Question

About 230 billion liters of water flow through a river each day. How many liters of water flows through that river in a week? How many liters of water flows through the river in a year? Write your answer in standard notation.

Answer 1

Hint:
First, we have to convert 230 billion into liters, Then for the week we have to multiply 230 billion with 7. Now, for the year we multiply with 360.

Complete step by step solution:
Here, we have given that about 230 billion liters of water flow through a river each day.
So, we have to find how many liters of water flow through that river in a week and in a year?
230 billion $ = 230 \times {10^9}$ liters.
 $ \Rightarrow \because $ we know that 1 week = 7 days and 1 year = 365 days
Now,
 $\therefore $ Liters of water that flow through that river in a week = $230 \times {10^9} \times 7$
  $\therefore = 1610 \times {10^9}$
In the standard notation $ = 1610 \times {10^9} = 1.16 \times {10^3} \times {10^9}$
 $\because $ We know the property of exponent, ${a^m} \times {a^n} = {a^{m + n}}$
 $ \Rightarrow 1.16 \times {10^3} \times {10^9} = 1.16 \times {10^{3 + 9}} = 1.16 \times {10^{12}}$
 $\because $ Liters of water that flow through that river in a week $ = 1.16 \times {10^{12}}$
Liters of water that flow through that river in a year $ = 230 \times {10^9} \times 365 = 83950 \times {10^9}$
In standard notation $ = 83950 \times {10^9} = 8.395 \times {10^4} \times {10^9}$
 $ \because $ We know the property of exponent, ${a^m} \times {a^n} = {a^{m + n}}$
 $\because $ Liters of water flow through that river in a year
 $ = 395 \times {10^4} \times {10^9}$
 $ = 8.395 \times {10^{4 + 9}}$
 $ = 8.395 \times {10^{13}}$

$\therefore $ Liters of water flow through that river in a year $ = 8.395 \times {10^{13}}$

Note:
Standard Notation: Standard notation is the special way of writing numbers:
For Example: $900 = 9 \times {10^2}$
 $\because 900 = 9 \times 100$
And
$100 = {10^2}$
So $900 = 9 \times {10^2}$