Which number is equivalent to \(3.2\times10^4\)?
- A \(3{,}200\)
- B \(32{,}000\)
- C \(320{,}000\)
- D \(3{,}200{,}000\)
Check answer and explanation
Answer B: \(32{,}000\)
\(3.2\times10^4=3.2\times10{,}000=32{,}000\). Move the decimal \(4\) places right.
CH03-11 lesson
Introduction to Scientific Notation Learning Activity
A focused Grade 7 learning session for Introduction to Scientific Notation using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of introduction to scientific notation using models, equations, and test-style reasoning.
Student goal: I can solve problems involving introduction to scientific notation.
Helpful first:
Rational Number Operations in Extended Contexts
Learn the Idea
Introduction to Scientific Notation is part of Grade 7 The Number System. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of introduction to scientific notation using models, equations, and test-style reasoning.
See the Math
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Follow a Worked Example
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Introduction to Scientific Notation, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving introduction to scientific notation.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsExpress \(0.0056\) in scientific notation and identify which form is NOT equivalent.
- A \(5.6\times10^{-3}\)
- B \(56\times10^{-4}\)
- C \(0.56\times10^{-2}\)
- D \(5.6\times10^{-2}\)
Check answer and explanation
Answer D: \(5.6\times10^{-2}\)
\(0.0056 = 5.6 \times 10^{-3}\) (proper form). Check: \(56\times10^{-4}=5.6\times10^{-3}\) (equiv.), \(0.56\times10^{-2}=5.6\times10^{-3}\) (equiv.), but \(5.6\times10^{-2}=0.056 \neq 0.0056\).
guided
1 questionWhen \(6.75\) is multiplied by a power of 10 to become \(0.000675\), what is the exponent?
- A \(10^{-2}\)
- B \(10^{-3}\)
- C \(10^{-4}\)
- D \(10^{-5}\)
Check answer and explanation
Answer C: \(10^{-4}\)
\(6.75 \times 10^{-4} = 6.75 \times 0.0001 = 0.000675\). The decimal moves 4 places left.
practice
5 questionsThe population of a city is \(1.5\times10^6\). How is this number written in standard form?
- A \(15{,}000\)
- B \(150{,}000\)
- C \(1{,}500{,}000\)
- D \(15{,}000{,}000\)
Check answer and explanation
Answer C: \(1{,}500{,}000\)
\(1.5\times10^6=1.5\times1{,}000{,}000=1{,}500{,}000\).
Express \(24{,}000{,}000\) in scientific notation.
- A \(2.4\times10^6\)
- B \(2.4\times10^7\)
- C \(24\times10^{7}\)
- D \(2.4\times10^{8}\)
Check answer and explanation
Answer B: \(2.4\times10^7\)
Place the decimal after the first digit: \(2.4\). Count places moved: \(7\) places left, so exponent is \(7\). Proper scientific notation requires \(1\leq a<10\).
A microscopic organism measures \(0.000003\) cm. What is this measurement in scientific notation?
- A \(3\times10^{-5}\)
- B \(3\times10^{-6}\)
- C \(3\times10^{5}\)
- D \(0.3\times10^{-5}\)
Check answer and explanation
Answer B: \(3\times10^{-6}\)
Move the decimal 6 places to the right to get \(3\). Exponent is \(-6\).
Which number is larger: \(4.1\times10^5\) or \(3.9\times10^6\)?
- A \(4.1\times10^5\)
- B \(3.9\times10^6\)
- C They are equal
- D Cannot be determined
Check answer and explanation
Answer B: \(3.9\times10^6\)
\(3.9\times10^6=3{,}900{,}000\) and \(4.1\times10^5=410{,}000\). Since the exponent \(6\) is larger, \(3.9\times10^6\) is larger.
The distance from Earth to the Sun is approximately \(1.5\times10^8\) kilometers. Express this in standard form.
- A \(15{,}000{,}000\) km
- B \(150{,}000{,}000\) km
- C \(1{,}500{,}000{,}000\) km
- D \(15{,}000{,}000{,}000\) km
Check answer and explanation
Answer B: \(150{,}000{,}000\) km
\(1.5\times10^8 = 1.5\times100{,}000{,}000 = 150{,}000{,}000\).
exit
3 questionsConvert \(0.00042\) to scientific notation.
- A \(4.2\times10^{-4}\)
- B \(4.2\times10^{-5}\)
- C \(4.2\times10^{-3}\)
- D \(42\times10^{-4}\)
Check answer and explanation
Answer A: \(4.2\times10^{-4}\)
Move the decimal 4 places right from the first nonzero digit: \(0.00042 \to 4.2\). Exponent is \(-4\).
Which value is NOT equivalent to \(5.0\times10^3\)?
- A \(5{,}000\)
- B \(50\times10^2\)
- C \(0.5\times10^4\)
- D \(0.05\times10^3\)
Check answer and explanation
Answer D: \(0.05\times10^3\)
\(5.0\times10^3=5{,}000\). Check: \(0.05\times10^3=0.05\times1{,}000=50 \neq 5{,}000\).
In the number \(0.0089\), what coefficient appears when converted to scientific notation?
- A \(0.89\)
- B \(8.9\)
- C \(89\)
- D \(890\)
Check answer and explanation
Answer B: \(8.9\)
\(0.0089 = 8.9 \times 10^{-3}\). The coefficient must satisfy \(1 \leq a < 10\).
