Question

How do you write \[53657\] nanoseconds in scientific notation?

Answer 1

Hint: To solve this question we need to know the expansion of milliseconds, microseconds, and Nanoseconds. Also, we need to know the relation between the power terms to decimal terms. We need to know how to convert whole numbers into decimal numbers. We need to know the arithmetic functions like addition/ subtraction/ multiplication/ division with the involvement of exponents.

Complete step-by-step answer:
To solve the given question we need to convert \[53657\] nanoseconds into scientific notation format.
Before that, we need to know the expansion of milliseconds, microseconds, and nanoseconds.
Let’s see
Milliseconds can also be written as \[{10^{ - 3}}s\] .
Microseconds can also be written as \[{10^{ - 6}}s\] .
Nanoseconds can also be written as \[{10^{ - 9}}s\] .
So, the given term can be modified as,
 \[53657\] Nanoseconds \[ = 53657 \times {10^{ - 9}} \to \left( 1 \right)\]
Next, we would convert the term \[53657\] into a decimal point term.
We know that for each one movement of a decimal point there is one modification that will happen in the exponent term.
If the decimal point is moved from the left side to the right side the exponent value will increase positively.
 \[100.0 = 1.00 \times {10^2}\]
If the decimal point is moved from the right side to the left side the exponent value will increase negatively.
 \[1.00 = 100.0 \times {10^{ - 2}}\]
So, the term \[53657\] can be written as,
 \[53657 = 53657.0\]
So, we get
 \[53657.0 = 5.3657 \times {10^4} \to \left( 2 \right)\]
Here we move the decimal point to \[4\] the digit left side. So, we put \[4\] in the place of \[10\] to the power.
Let’s substitute the equation \[\left( 2 \right)\] substitute the equation \[\left( 1 \right)\] , we get
 \[\left( 1 \right) \to 53657nano\sec onds = 53657 \times {10^{ - 9}}\]
 \[\left( 2 \right) \to 53657.0 = 5.3657 \times {10^4}\]
 \[53657\] Nanoseconds \[ = 5.3657 \times {10^4} \times {10^{ - 9}}\]
We know that,
 \[{x^a} \cdot {x^b} = {x^{a + b}}\]
By using the above-mentioned formula we get,
 \[{10^4} \times {10^{ - 9}} = {10^{4 - 9}} = {10^{ - 5}}\]
So, we get
 \[ \Rightarrow 5.3657 \times {10^4} \times {10^{ - 9}} = 5.3657 \times {10^{ - 5}}\]
So, the final answer is,
 \[53657\] Nanoseconds \[ = 5.3657 \times {10^{ - 5}}\]
So, the correct answer is “\[ = 5.3657 \times {10^{ - 5}}\] ”.

Note: Note that milliseconds, microseconds, and nanoseconds can be written as \[{10^{ - 3}},{10^{ - 6}}\] and \[{10^{ - 9}}\] respectively. Also, note that when we move the decimal point from the left side to the right side the exponent value increases positively. When we move the decimal point from the right side to the left side the exponent value increases negatively.