Standard form
Practice Flashcards
What does a number in standard form look like?
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All Flashcards in Topic 1.1
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1.1.18 cards
What does a number in standard form look like?
a × 10ᵏ, with 1 ≤ a < 10 and k a whole number. Example: 4.53 × 10⁴.
In a × 10ᵏ, what is the allowed range for the coefficient a?
1 ≤ a < 10 (at least 1, less than 10). So 7 × 10³ ✓ but 12 × 10³ ✗.
Big number (10 or more): is the exponent positive or negative?
Positive. Example: 52 000 = 5.2 × 10⁴.
Small number (less than 1): is the exponent positive or negative?
Negative. Example: 0.0007 = 7 × 10⁻⁴.
How do you find the exponent k?
Count how many places the point moves to leave one non-zero digit in front. Left → positive, right → negative.
Write 73 000 in standard form.
7.3 × 10⁴.
Your GDC shows 6.1ᴇ-5. What is this in standard form?
6.1 × 10⁻⁵ — the ᴇ symbol means × 10.
Why is 45.3 × 10⁶ not standard form? Fix it.
The coefficient 45.3 is not between 1 and 10. Correct: 4.53 × 10⁷.
1.1.28 cards
When you multiply powers of ten, what do you do to the exponents?
Add them. Example: 10³ × 10⁴ = 10⁷.
When you divide powers of ten, what do you do to the exponents?
Subtract them. Example: 10⁸ ÷ 10³ = 10⁵.
To raise a power of ten to a power, what do you do?
Multiply the exponents. Example: (10⁴)² = 10⁸.
How do you multiply two numbers in standard form?
Multiply the coefficients, add the powers of ten, then re-normalise. Example: (3×10⁴)(2×10³) = 6×10⁷.
Find (2 × 10³)² without a calculator.
4 × 10⁶ — square the coefficient (2² = 4) and double the exponent.
A cube has edge 3 × 10² cm. Find its volume in standard form.
(3×10²)³ = 27×10⁶ = 2.7 × 10⁷ cm³.
After multiplying you get 0.5 × 10⁻³. Fix it.
5 × 10⁻⁴ — 0.5 = 5 × 10⁻¹, so subtract 1 from the exponent.
After cubing you get 27 × 10⁶. Fix it.
2.7 × 10⁷ — 27 = 2.7 × 10¹, so add 1 to the exponent.
Topic 1.1 study notes
Full notes & explanations for Standard form
Math AA SL exam skills
Paper structures, command terms & tips
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