Sure! To solve the multiplication problem [tex]\( 116.70 \times 4.75 \)[/tex], follow these detailed steps:
1. Break Down the Factors:
- The first number is 116.70.
- The second number is 4.75.
2. Arrange the Numbers for Multiplication:
Place the larger number (116.70) on top and the smaller number (4.75) underneath it aligning by the decimal point.
3. Ignore the Decimal Point Temporarily:
- Treat the original numbers as whole numbers: [tex]\( 11670 \)[/tex] and [tex]\( 475 \)[/tex].
4. Multiply the Whole Numbers:
- Compute [tex]\( 11670 \times 475 \)[/tex].
5. Reintroduce the Decimal Points in the Final Step:
- The first number, 116.70, has two digits after the decimal.
- The second number, 4.75, has two digits after the decimal.
- Combine the total decimal places: [tex]\( 2 + 2 = 4 \)[/tex].
6. Insert the Decimal Point to Get the Final Result:
- After obtaining the product of the whole numbers, [tex]\( 5543250 \)[/tex], you need to place the decimal point four places from the right.
- Thus, [tex]\( 5543250 \)[/tex] becomes [tex]\( 554.3250 \)[/tex], which simplifies to [tex]\( 554.325 \)[/tex] since the trailing zero does not change the value.
Hence, the solution to [tex]\( 116.70 \times 4.75 \)[/tex] is:
[tex]\[ \boxed{554.325} \][/tex]
