Certainly! Let's convert the given numbers from scientific notation to standard form, step-by-step.
### Conversion Steps
1. Identify the coefficient and the exponent:
- The coefficient is the number that appears before the multiplication sign.
- The exponent is the number that the 10 is raised to.
2. Perform the operation indicated by the exponent:
- If the exponent is positive, move the decimal point to the right.
- If the exponent is negative, move the decimal point to the left.
### Working through each problem:
#### 7. [tex]\( 7.2 \times 10^3 \)[/tex]
- Coefficient: 7.2
- Exponent: 3
To convert [tex]\( 7.2 \times 10^3 \)[/tex] to standard form, move the decimal point 3 places to the right.
[tex]\( 7.2 \)[/tex] becomes [tex]\( 7200.0 \)[/tex]
Thus, [tex]\( 7.2 \times 10^3 = 7200.0 \)[/tex]
#### 8. [tex]\( 5.09 \times 10^{-4} \)[/tex]
- Coefficient: 5.09
- Exponent: -4
To convert [tex]\( 5.09 \times 10^{-4} \)[/tex] to standard form, move the decimal point 4 places to the left.
[tex]\( 5.09 \)[/tex] becomes [tex]\( 0.000509 \)[/tex]
Thus, [tex]\( 5.09 \times 10^{-4} = 0.000509 \)[/tex]
#### 9. [tex]\( 1.01 \times 10^6 \)[/tex]
- Coefficient: 1.01
- Exponent: 6
To convert [tex]\( 1.01 \times 10^6 \)[/tex] to standard form, move the decimal point 6 places to the right.
[tex]\( 1.01 \)[/tex] becomes [tex]\( 1010000.0 \)[/tex]
Thus, [tex]\( 1.01 \times 10^6 = 1010000.0 \)[/tex]
#### 10. [tex]\( 3.6 \times 10^{-2} \)[/tex]
- Coefficient: 3.6
- Exponent: -2
To convert [tex]\( 3.6 \times 10^{-2} \)[/tex] to standard form, move the decimal point 2 places to the left.
[tex]\( 3.6 \)[/tex] becomes [tex]\( 0.036000000000000004 \)[/tex]
Thus, [tex]\( 3.6 \times 10^{-2} = 0.036000000000000004 \)[/tex]
### Summary
The standard form of each number is:
1. [tex]\( 7.2 \times 10^3 = 7200.0 \)[/tex]
2. [tex]\( 5.09 \times 10^{-4} = 0.000509 \)[/tex]
3. [tex]\( 1.01 \times 10^6 = 1010000.0 \)[/tex]
4. [tex]\( 3.6 \times 10^{-2} = 0.036000000000000004 \)[/tex]
