Topic 1.1Math AI SL SL50 flashcards

Standard form

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1.1.1

Question

What is the coefficient in standard form?

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1.1.112 cards

Card 1definition

Question

What is the coefficient in standard form?

Answer

It is the front number in a × 10ⁿ. In valid standard form, it must be at least 1 but smaller than 10.

💡 Hint

Front number only.

Card 2formula

Question

What two rules must a × 10ⁿ satisfy to be valid standard form?

Answer

1. The coefficient must be at least 1 but smaller than 10. 2. The exponent must be an integer.

💡 Hint

Coefficient range + integer exponent.

Card 3concept

Question

How do you convert a large ordinary number to standard form?

Answer

Move the decimal so only the first non-zero digit stays before it. Count how many places it moved left. That count becomes the positive exponent.

💡 Hint

Move · count · positive.

Card 4concept

Question

Write 5 840 000 in standard form.

Answer

5.84 × 10⁶. The decimal moves 6 places left, so the exponent is +6.

💡 Hint

Large number means positive exponent.

Card 5concept

Question

How do you convert a small decimal to standard form?

Answer

Move the decimal so only the first non-zero digit stays before it. Count how many places it moved right. That count becomes the negative exponent.

💡 Hint

Move · count · negative.

Card 6concept

Question

Write 0.00052 in standard form.

Answer

5.2 × 10⁻⁴. The decimal moves 4 places right to make 5.2, so the exponent is −4.

💡 Hint

Small decimal means negative exponent.

Card 7concept

Question

What should you check before finalising any standard form answer?

Answer

Check that the coefficient is at least 1 but smaller than 10, the exponent sign matches the size of the number, and the question asks for standard form rather than ordinary form.

💡 Hint

Coefficient · sign · instruction.

Card 8concept

Question

Write 73 900 000 in standard form.

Answer

7.39 × 10⁷. Move the decimal 7 places left to get a coefficient between 1 and 10.

💡 Hint

Large number -> move left -> positive exponent.

Card 9concept

Question

Write 12 050 000 000 in standard form.

Answer

1.205 × 10¹⁰. Move the decimal 10 places left and keep all significant digits in the coefficient.

💡 Hint

Count decimal moves carefully.

Card 10concept

Question

Write 0.000084 in standard form.

Answer

8.4 × 10⁻⁵. Move the decimal 5 places right to make 8.4, so the exponent is −5.

💡 Hint

Small decimal -> negative exponent.

Card 11concept

Question

Write 0.000000302 in standard form.

Answer

3.02 × 10⁻⁷. Move the decimal 7 places right so the coefficient is between 1 and 10.

💡 Hint

Move right for tiny numbers.

Card 12concept

Question

Write 0.0096 in standard form.

Answer

9.6 × 10⁻³. Move the decimal 3 places right to get 9.6, so the exponent is −3.

💡 Hint

Keep coefficient between 1 and 10.

1.1.211 cards

Card 13concept

Question

7.2 × 10⁻³ in ordinary form?

Answer

0.0072. Move the decimal 3 places left.

💡 Hint

Negative exponent -> left.

Card 14concept

Question

3.06 × 10⁴ in ordinary form?

Answer

30 600. Move the decimal 4 places right.

💡 Hint

Positive exponent -> right.

Card 15concept

Question

Bigger or smaller than 1?

Answer

Positive exponent -> bigger than 1. Negative exponent -> smaller than 1.

💡 Hint

Use the sign.

Card 16definition

Question

Why is 0.48 × 10⁷ invalid?

Answer

Because 0.48 is less than 1, so the coefficient is not valid.

💡 Hint

Coefficient too small.

Card 17concept

Question

0.48 × 10⁷ in valid form?

Answer

4.8 × 10⁶

💡 Hint

Move right, exponent down 1.

Card 18definition

Question

Why is 31.5 × 10⁴ not valid standard form?

Answer

Because 31.5 is greater than 10. Rewrite it as 3.15 × 10⁵.

💡 Hint

Coefficient too big.

Card 19concept

Question

Fast final check?

Answer

Check coefficient, exponent sign, and the form asked for.

💡 Hint

Coefficient, sign, form.

Card 20concept

Question

4.7 × 10⁶ in ordinary form?

Answer

4 700 000. Move the decimal 6 places right.

💡 Hint

Positive exponent -> right.

Card 21definition

Question

Why is 0.6 × 10⁸ not valid standard form?

Answer

Because 0.6 is smaller than 1. Rewrite it as 6.0 × 10⁷.

💡 Hint

Coefficient too small.

Card 22concept

Question

Positive exponent tells you what?

Answer

It will be a large number greater than 1.

💡 Hint

Positive -> bigger number.

Card 23concept

Question

24.6 × 10⁴ in valid form?

Answer

2.46 × 10⁵

💡 Hint

Coefficient too big -> move left.

1.1.321 cards

Card 24formula

Question

Multiply in standard form?

Answer

Multiply coefficients. Add exponents.

💡 Hint

x coefficients, + exponents.

Card 25concept

Question

Final check after a calculation?

Answer

Check the coefficient is between 1 and 10.

💡 Hint

Re-normalise if needed.

Card 26concept

Question

0.6 × 10⁸: correct it.

Answer

Coefficient too small. Correct form: 6.0 × 10⁷.

💡 Hint

Move right, exponent down 1.

Card 27concept

Question

15 600 000 in standard form?

