To write the expression [tex]\( 3 \times 10^1 + 4 \times 10^0 + 0 \times 10^{-1} + 2 \times 10^{-2} + 1 \times 10^{-3} \)[/tex] in decimal notation, let's break down and evaluate each term step by step.
1. Evaluate [tex]\( 3 \times 10^1 \)[/tex]:
- [tex]\( 10^1 \)[/tex] means [tex]\( 10 \)[/tex].
- [tex]\( 3 \times 10 = 30 \)[/tex].
2. Evaluate [tex]\( 4 \times 10^0 \)[/tex]:
- [tex]\( 10^0 \)[/tex] means [tex]\( 1 \)[/tex].
- [tex]\( 4 \times 1 = 4 \)[/tex].
3. Evaluate [tex]\( 0 \times 10^{-1} \)[/tex]:
- [tex]\( 10^{-1} \)[/tex] means [tex]\( \frac{1}{10} = 0.1 \)[/tex].
- [tex]\( 0 \times 0.1 = 0 \)[/tex].
4. Evaluate [tex]\( 2 \times 10^{-2} \)[/tex]:
- [tex]\( 10^{-2} \)[/tex] means [tex]\( \frac{1}{100} = 0.01 \)[/tex].
- [tex]\( 2 \times 0.01 = 0.02 \)[/tex].
5. Evaluate [tex]\( 1 \times 10^{-3} \)[/tex]:
- [tex]\( 10^{-3} \)[/tex] means [tex]\( \frac{1}{1000} = 0.001 \)[/tex].
- [tex]\( 1 \times 0.001 = 0.001 \)[/tex].
Now, add all the evaluated terms together:
[tex]\[
30 + 4 + 0 + 0.02 + 0.001
\][/tex]
First, add the whole numbers:
[tex]\[
30 + 4 = 34
\][/tex]
Then, add the decimal parts:
[tex]\[
34 + 0.02 + 0.001 = 34.021
\][/tex]
Therefore, the expression [tex]\( 3 \times 10^1 + 4 \times 10^0 + 0 \times 10^{-1} + 2 \times 10^{-2} + 1 \times 10^{-3} \)[/tex] written in decimal notation is:
[tex]\[
34.021
\][/tex]
