Multiply Decimals By 2 Digit Whole Numbers

Multiplying decimals by two-digit whole numbers can be done by following a systematic approach. Here’s a detailed step-by-step guide with examples to help understand the process.

Steps to Multiply Decimals by 2-Digit Whole Numbers

1. Write the Numbers Vertically: Write the decimal number above the 2-digit whole number, aligning them to the right.
2. Ignore the Decimal Point: Treat the decimal number as a whole number temporarily.
3. Multiply Each Digit: Multiply the decimal number by each digit of the 2-digit whole number, starting from the rightmost digit (the ones place). Shift one position to the left for each digit.
4. Add the Products: Add the partial products together.
5. Place the Decimal Point: Place the decimal point in the final result based on the total number of decimal places in the original decimal number.

Step 1: Set Up the Problem

1. Write the Numbers Vertically: Align the 2-digit whole number on top and the decimal number underneath, making sure to line up the decimal point with the numbers above it. For example, if we want to multiply 3.25 by 14, write it as:

     14
   x 3.25

Step 2: Ignore the Decimal Temporarily

2. Remove the Decimal: For the purpose of the multiplication, ignore the decimal point. Convert the decimal into a whole number by multiplying it by a power of ten (based on how many decimal places there are). In this case, 3.25 has two decimal places, so multiply by 100:

• 3.25 × 100 = 325

2. Rewrite the Problem: Now, we are multiplying:

     14
   x 325

Step 3: Multiply as We Would with Whole Numbers

4. Multiply Each Digit: Multiply the 325 by each digit of 14, starting from the rightmost digit. Remember to shift one place to the left for each new row:

• First digit (4):
  14 x 325
• ————
• 1300 (4 x 325)
• Second digit (1): Since this is in the tens place, add a zero to the end before multiplying:
• 14 x 325
• ——
• 1300 (4 x 325)
  • 3250 (1 x 325, shifted left)
    ——
    

Step 4: Add the Results

5. Add the Two Products Together:

        1300
      + 3250
      ------
        4550

Step 5: Place the Decimal Back

6. Reinsert the Decimal: Since we initially multiplied by 100 (to account for the two decimal places in 3.25), we need to divide the final answer by 100 to place the decimal point correctly:

• 4550 ÷ 100 = 45.50

Final Result

So, the product of 3.25 and 14 is 45.50.

Example 1: Multiply 3.45 by 27

1. Write Vertically:

       3.45
   x     27

2. Ignore the Decimal Point: Treat 3.45 as 345.
3. Multiply Each Digit:

• Multiply by 7 (ones place):
  
  345
  x 7

---

   2415 (this is 345 x 7)

• Multiply by 2 (tens place) (shift left by one position):
  
  345
  x 20

---

   690 (this is 345 x 2, shifted one position left)
 

4. Add the Products:

      2415
      6900
   ___________
      9315

5. Place the Decimal Point: The original number 3.45 has 2 decimal places. Place the decimal point two places from the right in 93:

• Final Result: 93.15 or simply 93.15

---

Example 2: Multiply 5.67 by 34

1. Write Vertically:

       5.67
       x 34

2. Ignore the Decimal Point: Treat 5.67 as 567.
3. Multiply Each Digit:

• Multiply by 4 (ones place):
  
  567
  x 4

---

  2268 (this is 567 x 4)

• Multiply by 3 (tens place) (shift left by one position):
  
  567
  x 30

---

  17010 (this is 567 x 3, shifted one position left)

4. Add the Products:

       2268
      17010
   ___________
      19278

5. Place the Decimal Point: The original number 5.67 has 2 decimal places. Place the decimal point two places from the right in 19278:

• Final Result: 192.78

---

Example 3: Multiply 0.85 by 56

1. Write Vertically:

       0.85
   x     56

2. Ignore the Decimal Point: Treat 0.85 as 85.
3. Multiply Each Digit:

• Multiply by 6 (ones place):
  
  85
  x 6

---

  510 (this is 85 x 6)
 

• Multiply by 5 (tens place) (shift left by one position):
  
  85
  x 50

---

  4250   (this is 85 x 5, shifted one position left)
 

4. Add the Products:

       510
      4250
   ___________
      4760

5. Place the Decimal Point: The original number 0.85 has 2 decimal places. Place the decimal point two places from the right in 4760:

• Final Result: 47.60 or simply 47.6.

---

Example 4: Multiply 1.25 by 48

1. Write Vertically:

       1.25
       x 48

2. Ignore the Decimal Point: Treat 1.25 as 125.
3. Multiply Each Digit:

• Multiply by 8 (ones place):
  
  125
  x 8

---

   1000 (this is 125 x 8)
 

• Multiply by 4 (tens place) (shift left by one position):
  
  125
  x 40

---

   5000 (this is 125 x 4, shifted one position left)

4. Add the Products:

      1000
      5000
   ___________
      6000

5. Place the Decimal Point: The original number 1.25 has 2 decimal places. Place the decimal point two places from the right in 6000:

• Final Result: 60.00 or simply 60.

