How To Multiply Decimals By 3 Digit Whole Numbers
Multiply Decimals By 3 Digit Whole Numbers
Multiplying decimals by 3-digit whole numbers is straightforward.
Multiplying decimals by 3-digit whole numbers involves similar steps to multiplying by 2-digit numbers but requires careful attention to place values.
Here’s a detailed step-by-step explanation along with examples.
Steps to Multiply Decimals by 3-Digit Whole Numbers
- Write the Numbers: Start by writing the decimal number above the 3-digit whole number, aligning them to the right.
- Ignore the Decimal Point: Temporarily treat the decimal number as a whole number. This means we’ll consider only the digits without the decimal point during the multiplication process.
- Multiply Each Digit: Start multiplying the decimal number by each digit of the 3-digit whole number, beginning from the rightmost digit (the ones place). Remember to shift one position to the left for each digit we move up in the 3-digit number.
- Add the Products: Once we have all the partial products, add them together.
- Place the Decimal Point: Finally, place the decimal point in the result. The number of decimal places in the final product should equal the total number of decimal places in the original decimal number.
Example 1: Multiply 2.34 by 123
- Write Vertically:
2.34
x 123- Ignore the Decimal Point: Treat 2.34 as 234 for now.
- Multiply Each Digit:
- Multiply by 3 (ones place):
234
x 3
702 (this is 234 x 3)
- Multiply by 2 (tens place) (shift left by one position):
234
x 20
4680 (this is 234 x 2, shifted one position left)
- Multiply by 1 (hundreds place) (shift left by two positions):
234
x 100
23400 (this is 234 x 1, shifted two positions left)
- Add the Products:
702
4680
23400
___________
28782- Place the Decimal Point: The original number 2.34 has 2 decimal places. Therefore, we place the decimal point two places from the right in 28782:
- Final Result: 287.82
Example 2: Multiply 5.67 by 456
- Write Vertically:
5.67
x 456- Ignore the Decimal Point: Treat 5.67 as 567.
- Multiply Each Digit:
- Multiply by 6 (ones place):
567
x 6
3402
- Multiply by 5 (tens place) (shift left by one position):
567
x 50
28350
- Multiply by 4 (hundreds place) (shift left by two positions):
567
x 400
226800
- Add the Products:
3402
28350
226800
___________
258552- Place the Decimal Point: The original number 5.67 has 2 decimal places. Therefore, we place the decimal point two places from the right in 258552:
- Final Result: 2585.52
Example 3: Multiply 4.56 by 312
- Write Vertically:
4.56
x 312- Ignore the Decimal Point: Treat 4.56 as 456.
- Multiply Each Digit:
- Multiply by 2 (ones place):
456
x 2
912 (this is 456 x 2)
- Multiply by 1 (tens place) (shift left by one position):
456
x 10
4560 (this is 456 x 1, shifted one position left)
- Multiply by 3 (hundreds place) (shift left by two positions):
456
x 300
136800 (this is 456 x 3, shifted two positions left)
- Add the Products:
912
4560
136800
___________
142272- Place the Decimal Point: The original number 4.56 has 2 decimal places. Place the decimal point two places from the right in 142272:
- Final Result: 1422.72
Example 4: Multiply 7.89 by 245
- Write Vertically:
7.89
x 245- Ignore the Decimal Point: Treat 7.89 as 789.
- Multiply Each Digit:
- Multiply by 5 (ones place):
789
x 5
3945 (this is 789 x 5)
- Multiply by 4 (tens place) (shift left by one position):
789
x 40
31560 (this is 789 x 4, shifted one position left)
- Multiply by 2 (hundreds place) (shift left by two positions):
789
x 200
157800 (this is 789 x 2, shifted two positions left)
- Add the Products:
3945
31560
157800
___________
193305- Place the Decimal Point: The original number 7.89 has 2 decimal places. Place the decimal point two places from the right in 193305:
- Final Result: 1933.05
Example 5: Multiply 0.76 by 125
- Write Vertically:
0.76
x 125- Ignore the Decimal Point: Treat 0.76 as 76.
- Multiply Each Digit:
- Multiply by 5 (ones place):
76
x 5
380 (this is 76 x 5)
- Multiply by 2 (tens place) (shift left by one position):
76
x 20
1520 (this is 76 x 2, shifted one position left)
- Multiply by 1 (hundreds place) (shift left by two positions):
76
x 100
7600 (this is 76 x 1, shifted two positions left)
- Add the Products:
380
1520
7600
___________
9500- Place the Decimal Point: The original number 0.76 has 2 decimal places. Place the decimal point two places from the right in 9500:
- Final Result: 95.00 or simply 95.
Example 6: Multiply 1.23 by 456
- Write Vertically:
1.23
x 456- Ignore the Decimal Point: Treat 1.23 as 123.
- Multiply Each Digit:
- Multiply by 6 (ones place):
123
x 6
738 (this is 123 x 6)
- Multiply by 5 (tens place) (shift left by one position):
123
x 50
6150 (this is 123 x 5, shifted one position left)
- Multiply by 4 (hundreds place) (shift left by two positions):
123
x 400
49200 (this is 123 x 4, shifted two positions left)
- Add the Products:
738
6150
49200
___________
56088- Place the Decimal Point: The original number 1.23 has 2 decimal places. Place the decimal point two places from the right in 56088:
- Final Result: 560.88
Summary
These examples illustrate how to multiply decimals by 3-digit whole numbers in vertical form. Remember to ignore the decimal point during multiplication, shift for each digit, and finally add the products together before placing the decimal point based on the original decimal places.
Summary
- Write the numbers vertically and ignore the decimal temporarily.
- Multiply each digit and shift positions accordingly.
- Add all the products together.
- Place the decimal point based on the total decimal places from the original decimal number.
With practice, multiplying decimals by 3-digit whole numbers becomes easier.