Grade 4 · Scale one digit through powers of ten · 17 of 750
Scale one digit through powers of ten: digit: 3; places left of ones: 4
A place-value demonstration for a classroom activity moves the digit 3 through 4 places to the left of ones. Find the digit's value after the stated moves, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A place-value demonstration for a classroom activity moves the digit 3 through 4 places to the left of ones. First find the digit's value after the stated moves. Then answer: What is the value after one further move to the left?
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Each move one place left multiplies a digit's value by ten. Repeated moves multiply by powers of ten, not by the number of places moved.
Work through the reasoning
Step 1
Identify the quantities and the task
A place-value demonstration for a classroom activity moves the digit 3 through 4 places to the left of ones. The first task is to find the digit's value after the stated moves. Each move one place left multiplies a digit's value by ten. Repeated moves multiply by powers of ten, not by the number of places moved.
Step 2
Calculate the original result
3 × 10^4 = 30000. At its destination the digit contributes 30000. The animation moves a written symbol; intermediate locations between columns are not new place values.
Step 3
Complete the follow-up calculation
What is the value after one further move to the left? 300000, ten times 30000.
The answer
3 × 10^4 = 30000. At its destination the digit contributes 30000. The animation moves a written symbol; intermediate locations between columns are not new place values. Follow-up: 300000, ten times 30000.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
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From experiment to screen.
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The mathematical idea
A place-value demonstration for a classroom activity moves the digit 3 through 4 places to the left of ones. Each move one place left multiplies a digit's value by ten. Repeated moves multiply by powers of ten, not by the number of places moved. At its destination the digit contributes 30000. The animation moves a written symbol; intermediate locations between columns are not new place values.
3 × 10^4 = 30000
03 · Reflect and transfer
Explain what changes and why.
Follow the digit between place columns, then read its destination only when the motion reaches the selected place. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.