1.1.1Math AI SL SL12 flashcards

Converting to standard form

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Card 1 of 121.1.1

1.1.1

Question

What is the coefficient in standard form?

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All 12 Flashcards — Converting to standard form

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.

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Standard form

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