Standard Form Lecture Notes

Flashcards covering the definition, rules, and calculation methods for writing numbers in standard form as presented in the lecture notes.

Standard Form

A more convenient way of writing numbers which are very large or very small, written in the format $A \times 10^B$.

Standard Form Format

The format $A \times 10^B$ where $A$ is a whole number between 1 and 10 and $B$ is either a positive or negative whole number.

Rule for Multiplying Powers

The mathematical rule stated as $y^a \times y^b = y^{(a+b)}$, used for calculating standard form multiplication.

Rule for Dividing Powers

The mathematical rule stated as $y^a \text{ ÷ } y^b = y^{(a-b)}$.

Method for Adding Standard Form Numbers

To add two standard numbers, change them both to ordinary form, add them, and then convert them back to standard form.

Standard Form of 15700

$$1.57 \times 10^4$$

Standard Form of 200

$$2.00 \times 10^2$$

Standard Form of 0.00729

$$7.29 \times 10^{-3}$$

Standard Form of 0.000059

$$5.9 \times 10^{-5}$$

Hint for Large Numbers

Count the digits to the right of the first one; for example, in 5600 there are 3 digits after the 5, so the standard form uses $10^3$ because $10^3 = 10 \times 10 \times 10 = 1000$.

Hint for Small Numbers

Count the number of places the decimal place shifts; for example, in 0.0025 the decimal shifts 3 places to become 2.5, so the standard form uses $10^{-3}$ because $10^{-3} = \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}$.

Multiplication Example: $(2 \times 10^3) \times (6 \times 10^4)$

$$(6 \times 2) \times 10^{(3+4)} = 12 \times 10^7$$

Addition Example: $3 \times 10^4 + 5 \times 10^2$

$$30000 + 500 = 30500 = 3.05 \times 10^4$$