Place Shift
About This Worksheet
This worksheet helps students understand what happens to digits when a number is multiplied by 10, 100, or 1,000. Instead of simply adding zeros or moving a decimal point without knowing why, students are encouraged to think about how each digit changes its place value. For example, 47 becomes 470 when multiplied by 10 because each digit moves to a place worth ten times as much. The worksheet includes both whole numbers and decimals, giving students practice seeing the same place-value rule in different kinds of numbers.
Curriculum and Grade Alignment
This fifth-grade activity directly supports CCSS.MATH.CONTENT.5.NBT.A.2 and the understanding of place-value relationships when multiplying by powers of ten. Students should already be familiar with ones, tens, hundreds, tenths, hundredths, and thousandths before beginning. The place-value chart at the top provides extra support for children who still need to see those positions written out. Mastering this idea prepares students for multiplying and dividing decimals and for working more confidently with powers of ten in later math.
Student Tasks
On this worksheet, students will multiply whole numbers and decimals by 10, 100, or 1,000 and record each new value. After solving, they identify where a selected digit started and where that digit ends after the multiplication. A place-value chart gives them a visual tool for tracking movement from one position to another. Students finish by explaining the general pattern they notice when numbers are multiplied by these powers of ten.
Common Challenges
Some students may memorize that they should “move the decimal” but have trouble explaining what is actually happening to the digits. Others may shift a digit the wrong number of places, especially when multiplying by 100 or 1,000. Decimal examples can be especially tricky because children sometimes focus on the decimal point instead of the value of each digit. Encourage your child to place the number in the chart first and physically trace each digit as it moves to a greater place value.
Teaching Tips
Teachers can use this worksheet right after demonstrating powers of ten with a large place-value chart. Working one whole-number problem and one decimal problem together can show students that the same rule works in both situations. At home, a parent can point to the exponent or count the zeros in 10, 100, and 1,000 and ask how many places the digits should shift. The final pattern question is especially useful because it asks children to explain the idea instead of only getting answers.
Worksheet Features
A place-value chart across the top includes positions from thousands through thousandths, making it easier for students to follow each digit. The problems mix whole numbers with decimals so students cannot rely on only one type of example. Short prompts under the equations direct attention to a specific digit and ask where it moves. A final written-response box gives students room to describe the larger mathematical pattern in their own words.