Question

How do you multiply \[(5.67811 \times {10^5}) \times (3.15576 \times {10^7})\]

Answer 1

Hint: Here in this question, we have to find the product of 2 decimal and exponential numbers. So let us multiply 2 decimal and exponential numbers which are different from one another and then we use the arithmetic operation that is multiplication and then we simplify.

Complete step-by-step solution:
 The number which is present in the question is in the form of decimal. In the decimal number we have a decimal point. The exponential number is defined as a number of times the number is multiplied by itself. First we convert the decimal number by multiplying with the exponential number.

Now let us consider the two decimal and exponential numbers and they are\[(5.67811 \times {10^5})\], and \[(3.15576 \times {10^7})\]
First we simplify the first term
\[(5.67811 \times {10^5})\]
This can be written as
\[ \Rightarrow 5.67811 \times 100000\]
\[ \Rightarrow 567811\] -------(1)
First we simplify the second term
\[(3.15576 \times {10^7})\]
This can be written as
\[ \Rightarrow 3.15576 \times 10000000\]
\[ \Rightarrow 31557600\] -------(2)
On multiplying inequality (1) and (2) we get
\[ \Rightarrow 567811 \times 31557600\]
\[ \Rightarrow 17918752413600\]
this can be written in the form of exponent as
\[ \Rightarrow 1.79187524 \times {10^{13}}\]
We can also multiply the given question by the another method
Consider the given question \[(5.67811 \times {10^5}) \times (3.15576 \times {10^7})\]
Let we multiply the decimal numbers so we get
\[ \Rightarrow (5.67811 \times 3.15576) \times {10^5} \times {10^7}\]
\[ \Rightarrow 17.9187524136 \times {10^5} \times {10^7}\]
As we know the property \[{a^m}.{a^n} = {a^{m + n}}\], so by applying the property we get
\[ \Rightarrow 17.9187524136 \times {10^{5 + 7}}\]
\[ \Rightarrow 17.9187524136 \times {10^{12}}\]
This can be written as
\[ \Rightarrow 1.79187524 \times {10^{13}}\]

Hence the correct answer is \[ 1.79187524 \times {10^{13}}\]

Note: Multiplication is one of the arithmetic operations. While multiplying the decimal numbers the decimal point is placed on some rule. If we multiply the two numbers which are decimals, we count the numbers after the decimal point from both the numbers and then after multiplication we place the decimal point.