Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 3 Lesson 3.8 Multiplying Decimals Using Rules regularly and improve your accuracy in solving questions.
Spectrum Math Grade 5 Chapter 3 Lesson 3.8 Multiplying Decimals Using Rules Answers Key
When multiplying decimals, count the number of decimal places in each factor to figure out the placement of the decimal point in the product.
0 decimal places
1 decimal place
2 decimal places
3 decimal places
How many decimal places will be in the product of the following multiplication problems?
Question 1.
a. 3.25 × 4.2
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 3.25 = 2
And the number of decimal places in 4.2 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 2 + 1 = 3
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 3, the resultant product must contain the decimal point after 3 digits from the rightmost place.
– Therefore, the product of the given decimals is 13.650
b. 6.3 × 9.8
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 6.3 = 1
And the number of decimal places in 9.8 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 1 + 1 = 2
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 2, the resultant product must contain the decimal point after 2 digits from the rightmost place.
– Therefore, the product of the given decimals is 61.74
c. 5.6 × 8.2
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 5.6 = 1
And the number of decimal places in 8.2 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 1 + 1 = 2
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 2, the resultant product must contain the decimal point after 2 digits from the rightmost place.
– Therefore, the product of the given decimals is 45.92
Question 2.
a. 5.3 × 7
Answer:
Multiplying decimal numbers by whole numbers can be done as we do the multiplication of whole numbers. In this case, we should only take care of the decimal point. However, the operation of whole numbers multiplying with decimals
Steps:
1. Multiply both numbers as whole numbers, i.e. we ignore the decimal point here and proceed with the usual multiplication.
53 x 7 = 371
2. Count the number of digits to the right of the decimal point in the decimal number.
In this case, the required number of digits = 1
3. Put the decimal point in the product by counting the digits from the rightmost place.
As the total number of decimal places is 1, the resultant product must contain the decimal point after 1 digit from the rightmost place.
Therefore, 5.3 x 7 = 37.1
b. 9.35 × 8.43
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 9.35 = 2
And the number of decimal places in 8.43 = 2
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 2 + 2 = 4
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 4, the resultant product must contain the decimal point after 4 digits from the rightmost place.
– Therefore, the product of the given decimals is 78.8205
c. 2.8 × 7.46
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
28 x 746 = 20888
2. Count the number of digits to the right of the decimal point in both decimal numbers.
– Thus, the number of digits after the decimal point in 2.8 = 1
And the number of decimal places in 7.46 = 2
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 1 + 2 = 3
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 3, the resultant product must contain the decimal point after 3 digits from the rightmost place.
– Therefore, the product of the given decimals is 20.888
Multiply to find the answer. Underline the decimal places in the factors and in the product.
Question 3.
a.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 5.44 = 2
And the number of decimal places in 901.02 = 2
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 2 + 2 = 4
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 4, the resultant product must contain the decimal point after 4 digits from the rightmost place.
– Therefore, the product of the given decimals is 4901.5488
b.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
259 x 476 = 123284
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 25.9 = 1
And the number of decimal places in 47.6 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 1 + 1 = 2
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 2, the resultant product must contain the decimal point after 2 digits from the rightmost place.
– Therefore, the product of the given decimals is 1232.84
c.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
29123 x 434 = 12639382
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 291.23 = 2
And the number of decimal places in 4.34 = 2
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 2 + 2 = 4
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 4, the resultant product must contain the decimal point after 4 digits from the rightmost place.
– Therefore, the product of the given decimals is 1263.9382
d.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
308 x 6088 = 1875104
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 3.08 = 2
And the number of decimal places in 608.8 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 2 + 1 = 3
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 3, the resultant product must contain the decimal point after 3 digits from the rightmost place.
– Therefore, the product of the given decimals is 1875.104
Question 4.
a.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
90801 x 411 = 37319211
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 908.01 = 2
And the number of decimal places in 4.11 = 2
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 2 + 2 = 4
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 4, the resultant product must contain the decimal point after 4 digits from the rightmost place.
– Therefore, the product of the given decimals is 3731.9211
b.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
925 x 507 = 468975
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 92.5 = 1
And the number of decimal places in 50.7 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 1 + 1 = 2
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 2, the resultant product must contain the decimal point after 2 digits from the rightmost place.
– Therefore, the product of the given decimals is 4689.75
c.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
9013 x 82 = 739066
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 901.3 = 1
And the number of decimal places in 8.2 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 1 + 1 = 2
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 2, the resultant product must contain the decimal point after 2 digits from the rightmost place.
– Therefore, the product of the given decimals is 7390.66
d.
Answer:
Multiplication of a decimal number by another decimal can be performed similarly to the multiplication of whole numbers except keeping the decimal point in the result. The below figure shows the process of multiplying decimal numbers by another decimal number.
steps:
1. Multiply both decimal numbers as whole numbers by removing the decimal point.
114 x 224 = 25536
2. Count the number of digits to the right of the decimal point in both decimal numbers.
Thus, the number of digits after the decimal point in 11.4 = 1
And the number of decimal places in 22.4 = 1
3. Add the number of digits counted for the decimal point.
Total number of decimal places = 1 + 1 = 2
4. Put the decimal point in the product by counting the same digits as obtained in the previous step from its rightmost place.
– As the total number of decimal places is 2, the resultant product must contain the decimal point after 2 digits from the rightmost place.
– Therefore, the product of the given decimals is 255.36