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Flip to reveal answersWhen you multiply powers of ten, what do you do to the exponents?
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All 8 Flashcards — Standard form by hand
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Question
When you multiply powers of ten, what do you do to the exponents?
Answer
Add them. Example: 10³ × 10⁴ = 10⁷.
Question
When you divide powers of ten, what do you do to the exponents?
Answer
Subtract them. Example: 10⁸ ÷ 10³ = 10⁵.
Question
To raise a power of ten to a power, what do you do?
Answer
Multiply the exponents. Example: (10⁴)² = 10⁸.
Question
How do you multiply two numbers in standard form?
Answer
Multiply the coefficients, add the powers of ten, then re-normalise. Example: (3×10⁴)(2×10³) = 6×10⁷.
Question
Find (2 × 10³)² without a calculator.
Answer
4 × 10⁶ — square the coefficient (2² = 4) and double the exponent.
Question
A cube has edge 3 × 10² cm. Find its volume in standard form.
Answer
(3×10²)³ = 27×10⁶ = 2.7 × 10⁷ cm³.
Question
After multiplying you get 0.5 × 10⁻³. Fix it.
Answer
5 × 10⁻⁴ — 0.5 = 5 × 10⁻¹, so subtract 1 from the exponent.
Question
After cubing you get 27 × 10⁶. Fix it.
Answer
2.7 × 10⁷ — 27 = 2.7 × 10¹, so add 1 to the exponent.
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