Answer :
Certainly! Let's convert each number into standard form (also known as scientific notation). The standard form of a number is written as [tex]\( a \times 10^n \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
### (i) 0.00000000000000000000035
To express [tex]\( 0.00000000000000000000035 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 22 places to the right to get 3.5. Therefore, we write:
[tex]\[ 3.5 \times 10^{-22} \][/tex]
So, the standard form is:
[tex]\[ 3.50e-22 \][/tex]
### (ii) 4050000000000
To express [tex]\( 4050000000000 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 12 places to the left to get 4.05. Therefore, we write:
[tex]\[ 4.05 \times 10^{12} \][/tex]
So, the standard form is:
[tex]\[ 4.05e+12 \][/tex]
### (iii) 51000000000000000000
To express [tex]\( 51000000000000000000 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 19 places to the left to get 5.1. Therefore, we write:
[tex]\[ 5.1 \times 10^{19} \][/tex]
So, the standard form is:
[tex]\[ 5.10e+19 \][/tex]
### (iv) 0.0000000000000000000000000000625
To express [tex]\( 0.0000000000000000000000000000625 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 29 places to the right to get 6.25. Therefore, we write:
[tex]\[ 6.25 \times 10^{-29} \][/tex]
So, the standard form is:
[tex]\[ 6.25e-29 \][/tex]
### (v) 0.000000000000001257
To express [tex]\( 0.000000000000001257 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 15 places to the right to get 1.257, which is rounded to 1.26 because of significant figures. Therefore, we write:
[tex]\[ 1.26 \times 10^{-15} \][/tex]
So, the standard form is:
[tex]\[ 1.26e-15 \][/tex]
So, summarizing all the expressions in standard form, we have:
1. [tex]\( 0.00000000000000000000035 \)[/tex] in standard form is [tex]\( 3.50e-22 \)[/tex]
2. [tex]\( 4050000000000 \)[/tex] in standard form is [tex]\( 4.05e+12 \)[/tex]
3. [tex]\( 51000000000000000000 \)[/tex] in standard form is [tex]\( 5.10e+19 \)[/tex]
4. [tex]\( 0.0000000000000000000000000000625 \)[/tex] in standard form is [tex]\( 6.25e-29 \)[/tex]
5. [tex]\( 0.000000000000001257 \)[/tex] in standard form is [tex]\( 1.26e-15 \)[/tex]
These are our final converted values.
### (i) 0.00000000000000000000035
To express [tex]\( 0.00000000000000000000035 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 22 places to the right to get 3.5. Therefore, we write:
[tex]\[ 3.5 \times 10^{-22} \][/tex]
So, the standard form is:
[tex]\[ 3.50e-22 \][/tex]
### (ii) 4050000000000
To express [tex]\( 4050000000000 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 12 places to the left to get 4.05. Therefore, we write:
[tex]\[ 4.05 \times 10^{12} \][/tex]
So, the standard form is:
[tex]\[ 4.05e+12 \][/tex]
### (iii) 51000000000000000000
To express [tex]\( 51000000000000000000 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 19 places to the left to get 5.1. Therefore, we write:
[tex]\[ 5.1 \times 10^{19} \][/tex]
So, the standard form is:
[tex]\[ 5.10e+19 \][/tex]
### (iv) 0.0000000000000000000000000000625
To express [tex]\( 0.0000000000000000000000000000625 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 29 places to the right to get 6.25. Therefore, we write:
[tex]\[ 6.25 \times 10^{-29} \][/tex]
So, the standard form is:
[tex]\[ 6.25e-29 \][/tex]
### (v) 0.000000000000001257
To express [tex]\( 0.000000000000001257 \)[/tex] in standard form, we identify where the decimal place would need to be moved to leave a number between 1 and 10. In this case, you would move the decimal 15 places to the right to get 1.257, which is rounded to 1.26 because of significant figures. Therefore, we write:
[tex]\[ 1.26 \times 10^{-15} \][/tex]
So, the standard form is:
[tex]\[ 1.26e-15 \][/tex]
So, summarizing all the expressions in standard form, we have:
1. [tex]\( 0.00000000000000000000035 \)[/tex] in standard form is [tex]\( 3.50e-22 \)[/tex]
2. [tex]\( 4050000000000 \)[/tex] in standard form is [tex]\( 4.05e+12 \)[/tex]
3. [tex]\( 51000000000000000000 \)[/tex] in standard form is [tex]\( 5.10e+19 \)[/tex]
4. [tex]\( 0.0000000000000000000000000000625 \)[/tex] in standard form is [tex]\( 6.25e-29 \)[/tex]
5. [tex]\( 0.000000000000001257 \)[/tex] in standard form is [tex]\( 1.26e-15 \)[/tex]
These are our final converted values.
