MA19.5.3

Mathematics (2019) Grade(s): 5

Students know:

Each place value position represents 10 times what it represents in the place to its right.
Example: In 433, the underlined 3 represents 3 tens and has a value of 30 which is ten times the value of the 3 ones to its right.
Place value understanding is extended to apply reasoning that a place value position represents 1/10 of what it represents in the place value to its left.
Example: In 433, the underlined 3 represents 3 ones and has a value of 3 which is one-tenth of the value of the 3 tens or 30 to its left.
A given number multiplied by a power of 10 shifts the digits in the given number one place value greater (to the left) for each factor of 10.-A given number divided by a power of 10 shifts the digits in the given number one-tenth of the value (to the right) for each factor of 10.

Students are able to:

Reason and explain the relationship between two successive place values.
Explain patterns of zeros of the product when multiplying by powers of 10.
Explain patterns in placement of decimals when multiplying or dividing by power of 10.
Write powers of 10 using exponential notation.

Students understand that:

The relationship of adjacent places values in the base ten system extend beyond whole numbers to decimal values.
Multiplying or dividing by a power of 10 shifts the digits in a whole number or decimal that many places to the left or right respectively.