Standard Form

Q: How do you multiply numbers in standard form?

Multiply the front numbers together, then multiply the powers of 10 by adding their indices. If the front number is not between 1 and 10, adjust it into standard form and add the powers again. For example, 16 × 10⁻⁵ becomes 1.6 × 10⁻⁴.

Q: What do you do if a is not between 1 and 10?

You adjust it into standard form. If multiplying gives 16 × 10⁻⁵, then 16 is too big. Write 16 as 1.6 × 10¹, then add the indices again to get 1.6 × 10⁻⁴. Forgetting to do this is a common pitfall.

Key concept

Standard form (or scientific notation) writes very large or very small numbers as A × 10ⁿ, where A is between 1 and 10. The power n counts how many places the decimal point moves. So 0.007 becomes 7 × 10⁻³, a negative power.

Video Lesson

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$Standard Form poster$

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Flashcards

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Standard form explained as a method of expressing large or small numbers in the form A × 10ⁿ.

Converting 0.007 to standard form: 7 × 10⁻³ by moving the decimal three places right

Converting 384,000 to standard form: 3.84 × 10⁵ by moving the decimal five places left

Multiplying in standard form: (2 × 10⁷) × (8 × 10⁻¹²) worked step by step

Calculating in standard form: 3 × 10⁻⁵ × 40,000,000 = (3 × 4) × 10⁻⁵⁺⁷ = 12 × 10² = 1.2 × 10³

What Is Standard Form (Scientific Notation)?

A way to write very large or very small numbers so they are easier to work with.
It always looks like A × 10ⁿ, where A is between 1 and 10

Practice Questions

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Q1Easy

What is 25000 in standard form?

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Interactive Activity

Standard form (scientific notation)

Construct Standard Form

1. Choose Base Number

2. Set Power of 10

Exponent3

10⁻⁶010⁶

Positive Power

Multiplying by 10³ moves the decimal 3 places right (making it larger).

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Students Also Ask

The questions students bump into most on this topic

What is standard form used for?

Standard form is used to write very large or very small numbers in a short, tidy way. Instead of writing out many zeros, you use a number between 1 and 10 multiplied by a power of 10. This keeps big and small values easy to read and work with.

How do you write a small number in standard form?

Move the decimal point to the right until you reach a number between 1 and 10. For 0.007 this gives 7. Each move to the right makes the number ten times bigger, so the power is negative. After three moves, 0.007 becomes 7 × 10⁻³.

Why is the power of 10 negative for small numbers?

For a number below 1, you move the decimal point to the right to reach a value between 1 and 10. Each move to the right makes the number ten times bigger, so you balance this with a negative power of 10. This keeps the value the same.

What does the power of 10 tell you in standard form?

The power of 10, written as n, tells you how many places the decimal point moves to reach a number between 1 and 10. A positive power means a large number, where the point moved left. A negative power means a small number, where the point moved right.

How do you multiply numbers in standard form?

Multiply the front numbers together, then multiply the powers of 10 by adding their indices. If the front number is not between 1 and 10, adjust it into standard form and add the powers again. For example, 16 × 10⁻⁵ becomes 1.6 × 10⁻⁴.

What do you do if a is not between 1 and 10?

You adjust it into standard form. If multiplying gives 16 × 10⁻⁵, then 16 is too big. Write 16 as 1.6 × 10¹, then add the indices again to get 1.6 × 10⁻⁴. Forgetting to do this is a common pitfall.

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