Q. 1384.0( 2 Votes )

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

Answer :

Given litres of water that flow through the river in a day = 230 billion = 230, 000, 000, 000 = 230 × 10^{9} litres

__We know that 1 week = 7 days and 1 year = 365 days.__

Litres of water that flow through that river in a week = 230 × 10^{9} × 7 = 1610 × 10^{9}

In standard notation, 1610 × 10^{9} = 1.61 × 10^{3} × 10^{9}

__We know that by properties of exponents, a ^{m} × a^{n} = a^{m + n}.__

⇒ 1.61 × 10^{3} × 10^{9} = 1.61 × 10^{3 + 9} = 1.61 × 10^{12}

∴ Litres of water that flow through that river in a week = 1.61 × 10^{12} litres

Litres of water that flow through that river in a year = 230 × 10^{9} × 365 = 83950 × 10^{9}

In standard notation, 83950 × 10^{9} = 8.395 × 10^{4} × 10^{9}

__We know that by properties of exponents, a ^{m} × a^{n} = a^{m + n}.__

⇒ 8.395 × 10^{4} × 10^{9} = 8.395 × 10^{4 + 9} = 8.395 × 10^{1}

∴ Litres of water that flow through that river in a year = 8.395 × 10^{13} litres

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