Question

It says write each number in standard notation 2.350 × 10^-4:6.5 × 10^-3:7.07 × 10^-5:

Answer 1

To write the expressions in standard notation we need to follow this rule:

• When we multiply by a power of 10 we will move the decimal point to the right if the exponent of the 10 is a positive number and to the left, if the exponent of the 10 is a negative number.

We start with the first expression:

`2.350*10^(-4)`

Since the exponent of 10 is negative, we will move the decimal point to the left. And we move it the number of times that the exponent indicates: 4

The following image shows the result after moving the decimal place:

As you can see we have moved the decimal point 4 places to the left and it is important to fill the spaces with 0.

Thus:

`2.350*10^(-4)=0.0002350`

Now we solve the second expression:

`6.5*10^(-3)`

Again the exponent of 10 is negative so we will move the decimal point to the left the number of times the exponent indicates: 3 times.

The following image shows the result after moving the decimal point:

Thus:

`6.5*10^(-3)=0.0065`

Finally, we solve the third expression:

`7.07*10^(-5)`

We will move the decimal point 5 times to the left:

And again we have filled the blank spaces with 0.

The result is:

`7.07*10^(-5)=0.0000707`

Answer:

`\begin{gathered} 2.350*10^(-4)=0.0002350 \\ 6.5*10^(-3)=0.0065 \\ 7.07*10^(-5)=0.0000707 \end{gathered}`