# How do you write 3.77 times 10^4  in standard notation?

Jun 15, 2016

$3.77 \times {10}^{3} = 37700$

#### Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of $10$.

In other words, in scientific notation, a number is written as $a \times {10}^{n}$, where $1 \le a < 10$ and $n$ is an integer and $1 \le a < 10$.

To write the number in normal or standard notation one just needs to multiply by the power ${10}^{n}$ (or divide if $n$ is negative). This means moving decimal $n$ digits to right if multiplying by ${10}^{n}$ and moving decimal $n$ digits to left if dividing by ${10}^{n}$ (i.e. multiplying by ${10}^{- n}$).

In the given case, as we have the number as $3.77 \times {10}^{4}$, we need to move decimal digit to the right by four points. For this, let us write $3.77$ as $3.770000$ and moving decimal point four points to right means $37700.00$

Hence in standard notation $3.77 \times {10}^{3} = 37700$

Jun 16, 2016

$3.77 \times {10}^{4} \equiv 37700$

Where $\equiv$ means equivalent to.

#### Explanation:

$\textcolor{b r o w n}{3.77 \times 10 = 37.7} \textcolor{b l u e}{\text{ "larr" } 3.77 \times {10}^{1} = 37.7}$

'.....................................................................................
color(brown)(3.77xx10xx10=377color(blue)(" "larr 3.77xx10^2=377)

,..................................................................................................
color(brown)(3.77xx10xx10xx10=3770color(blue)(" "larr 3.77xx10^3=3770)

,.....................................................................................................
color(brown)(3.77xx10xx10xx10xx10=37700color(blue)(" "larr 3.77xx10^4=37700)