To convert each of these numbers into standard numerical form, we will follow the rules of scientific notation, which express numbers in the form [tex]\( a \times 10^{n} \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer. Let's go through each number step-by-step.
1. [tex]\( 56 \times 10^{4} \)[/tex]
- To convert this to standard form, multiply 56 by [tex]\( 10^{4} \)[/tex] (which is 10,000).
- Calculation: [tex]\( 56 \times 10,000 = 560,000 \)[/tex]
2. [tex]\( 56 \times 10^{-4} \)[/tex]
- To convert this to standard form, multiply 56 by [tex]\( 10^{-4} \)[/tex] (which is 0.0001).
- Calculation: [tex]\( 56 \times 0.0001 = 0.0056 \)[/tex]
3. [tex]\( 5.6 \times 10^{5} \)[/tex]
- To convert this to standard form, multiply 5.6 by [tex]\( 10^{5} \)[/tex] (which is 100,000).
- Calculation: [tex]\( 5.6 \times 100,000 = 560,000 \)[/tex]
4. [tex]\( 5.6 \times 10^{-5} \)[/tex]
- To convert this to standard form, multiply 5.6 by [tex]\( 10^{-5} \)[/tex] (which is 0.00001).
- Calculation: [tex]\( 5.6 \times 0.00001 = 0.000056 \)[/tex]
Note: [tex]\( 0.000056 \)[/tex] is often written in scientific notation as [tex]\( 5.6 \times 10^{-5} \)[/tex], so this value can remain in its current form.
5. [tex]\( 50 \times 10^{5} \)[/tex]
- To convert this to standard form, multiply 50 by [tex]\( 10^{5} \)[/tex] (which is 100,000).
- Calculation: [tex]\( 50 \times 100,000 = 5,000,000 \)[/tex]
6. [tex]\( 5.60 \times 10^{-5} \)[/tex]
- To convert this to standard form, multiply 5.60 by [tex]\( 10^{-5} \)[/tex] (which is 0.00001).
- Calculation: [tex]\( 5.60 \times 0.00001 = 0.000056 \)[/tex]
Similar to number 4, [tex]\( 0.000056 \)[/tex] is often written in scientific notation as [tex]\( 5.60 \times 10^{-5} \)[/tex], so this value can also remain in its current form.
Putting it all together, the standard forms for the given numbers are:
1. [tex]\( 56 \times 10^{4} = 560,000 \)[/tex]
2. [tex]\( 56 \times 10^{-4} = 0.0056 \)[/tex]
3. [tex]\( 5.6 \times 10^{5} = 560,000 \)[/tex]
4. [tex]\( 5.6 \times 10^{-5} = 0.000056 \)[/tex]
5. [tex]\( 50 \times 10^{5} = 5,000,000 \)[/tex]
6. [tex]\( 5.60 \times 10^{-5} = 0.000056 \)[/tex]
