$$ a \times 10^n$$

Standard form is a way of writing large numbers or small numbers using powers of $10$.

1. $1 \le a < 10$
2. $n$ is an integer

The number $6.7 \times 10^{67}$ is in standard form. On the other hand, the number $0.12 \times 10^{-12}$ is not in standard form since $0.12$ does not satisfy $1 \le a < 10$.

$ 52900 = \phantom{.} $ $ 5.29 \times 10^4 $

Sometimes, the number is already written using powers of $10$, but it is not yet in standard form. For the following example, since $3845.7$ does not satisfy $1 \le a < 10$.

$ 3845.7 \times 10^4 = \phantom{.} $ $ 3.8457 \times 10^7 $

Solutions

$ 0.0342 = \phantom{.} $ $ 3.42 \times 10^{-3} $

$ 0.008 \phantom{.} 291 \times 10^{-4} = \phantom{.} $ $ 8.291 \times 10^{-7} $

Solutions

To convert a number from standard form to an ordinary number, use the power of $10$ to decide where the decimal point moves.

$ 4.37 \times 10^5 = \phantom{.} $ $ 437 \phantom{.} 000 $

$ 6.82 \times 10^{-4} = \phantom{.} $ $ 0.000 \phantom{.} 682 $

For very large or very small numbers, the calculator may display the answer in standard form, such as $3.84 \times 10^{12}$ or 3.84E12.

$ 1 \text{ million} = \phantom{.} $ $ 1 \times 10^6 $

$ 1 \text{ billion} = \phantom{.} $ $ 1 \times 10^9 $

$ 1 \text{ trillion} = \phantom{.} $ $ 1 \times 10^{12} $

$ 0.455 \text{ million} = \phantom{.} $ $ 4.55 \times 10^5 $

Solutions

$ 7.38 \times 10^8 = \phantom{.} $ $ 0.738 $$ \text{ billion}$

Solutions