1.1.3Math AI SL SL21 flashcards

Calculations with standard form

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1.1.3

Question

Multiply in standard form?

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All 21 Flashcards — Calculations with standard form

Card 1formula

Question

Multiply in standard form?

Answer

Multiply coefficients. Add exponents.

💡 Hint

x coefficients, + exponents.

Card 2concept

Question

Final check after a calculation?

Answer

Check the coefficient is between 1 and 10.

💡 Hint

Re-normalise if needed.

Card 3concept

Question

0.6 × 10⁸: correct it.

Answer

Coefficient too small. Correct form: 6.0 × 10⁷.

💡 Hint

Move right, exponent down 1.

Card 4concept

Question

15 600 000 in standard form?

Answer

1.56 × 10⁷

💡 Hint

Calculator output is not the final form.

Card 5formula

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 6concept

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 7concept

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 8concept

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 9concept

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 10definition

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 11definition

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 12definition

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 13concept

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 14concept

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 15concept

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 16formula

Question

Multiply in standard form?

Answer

Multiply coefficients. Add exponents.

💡 Hint

x coefficients, + exponents.

Card 17formula

Question

Divide in standard form?

Answer

Divide coefficients. Subtract exponents.

💡 Hint

/ coefficients, - exponents.

Card 18concept

Question

Add or subtract in standard form?

Answer

Match the powers first.

💡 Hint

Match powers first.

Card 19concept

Question

0.5 × 10² in valid form?

Answer

5 × 10¹

💡 Hint

Coefficient must be between 1 and 10.

Card 20concept

Question

0.48 × 10⁷: final answer?

Answer

4.8 × 10⁶

💡 Hint

Move right, exponent down 1.

Card 21concept

Question

3 quick checks?

Answer

Coefficient, sign, requested form.

💡 Hint

Quick final scan.

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