Question

How do you write 0.000000728+ in the scientific notation?

Answer 1

Hint: Here in this question the number is given in the numeral form and now we have to convert the number into a scientific notation or form. First, we express the number by its place value. The place values other than units are the multiple of 10 we can write in terms of exponent.

Complete step-by-step answer:
This question comes under the topic number system. The number can be expressed in many different ways but it has the same value. The number can be written in the words form or in the numeral form or in the scientific form etc.
Here in this question, they have mentioned 0.000000728. This is in the numeral form. The number is a decimal number.
Let we draw the place value table for the given number \[0.000000728\]

one1	Decimal point	Tenths \[\dfrac{1}{{10}}\]	Hundredths \[\dfrac{1}{{100}}\]	Thousandths \[\dfrac{1}{{1000}}\]	Ten Thousandths \[\dfrac{1}{{10000}}\]	HundredThousandths \[\dfrac{1}{{100000}}\]	Millionths \[\dfrac{1}{{1000000}}\]	Ten Millionths \[\dfrac{1}{{10000000}}\]	Hundred Millionths \[\dfrac{1}{{100000000}}\]	Billionths \[\dfrac{1}{{1000000000}}\]
0	.	0	0	0	0	0	0	7	2	8

The number \[0.000000728\] written using the place value is
 \[
   \Rightarrow 0.000000728 = 0 \times 1 + 0 \times \dfrac{1}{{10}} + 0 \times \dfrac{1}{{100}} + 0 \times \dfrac{1}{{1000}} + 0 \times \dfrac{1}{{10000}} + 0 \times \dfrac{1}{{100000}} + \\
  0 \times \dfrac{1}{{1000000}} + 7 \times \dfrac{1}{{10000000}} + 2 \times \dfrac{1}{{100000000}} + 8 \times \dfrac{1}{{1000000000}} \\
 \]
The \[\dfrac{1}{{10}}\] , \[\dfrac{1}{{100}}\] , \[\dfrac{1}{{1000}}\] , \[\dfrac{1}{{10000}}\] , \[\dfrac{1}{{100000}}\] , \[\dfrac{1}{{1000000}}\] , \[\dfrac{1}{{10000000}}\] , \[\dfrac{1}{{100000000}}\] , \[\dfrac{1}{{1000000000}}\] are the multiple of 10 and these numbers can be written in the form of exponent we have
 \[
   \Rightarrow 0.000000728 = 0 \times 1 + 0 \times {10^{ - 1}} + 0 \times {10^{ - 2}} + 0 \times {10^{ - 3}} + 0 \times {10^{ - 4}} + 0 \times {10^{ - 5}} + \\
  0 \times {10^{ - 6}} + 7 \times {10^{ - 7}} + 2 \times {10^{ - 8}} + 8 \times {10^{ - 9}} \\
 \]
As we know that any number divide by zero the product will be zero so we have
 \[ \Rightarrow 7 \times {10^{ - 7}} + 2 \times {10^{ - 8}} + 8 \times {10^{ - 9}}\]
Therefore it can be written as
 \[ \Rightarrow 0.000000728 = 7 \times {10^{ - 7}} + 2 \times {10^{ - 8}} + 8 \times {10^{ - 9}}\]

Note: There are many different ways to express or to write the number or to express the number. The exponent form is defined as the number of times the number is multiplied by the number itself. The place value table of numbers should be known to place the number in particular that position.