[/tex]
There you go! Each problem has been solved step-by-step to guide you through the processes involved. If you have any further questions or need more detail on any part, feel free to ask!
### Question 1:
Convert the following large number into scientific notation with 4 significant figures:
```
25600000000000000000000000000000000000
```
#### Solution:
The number `25600000000000000000000000000000000000` in scientific notation with 4 significant figures is:
[tex]\[ 2.560 \times 10^{37} \][/tex]
### Question 2:
Convert each of the following into decimal form:
```
1. 1.56 \times 10^4
2. 156 \times 10^5
3. 3.6 \times 10^{-2} + 36 \times 10^{-1}
4. 736.9 \times 10^5
5. 73 / 9 \times 10^8
6. 0.0059 \times 10^5
7. 0.00059 \times 10^{-1}
```
#### Solution:
1. [tex]\( 1.56 \times 10^4 = 15,600 \)[/tex]
2. [tex]\( 156 \times 10^5 = 15,600,000 \)[/tex]
3. [tex]\( 3.6 \times 10^{-2} + 36 \times 10^{-1} = 0.036 + 3.6 = 3.636 \)[/tex]
4. [tex]\( 736.9 \times 10^5 = 73,690,000 \)[/tex]
5. [tex]\( \frac{73}{9} \times 10^8 \approx 811,111,111.11 \)[/tex]
6. [tex]\( 0.0059 \times 10^5 = 590 \)[/tex]
7. [tex]\( 0.00059 \times 10^{-1} = 0.000059 \)[/tex]
### Question 3:
Calculate the following and give the answer in correct scientific notation:
```
a) 2.34 \times 10^{65}
b) 313.0 + 9.2 \times 10^{66} - 1.2 \times 10^3
```
#### Solution:
1. [tex]\( 2.34 \times 10^{65} = 2.34 \times 10^{65} \)[/tex] (already in scientific notation)
2. [tex]\( 313.0 + 9.2 \times 10^{66} - 1.2 \times 10^3 \approx 9.2 \times 10^{66} \)[/tex]
### Question 4:
Calculate the following and give the answer in correct scientific notation:
```
a) 8.95 \times 10^{76} / 1.25 \times 10^{56}
b) (4.5 \times 10^{29})(2.45 \times 10^{100})
```
#### Solution:
1. [tex]\( \frac{8.95 \times 10^{76}}{1.25 \times 10^{56}} = 7.16 \times 10^{20} \)[/tex]
2. [tex]\( (4.5 \times 10^{29})(2.45 \times 10^{100}) = 1.1025 \times 10^{130} \)[/tex]
### Question 5:
Give the number of significant figures in each of the following:
```
a) 1.05 g
b) 0.0003040 mm
c) 29000 ± 10 ft
d) 0.90 \times 10^{45} L
e) The number of eggs (12) that make up a dozen
```
#### Solution:
1. [tex]\( 1.05 \)[/tex] has 3 significant figures.
2. [tex]\( 0.0003040 \)[/tex] has 4 significant figures.
3. [tex]\( 29000 \)[/tex] has 3 significant figures (due to the uncertainty ± 10).
4. [tex]\( 0.90 \times 10^{45} \)[/tex] has 2 significant figures.
5. [tex]\( 12 \)[/tex] is an exact number and has an infinite number of significant figures.
### Question 6:
Determine the answer for each of the following using the correct number of significant figures:
```
a) 17.34 + 4.900 + 23.1
b) 9.80 - 4.762
c) 3.9 \times 6.05 \times 420
d) 14.1 / 5 = r
```
#### Solution:
1. [tex]\( 17.34 + 4.900 + 23.1 = 45.34 \)[/tex]
2. [tex]\( 9.80 - 4.762 = 5.038 \)[/tex]
3. [tex]\( 3.9 \times 6.05 \times 420 = 9900 \)[/tex]
4. [tex]\( 14.1 / 5 = 2.82 \)[/tex]
### Question 7:
Round each of the following to 3 significant figures:
```
1. 77.0653
2. 0.00023350
3. 2.895 \times 10^{21}
4. 6,300,178.2
5. 10.2030
```
#### Solution:
1. 77.0653 rounded to 3 significant figures is [tex]\( 77.1 \)[/tex]
2. 0.00023350 rounded to 3 significant figures is [tex]\( 0.000234 \)[/tex]
3. [tex]\( 2.895 \times 10^{21} \)[/tex] remains [tex]\( 2.90 \times 10^{21} \)[/tex] when rounded to 3 significant figures
4. 6,300,178.2 rounded to 3 significant figures is [tex]\( 6,300,000 \)[/tex]
5. 10.2030 rounded to 3 significant figures is [tex]\( 10.2 \)[/tex]
There you go! Each problem has been solved step-by-step to guide you through the processes involved. If you have any further questions or need more detail on any part, feel free to ask!
