Question

How do you write `0.000 000 000 154` in scientific notation?

Answer 1

`0.000000000154=1.54*10^-10`

Explanation:

`0.000000000154=1.54*10^-10`[Ans]

Answer 2

In depth explanation of how to obtain`" "1.54xx10^(-10)`

Explanation:

We need to be able to convert this number so that it looks line 1.54 but in such a way that its actual value has not changed.

Consider the example of 32. This would will to look like 3.2

If we divide it by 10 we then have`" "32/10 =3.2`

But this has changed its value so we need a slightly different approach.

`color(blue)("Point 1")`

`color(brown)("If we multiply a number by 1 we do not change its value")`

`color(blue)("Point 2")`

`color(brown)("The value of 1 can be presented in many ways")`
For this type of calculation we need it to be of format `n/n` where `n` is any number other than zero

`color(blue)("Method")`

The way to use this method for our example is to do this:

`32xx10/10`

`32/10 xx10`

Divide the denominator of 10 into 32 giving

`3.2xx10`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using this method to solve your question")`

Given:`" "0.000000000154`

To achieve 1.54 we need to keep the decimal point where it is and slide the number towards the left for 10 digits.

To mathematically achieve this we have `0.000000000154xx10^10`

But `10^10` is not the value 1

So we need to multiply by `10^10/10^10` giving

`0.000000000154xx10^10xx1/10^10`

Apply the process of `0.000000000154xx10^10` leaving

`1.54xx 1/10^10`

But another way of writing `1/10^10" is "10^(-10)` which means `-: 10^10`

This gives: `1.54xx10^(-10)`