Question

Express the following numbers in scientific notation:

a. 60200 L
b. 4520 J
c. 0.00600 mg
d. 0.01023 km
e. 80.70 mL

Answer 1

(a) The number in scientific notation is,
`6.0200* 10^4L`

(b) The number in scientific notation is,
`4.520* 10^3J`

(c) The number in scientific notation is,
`6.00* 10^(-3)mg`

(d) The number in scientific notation is,
`1.023* 10^(-2)km`

(e) The number in scientific notation is,
`8.070* 10^1mL`

Explanation :

Scientific notation : It is the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.

For example :

5000 is written as
`5.0* 10^3`

889.9 is written as
`8.899* 10^(-2)`

In this examples, 5000 and 889.9 are written in the standard notation and
`5.0* 10^3` and
`8.899* 10^(-2)` are written in the scientific notation.

`8.89* 10^(-2)` this is written in the scientific notation and the standard notation of this number will be, 0.00889.

If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive.

(a) As we are given the 60200 L in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 60200L=6.0200* 10^4L`

As, the decimal point is shifting to left side, thus the power of 10 is positive.

Hence, the correct answer is,
`6.0200* 10^4L`

(b) As we are given the 4520 J in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 4520J=4.520* 10^3J`

As, the decimal point is shifting to left side, thus the power of 10 is positive.

Hence, the correct answer is,
`4.520* 10^3J`

(c) As we are given the 0.00600 mg in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 0.00600mg=6.00* 10^(-3)mg`

As, the decimal point is shifting to right side, thus the power of 10 is negative.

Hence, the correct answer is,
`6.00* 10^(-3)mg`

(d) As we are given the 0.01023 km in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 0.01023km=1.023* 10^(-2)km`

As, the decimal point is shifting to right side, thus the power of 10 is negative.

Hence, the correct answer is,
`1.023* 10^(-2)km`

(e) As we are given the 80.70 mL in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 80.70mL=8.070* 10^1mL`

As, the decimal point is shifting to left side, thus the power of 10 is positive.

Hence, the correct answer is,
`8.070* 10^1mL`