Question

Express each of the following numbers in exponential notation with correct significant figures:

(a) 704
(b) 0.03344
(c) 547.9
(d) 22086
(e) 1000.00
(f) 0.0000000651
(g) 0.007157

Answer 1

A) 7.04 x 10^2
B) 3.344 x 10^-2
C) 5.479 x 10^2
D) 2.2086 x 10^4
E) 1.00000 x 10^3
F) 6.51 x 10^-8
G) 7.157 x 10^-3

Answer 2

Answer : The numbers in exponential notation with correct significant figures:

(a)
`7.04* 10^2`

(b)
`3.344* 10^(-2)`

(c)
`5.479* 10^2`

(d)
`2.2086* 10^4`

(e)
`1.00000* 10^3`

(f)
`6.51* 10^(-8)`

(g)
`7.157* 10^(-3)`

Explanation :

Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

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.

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 704 in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 704=7.04* 10^2`

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

Hence, the correct answer is,
`7.04* 10^2`

(b) As we are given the 0.03344 in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 0.03344=3.344* 10^(-2)`

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

Hence, the correct answer is,
`3.344* 10^(-2)`

(c) As we are given the 547.9 in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 547.9=5.479* 10^2`

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

Hence, the correct answer is,
`5.479* 10^2`

(d) As we are given the 22086 in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 22086=2.2086* 10^4`

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

Hence, the correct answer is,
`2.2086* 10^4`

(e) As we are given the 1000.00 in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 1000.00=1.00000* 10^3`

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

Hence, the correct answer is,
`1.00000* 10^3`

(f) As we are given the 0.0000000651 in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 0.0000000651=6.51* 10^(-8)`

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

Hence, the correct answer is,
`6.51* 10^(-8)`

(g) As we are given the 0.007157 in standard notation.

Now converting this into scientific notation, we get:

`\Rightarrow 0.007157=7.157* 10^(-3)`

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

Hence, the correct answer is,
`7.157* 10^(-3)`