To complete the standard multiplication algorithm for [tex]\( 59 \times 8.1 \)[/tex], we can follow these detailed steps:
1. Ignore the decimal for now: First, treat [tex]\( 8.1 \)[/tex] as [tex]\( 81 \)[/tex] (just imagining it as a whole number). We'll account for the decimal place at the end.
2. Multiply the numbers as if they were integers:
[tex]\[
59 \times 81
\][/tex]
3. Break down the multiplication using the distributive property:
[tex]\[
59 \times 81 = 59 \times (80 + 1)
\][/tex]
4. Execute the multiplications separately:
[tex]\[
59 \times 80 = 59 \times (8 \times 10) = (59 \times 8) \times 10
\][/tex]
Calculate [tex]\( 59 \times 8 \)[/tex]:
[tex]\[
59 \times 8 = 472
\][/tex]
Then multiply by 10:
[tex]\[
472 \times 10 = 4720
\][/tex]
Now, calculate [tex]\( 59 \times 1 \)[/tex]:
[tex]\[
59 \times 1 = 59
\][/tex]
5. Add these partial products:
[tex]\[
4720 + 59 = 4779
\][/tex]
6. Adjust for the decimal point: Since we initially multiplied by [tex]\( 81 \)[/tex] instead of [tex]\( 8.1 \)[/tex], we must adjust the final result. [tex]\( 8.1 \)[/tex] has one decimal place, so the final result must also have one decimal place.
Therefore,
[tex]\[
4779 \div 10 = 477.9
\][/tex]
So, [tex]\( 59 \times 8.1 = 477.9 \)[/tex].
