Answer :
To solve [tex]\((0.01)^3\)[/tex], follow these detailed steps:
1. Identify the base and the exponent:
- The base is [tex]\(0.01\)[/tex].
- The exponent is [tex]\(3\)[/tex].
2. Understand what cubing a number means:
- Cubing a number means multiplying the number by itself three times.
- Mathematically, [tex]\((0.01)^3\)[/tex] can be expanded and written as [tex]\(0.01 \times 0.01 \times 0.01\)[/tex].
3. Perform the multiplication step-by-step:
- First, multiply [tex]\(0.01 \times 0.01\)[/tex]:
[tex]\[ 0.01 \times 0.01 = 0.0001 \][/tex]
- Then, multiply the result by [tex]\(0.01\)[/tex] again:
[tex]\[ 0.0001 \times 0.01 = 0.000001 \][/tex]
4. Express the final result in scientific notation:
- The result of these multiplications is [tex]\(0.000001\)[/tex].
- This can be written in scientific notation as [tex]\(1.0 \times 10^{-6}\)[/tex].
Therefore, [tex]\((0.01)^3 = 1.0000000000000002 \times 10^{-6}\)[/tex], or simply [tex]\(1.0 \times 10^{-6}\)[/tex].
1. Identify the base and the exponent:
- The base is [tex]\(0.01\)[/tex].
- The exponent is [tex]\(3\)[/tex].
2. Understand what cubing a number means:
- Cubing a number means multiplying the number by itself three times.
- Mathematically, [tex]\((0.01)^3\)[/tex] can be expanded and written as [tex]\(0.01 \times 0.01 \times 0.01\)[/tex].
3. Perform the multiplication step-by-step:
- First, multiply [tex]\(0.01 \times 0.01\)[/tex]:
[tex]\[ 0.01 \times 0.01 = 0.0001 \][/tex]
- Then, multiply the result by [tex]\(0.01\)[/tex] again:
[tex]\[ 0.0001 \times 0.01 = 0.000001 \][/tex]
4. Express the final result in scientific notation:
- The result of these multiplications is [tex]\(0.000001\)[/tex].
- This can be written in scientific notation as [tex]\(1.0 \times 10^{-6}\)[/tex].
Therefore, [tex]\((0.01)^3 = 1.0000000000000002 \times 10^{-6}\)[/tex], or simply [tex]\(1.0 \times 10^{-6}\)[/tex].
