## Grade 5 Math: Powers of 10 and Decimal Multiplication

### Multiplying by Powers of 10

In this lesson, students learn to multiply by powers of 10 – 10, 100, and 1000. The process is supported by the use of a Place Value Table that illustrates conceptually why multiplication by ten results in adding one or more zeros to the starting number.

In multiplying by 10, each unit in the starting number becomes a ten, so the resulting number is the same number of tens as there are units in the starting number.

In multiplying by 100, 100 is first represented as the product of 10 times 10. Thus, when multiplying by ten each unit in the starting number first becomes ten tens. Then each ten becomes one hundred. The result is that there are the same number of hundreds in the product as there are ones in the starting number.

In multiplying by 1000, the process is extended with the representation of 1000 as the product of 10 times 10 times 10.

This process is used to illustrate multiplication of powers of tens times whole numbers and decimal numbers to thousandths.

### Dividing by Powers of 10

In this lesson students extend what they learned in the prior lesson to learn to divide by powers of 10. The division is represented as its inverse - the multiplication by a decimal number. The decimal numbers are then converted to fractions, which is just another way to write division. For example, dividing by 10 is the same as multiplying by one-tenth.

In dividing by 10, which is the same as multiplying by one-tenth, each ten in the starting number becomes a one, so the resulting number is the same number of units as there are tens in the starting number.

Dividing by 100 is the same as multiplying by one-hundredth, which is represented as the product of one-tenth and one-tenth. Thus, multiplying by one-hundredth, each hundred in the starting number becomes a ten in the product. The result is that there are the same number of units in the product as there are hundreds in the starting number.

In dividing by 1000, the process is extended with the representation of dividing by 1000 is the same as multiplying by one-thousandth, which is the same as one-tenth times one-tenth times one-tenth.

This process is used to illustrate division of whole numbers and decimal numbers to thousandths by powers of ten.

### Multiplying Decimals by Whole Numbers

In prior lessons, students have learned to multiply multi-digit whole numbers. In this lesson, they extend what they have learned in those lessons to multiply decimal numbers by whole numbers using the standard algorithm.

### Multiplying Decimals by Decimals

In the previous lesson, students learn to multiply a decimal number by a whole number using the standard algorithm. In this lesson, they extend what they learned in that lesson to learn to multiply decimal numbers by decimal numbers using the standard algorithm.

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