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Conceptual arithmetic methods with decimals. Multiplication. Multiplication with decimals. The following three techniques will be covered in this presentation: Using upper and lower product bounds to correctly place the decimal point Converting to fractions Place value multiplication.

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multiplication with decimals
Multiplication with decimals
  • The following three techniques will be covered in this presentation:
    • Using upper and lower product bounds to correctly place the decimal point
    • Converting to fractions
    • Place value multiplication
technique 1
Technique 1

Using upper and lower product bounds to correctly place the decimal point

example 1 find the product of 3 8 and 0 52
Example 1: Find the product of 3.8 and 0.52

1. Find upper and lower bounds for the factors:3 < 3.8 < 4 and 0.5 < 0.52 < 0.6

2. Find upper and lower bounds for the product:

example 1 find the product of 3 8 and 0 521
Example 1: Find the product of 3.8 and 0.52

3. Multiply the factors as if they were whole numbers:

4. Use the upper and lower bounds for the product to correctly place the decimal point.

Answer:

example 2 find the product of 72 3 and 8 201
Example 2: Find the product of 72.3 and 8.201

1. 70 < 72.3 < 80 and 8 < 8.201 < 9

2.

3. Multiply the factors as if they were whole numbers:

4.Correctly place the decimal point using the bounds.Answer:

technique 2
Technique 2

Convert to fractions

example 3 find the product of 1 2 and 0 03
Example 3: Find the product of 1.2 and 0.03
  • Convert each decimal to fraction form:
  • Multiply the fractions:
  • Rewrite in decimal form: 1.2 x 0.03 = 0.036
    • If you have trouble seeing the decimal form, note that 36/1000 = 30/1000 + 6/1000 = 3/100 + 6/1000 = 0.03 + 0.006 = 0.036
example 4 find the product of 0 025 and 0 08
Example 4: Find the product of 0.025 and 0.08
  • Convert each decimal to fraction form:
  • Multiply the fractions:
  • Rewrite in decimal form: 0.025 x 0.08 = 0.002
example 5 find the product of 34 23 and 0 011
Example 5: Find the product of34.23 and 0.011
  • Convert each decimal to fraction form:
  • Multiply the fractions:
  • Rewrite in decimal form: 34.23 x 0.011 = 0.37653
    • Note that the final digit of 3 in the numerator 37653 from step 2 must be in the 100,000ths (hundred thousandths) place.
technique 3
Technique 3

Place Value Multiplication

multiplication of decimals using place value
Multiplication of decimals using place value
  • Use a place value chart to organize the factors and partial products.
    • The number of columns depends on the problems. Leave room to add more columns if necessary.
example 6 find the product of 2 3 and 4 5
Example 6: Find the product of 2.3 and 4.5
  • Step 1: Enter the factors into a place value chart.
example 6 find the product of 2 3 and 4 51
Example 6: Find the product of 2.3 and 4.5
  • Step 2: Find the partial products.
example 6 find the product of 2 3 and 4 52
Example 6: Find the product of 2.3 and 4.5
  • Step 2: Find the partial products.
example 6 find the product of 2 3 and 4 53
Example 6: Find the product of 2.3 and 4.5
  • Step 2: Find the partial products.
example 6 find the product of 2 3 and 4 54
Example 6: Find the product of 2.3 and 4.5
  • Step 2: Find the partial products.
example 6 find the product of 2 3 and 4 55
Example 6: Find the product of 2.3 and 4.5
  • Step 3: Sum the partial products to obtain the final product.
example 7 find the product of 08 and 907
Example 7: Find the product of.08 and .907
  • Example: Find the product of .08 and .907
    • Estimate practice: The answer should lie between
example 8 find the product of 2 305 and 70 89
Example 8: Find the product of 2.305 and 70.89
  • Find the product of 2.305 and 70.89.
    • Estimating, we see that our answer should be between2 x 70 = 140 and 3 x 71 = 213. We can use this as a check at the end.