Converting to & from Standard Form Flashcards

All 6 cards in this deck

What form must a number written in standard form take?

$A \times 10^n$, where $1 \le A < 10$ and $n$ is an integer.

What are the steps to write a large ordinary number in standard form?

e.g. $438\,000$

1. Put the decimal point after the first non-zero digit: $4.38$
2. Count how many places the point moved: $5$
3. Number is $\ge 10$, so the power is positive: $4.38 \times 10^{5}$

In standard form, is the power of $10$ positive or negative for a number less than $1$?

e.g. $0.007$

Negative.
$0.007 = 7 \times 10^{-3}$

What are the steps to write a number in standard form as an ordinary number?

e.g. $3.42 \times 10^{4}$

1. Look at the power: $4$, and it is positive
2. Move the decimal point that many places right (left if negative): $34200$
3. Fill any gaps with zeros: $34\,200$

True or false? $0.6 \times 10^{5}$ is written in standard form.

False. $A$ must satisfy $1 \le A < 10$; in standard form it is $6 \times 10^{4}$.

How do you order numbers written in standard form?

e.g. $5.6 \times 10^{4}$ and $9 \times 10^{3}$

Compare the powers of $10$ first; if they are equal, compare the $A$ parts.
$9 \times 10^{3} < 5.6 \times 10^{4}$