Answer

1.56 × 10⁷

💡 Hint

Calculator output is not the final form.

Card 28formula

Question

What is the rule for dividing two numbers in standard form?

Answer

(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10^(m-n). Divide the coefficients and subtract the exponents, then re-normalise if needed.

💡 Hint

Coefficients ÷, exponents subtract.

Card 29concept

Question

What must be true before you add or subtract numbers in standard form?

Answer

The powers of 10 must match first. Rewrite one number so both terms use the same power of 10, then add or subtract the coefficients.

💡 Hint

Same power first.

Card 30concept

Question

Rewrite 3.0 x 10^4 so it can be subtracted from 1.8 x 10^5 easily.

Answer

3.0 x 10^4 = 0.3 x 10^5. Then 1.8 x 10^5 - 0.3 x 10^5 = 1.5 x 10^5.

💡 Hint

Match the power of 10 first.

Card 31concept

Question

Rewrite 3 x 10^4 so it can be subtracted from 18 x 10^4 easily.

Answer

Use matching powers first. Keep both terms as x 10^4, then subtract the coefficients.

💡 Hint

Match the power of 10 first.

Card 32concept

Question

Rewrite 3.0 × 10⁴ so it can be subtracted from 1.8 × 10⁵ easily.

Answer

3.0 × 10⁴ = 0.3 × 10⁵. Then 1.8 × 10⁵ - 0.3 × 10⁵ = 1.5 × 10⁵.

💡 Hint

Match the power of 10 first.

Card 33definition

Question

Why is 0.5 × 10² not a finished final answer in standard form?

Answer

Because the coefficient 0.5 is less than 1. Re-normalise it to 5.0 × 10¹.

💡 Hint

Coefficient must be between 1 and 10.

Card 34definition

Question

Why is 1/2 x 10^2 not a finished final answer in standard form?

Answer

Because the coefficient is less than 1. Re-normalise it to 5 x 10^1.

💡 Hint

Coefficient must be between 1 and 10.

Card 35definition

Question

Why is 0.5 x 10^2 not a finished final answer in standard form?

Answer

Because the coefficient 0.5 is less than 1. Re-normalise it to 5.0 x 10^1.

💡 Hint

Coefficient must be between 1 and 10.

Card 36concept

Question

A question says "calculate" and your calculator gives 24.6 x 10^4. What should your final line be?

Answer

2.46 x 10^5, because the coefficient must be between 1 and 10 in valid standard form.

💡 Hint

Do not copy unfinished calculator form.

Card 37concept

Question

A question says “calculate” and your calculator gives 24.6 × 10⁴. What should your final line be?

Answer

2.46 × 10⁵, because the coefficient must be between 1 and 10 in valid standard form.

💡 Hint

Do not copy unfinished calculator form.

Card 38concept

Question

A question says "calculate" and your calculator gives a coefficient above 10. What should your final line do?

Answer

Rewrite to valid standard form by making the coefficient between 1 and 10, and adjust the exponent to keep the same value.

💡 Hint

Do not copy unfinished calculator form.

Card 39formula

Question

Multiply in standard form?

Answer

Multiply coefficients. Add exponents.

💡 Hint

x coefficients, + exponents.

Card 40formula

Question

Divide in standard form?

Answer

Divide coefficients. Subtract exponents.

💡 Hint

/ coefficients, - exponents.

Card 41concept

Question

Add or subtract in standard form?

Answer

Match the powers first.

💡 Hint

Match powers first.

Card 42concept

Question

0.5 × 10² in valid form?

Answer

5 × 10¹

💡 Hint

Coefficient must be between 1 and 10.

Card 43concept

Question

0.48 × 10⁷: final answer?

Answer

4.8 × 10⁶

💡 Hint

Move right, exponent down 1.

Card 44concept

Question

3 quick checks?

Answer

Coefficient, sign, requested form.

💡 Hint

Quick final scan.

1.1.46 cards

Card 45concept

Question

Your GDC shows 5.08E-4. Write as standard form and as an ordinary number.

Answer

5.08 × 10⁻⁴ = 0.000508

💡 Hint

Negative exponent → small number. Move decimal 4 places left.

Card 46concept

Question

What is the two-step habit for reading GDC output?

Answer

Step 1: Read the number before E → that is your coefficient a. Step 2: Read the number after E → that is your exponent n. Then write a × 10ⁿ.

💡 Hint

Before E = a, after E = n.

Card 47concept

Question

Your GDC shows 3.7E9. Write this in standard form.

Answer

3.7 × 10⁹

💡 Hint

Before E = coefficient, after E = exponent.

Card 48concept

Question

Your GDC shows 6.4E-3. Write as (a) standard form and (b) ordinary number.

Answer

(a) 6.4 × 10⁻³ (b) 0.0064

💡 Hint

Negative exponent → decimal moves left.

Card 49definition

Question

Your GDC shows 1.25E11 after a calculation. Can you write 1.25E11 as your final answer?

Answer

No. Writing E notation earns zero marks. You must write 1.25 × 10¹¹.

💡 Hint

GDC notation ≠ standard form.

Card 50definition

Question

What does 'E' mean on a GDC display?

Answer

E means × 10^(the number after E). So 3.7E9 means 3.7 × 10⁹, and 5.1E-4 means 5.1 × 10⁻⁴.

💡 Hint

E replaces "× 10^..."

Topic 1.1 study notes

Full notes & explanations for Standard form

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