Match the Power of Ten before Adding

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Add 3×10^2 and 4×10^1; give scientific notation. Candidate answers: (A) 3.4×10^1 (B) 3.4×10^2 (C) 7×10^2 (D) 7×10^3.
• Independent check inputs: Add 3×10^3 and 4×10^2; give scientific notation. Candidate answers: (A) 3.4×10^2 (B) 3.4×10^3 (C) 7×10^3 (D) 7×10^5.

Learn the idea

Powers encode repeated multiplication. Integer exponent rules preserve that structure, while scientific notation separates a number’s scale from a coefficient that can be compared or operated on efficiently. Adding scaled quantities requires equal scale factors. Rewrite one term with the other’s power of ten, then combine coefficients while preserving that shared power of ten.

Here is the method on the supplied teaching case. Rewrite 4×10^1 as 0.4×10^2. Add coefficients only after matching powers: (3+0.4)×10^2=3.4×10^2.

Adding exponent values is not an addition rule. First align scales, just as matching place values aligns ordinary decimals; only then add and normalize the resulting coefficient.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: Add 3×10^9 and 4×10^8; give scientific notation. Candidate answers: (A) 3.4×10^8 (B) 3.4×10^9 (C) 7×10^17 (D) 7×10^9. Show the mathematical reason, not only the selected answer. Expected result: 3.4×10^9. Rewrite 4×10^8 as 0.4×10^9. Add coefficients only after matching powers: (3+0.4)×10^9=3.4×10^9.

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