Question

How do you convert `3.5 * 10^4` to standard form?

Answer 1

In standard notation `3.5xx10^4=35000`

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 `axx10^n`, where `1<=a<10` and `n` is an integer and `1<=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 `3.5xx10^4`, we need to move decimal digit to the right by three points. For this, let us write `3.5` as `3.50000` and moving decimal point four points to right means `35000.0`

Hence in standard notation `3.5xx10^4=35000`

Answer 2

`3.5xx10 = 35`
`3.5xx10^2=350`
`3.5xx10^3=3500`
`3.5xx10^4=35000`

,~~~~~~~~~~`color(blue)(" Explaining what is happening ")`~~~~~~~~~~~~~~~~~

Consider the value `3.5` we are saying that we are counting in units (1's) in that we have `3 1/2" of 1's"`

'.....................................................................................
Consider the value `3.5xx10`. Now we are saying we have `3 1/2` of tens. That is; 3 lots of 10 is 30 and `1/2` of 10 is 5 so we have `30+5=35`
'.................................................................................

Note that `10^2` is 100
Consider the value `3.5xx10^2`. Now we are saying we have `3 1/2" of "100's`

`color(brown)("So if we are counting in 100's then the decimal point stays where")` `color(brown)("it is and we move the number of 3.5 to the left until the")` `color(brown)("3 becomes hundreds.")`

Note that we have to insert a place holder of 0 just to the left of the decimal point to make sure the three is viewed as in the hundreds.

`color(brown)(3.5xx10^2) color(blue)(" "vec("slide to the left 2 places")" "350.0`
`" "color(green)(uarr)`
`" "color(green)("Place keeper of 0")`