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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to normalize very small numbers in scientific notation.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Decimal place value and powers of ten.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Write 0.000072 in scientific notation and explain the sign of its exponent.
Why this math matters
Scientific notation writes a positive number as a coefficient from 1 up to but not including 10 times a power of ten. Estimate whether the original number is above or below one before choosing the exponent sign.
Set up the model
A useful answer starts with clear assumptions:
- The number is exact as written.
- Use the standard positive-coefficient scientific-notation convention.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Normalize very small numbers in scientific notation
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Write 0.000072 in scientific notation and explain the sign of its exponent.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
coefficient = 7.2
Move the decimal until the coefficient is at least 1 but less than 10.
Apply the relationship
0.000072 = 7.2 × 0.00001
The coefficient must be multiplied by one hundred-thousandth to restore the original size.
Check and interpret
0.000072 = 7.2 × 10⁻⁵
A negative power of ten reduces the coefficient to a number below one.
The result
0.000072 = 7.2 × 10⁻⁵
A negative power of ten reduces the coefficient to a number below one.
Common mistakes to catch
- A coefficient of 42 is not normalized scientific notation.
- A small positive number needs a negative exponent, not a negative coefficient.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Write 53,000,000 in scientific notation.
Show a hint
Count how many places separate 5.3 and the original decimal position.
Reveal answer and explanation
5.3 × 10⁷
Multiplying 5.3 by ten million restores 53,000,000.
Practice 2
Normalize 42 × 10⁻⁶.
Show a hint
Replace 42 by 4.2 × 10.
Reveal answer and explanation
4.2 × 10⁻⁵
(4.2 × 10)(10⁻⁶) = 4.2 × 10⁻⁵.
Take the idea with you
Estimate whether the original number is above or below one before choosing the exponent sign.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Align powers of ten before adding
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