---

Example 5: Multiply 2.4 by 19

1. Write Vertically:

        2.4
       x 19

2. Ignore the Decimal Point: Treat 2.4 as 24.
3. Multiply Each Digit:

• Multiply by 9 (ones place):
  
  24
  x 9

---

  216 (this is 24 x 9)
 

• Multiply by 1 (tens place) (shift left by one position):
  
  24
  x 10

---

   240 (this is 24 x 1, shifted one position left)
 

4. Add the Products:

      216
      240
   ___________
      456

5. Place the Decimal Point: The original number 2.4 has 1 decimal place. Place the decimal point one place from the right in 456:

• Final Result: 45.6

---

Sure! Here are more examples of multiplying decimals by 2-digit whole numbers in vertical form.

Example 6: Multiply 4.32 by 36

1. Write Vertically:

       4.32
       x 36

2. Ignore the Decimal Point: Treat 4.32 as 432.
3. Multiply Each Digit:

• Multiply by 6 (ones place):
  
  432
  x 6

---

   2592 (this is 432 x 6)
 

• Multiply by 3 (tens place) (shift left by one position):
  
  432
  x 30

---

   12960 (this is 432 x 3, shifted one position left)
 

4. Add the Products:

       2592
      12960
   ___________
      15552

5. Place the Decimal Point: The original number 4.32 has 2 decimal places. Place the decimal point two places from the right in 15552:

• Final Result: 155.52

---

Example 7: Multiply 6.89 by 25

1. Write Vertically:

       6.89
       x 25

2. Ignore the Decimal Point: Treat 6.89 as 689.
3. Multiply Each Digit:

• Multiply by 5 (ones place):
  
  689
  x 5

---

   3445 (this is 689 x 5)

• Multiply by 2 (tens place) (shift left by one position):
  
  689
  x 20

---

     13780 (this is 689 x 2, shifted one position left)
 

4. Add the Products:

       3445
      13780
   ___________
      17225

5. Place the Decimal Point: The original number 6.89 has 2 decimal places. Place the decimal point two places from the right in 17225:

• Final Result: 172.25

---

Example 8: Multiply 0.56 by 42

1. Write Vertically:

       0.56
       x 42

2. Ignore the Decimal Point: Treat 0.56 as 56.
3. Multiply Each Digit:

• Multiply by 2 (ones place):
  
  56
  x 2

---

    112 (this is 56 x 2)
 

• Multiply by 4 (tens place) (shift left by one position):
  
  56
  x 40

---

     2240 (this is 56 x 4, shifted one position left)
 

4. Add the Products:

       112
      2240
   ___________
      2352

5. Place the Decimal Point: The original number 0.56 has 2 decimal places. Place the decimal point two places from the right in 2352:

• Final Result: 23.52

---

Example 9: Multiply 3.14 by 18

1. Write Vertically:

       3.14
       x 18

2. Ignore the Decimal Point: Treat 3.14 as 314.
3. Multiply Each Digit:

• Multiply by 8 (ones place):
  
  314
  x 8

---

    2512 (this is 314 x 8)
 

• Multiply by 1 (tens place) (shift left by one position):
  
  314
  x 10

---

    3140 (this is 314 x 1, shifted one position left)
 

4. Add the Products:

      2512
      3140
   ___________
      5652

5. Place the Decimal Point: The original number 3.14 has 2 decimal places. Place the decimal point two places from the right in 5652:

• Final Result: 56.52

---

Example 10: Multiply 1.75 by 29

1. Write Vertically:

       1.75
       x 29

2. Ignore the Decimal Point: Treat 1.75 as 175.
3. Multiply Each Digit:

• Multiply by 9 (ones place):
  
  175
  x 9

---

    1575 (this is 175 x 9)
 

• Multiply by 2 (tens place) (shift left by one position):
  
  175
  x 20

---

    3500 (this is 175 x 2, shifted one position left)
 

4. Add the Products:

      1575
      3500
   ___________
      5075

5. Place the Decimal Point: The original number 1.75 has 2 decimal places. Place the decimal point two places from the right in 5075:

• Final Result: 50.75

---

Example 11: Multiply 2.6 by 37

1. Write Vertically:

       2.6
      x 37

2. Ignore the Decimal Point: Treat 2.6 as 26.
3. Multiply Each Digit:

• Multiply by 7 (ones place):
  
  26
  x 7

---

    182 (this is 26 x 7)
 

• Multiply by 3 (tens place) (shift left by one position):
  
  26
  x 30

---

780 (this is 26 x 3, shifted one position left)
 

4. Add the Products:

      182
      780
   ___________
      962

5. Place the Decimal Point: The original number 2.6 has 1 decimal place. Place the decimal point one place from the right in 962:

• Final Result: 96.2

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These additional examples should provide a solid understanding of multiplying decimals by 2-digit whole numbers.

Summary of Steps

1. Write the numbers vertically.
2. Ignore the decimal and convert the decimal to a whole number.
3. Multiply as we would with whole numbers.
4. Add the results together.
5. Place the decimal back by dividing by the power of ten used.

This method keeps everything organized and makes it easier to ensure accuracy in our calculations.