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Write the number in decimal notation.

[tex]\[ 3 \times 10^1 + 4 \times 10^0 + 0 \times 10^{-1} + 2 \times 10^{-2} + 1 \times 10^{-3} \][/tex]

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GinnyAnsweridn
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]
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