Math With AmarA C A D E M Y

Grade 8 · Follow decimal place-value scaling · 61 of 750

Follow decimal place-value scaling · practice 6

Write 7.5 × 10^(6) as an ordinary decimal number. Follow the calculation, then test the quantities in the animated example.

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

Write 7.5 × 10^(6) as an ordinary decimal number.

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.

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

Paused
Follow decimal place-value scaling · practice 6. Current exponent: 0. Current value: 7.5. Final value: 7,500,000. Scale direction: Multiply repeatedlyA coefficient carried through powers of tenStart7.5Scale operation× 10Current result7.5Exponent reached: 0 of 6Final value: 7,500,000
The coefficient is between 1 and 9.5 and the exponent is an integer from −6 to 6. Values are exact mathematical inputs rather than significant-figure statements about measured accuracy. Stage boxes do not form a linear number line.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Current exponent
0
Current value
7.5
Final value
7,500,000
Scale direction
Multiply repeatedly

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

The mathematical idea

Scientific notation separates a number into a coefficient from one up to but not including ten and a power of ten. Moving between powers changes place value without changing the coefficient. Negative exponents represent small positive quantities, not negative measurements. Starting quantities: Coefficient = 7.5; Power of ten = 6.

value = coefficient × 10ᵉ, 1 ≤ coefficient < 10

03 · Reflect and transfer

Explain what changes and why.

How would the exponent change if the coefficient were divided by ten while the value stayed fixed?

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.