These problems practice Common Core standards 8.EE.A.3 and 8.EE.A.4. Write very large and very small numbers in scientific notation, compare them using how many times as much, multiply, divide, add, and read calculator notation such as 3.2E5.
The last six problems are word problems with real-world quantities such as light travel, memory and weight. Work from easiest to hardest.
Problem 1: Thousands
Write 5,000 in scientific notation.
Problem 2: Ten thousands
Write 72,000 in scientific notation.
Problem 3: A very large number
Write 380,000,000 in scientific notation.
Problem 4: A small number
Write 0.0004 in scientific notation.
Problem 5: Small number with two digits
Write 0.00062 in scientific notation.
Problem 6: Standard form
Write \(3.5\times 10^{5}\) in standard form.
Problem 7: Negative exponent to decimal
Write \(8.1\times 10^{-3}\) in standard form.
Problem 8: Millions
Write \(2.04\times 10^{6}\) in standard form.
Problem 9: Tiny decimal
Write 0.000000705 in scientific notation.
Problem 10: Compare two numbers
Compare \(4.2\times 10^{5}\) and \(3.9\times 10^{6}\). Write \(<\), \(>\) or \(=\) and explain.
Problem 11: Order small numbers
Order from least to greatest: \(6.1\times 10^{-3}\), \(2.5\times 10^{-2}\), \(9.9\times 10^{-4}\).
Problem 12: How many times as much?
How many times as large is \(6\times 10^{8}\) as \(3\times 10^{5}\)?
Problem 13: Small numbers: how many times
How many times as large is \(9\times 10^{-2}\) as \(3\times 10^{-5}\)?
Problem 14: Multiply
Find \((3\times 10^{4})(2\times 10^{3})\). Write the answer in scientific notation.
Problem 15: Multiply and fix
Find \((4\times 10^{5})(5\times 10^{-2})\). Write the answer in scientific notation.
Problem 16: Divide
Find \(\frac{8.4\times 10^{7}}{2.1\times 10^{3}}\). Write the answer in scientific notation.
Problem 17: Add
Find \(4.8\times 10^{5}+3.7\times 10^{6}\). Write the answer in scientific notation.
Problem 18: Calculator notation
A calculator displays 3.2E5. Another displays 7.5E-3. Write each value in standard form and in scientific notation.
Problem 19: Miles to feet
The distance from Chicago to Los Angeles is about 2,450 miles. One mile is 5,280 feet. Write the distance in feet using scientific notation.
Problem 20: Population comparison
A city has about \(2.5\times 10^{5}\) people. The country has about \(3\times 10^{8}\) people. About how many times as large is the population of the country?
Problem 21: Sunlight to Earth
Earth is \(9.3\times 10^{7}\) miles from the Sun. Light travels \(1.86\times 10^{5}\) miles per second. How many seconds does sunlight take to reach Earth? Give the answer in minutes and seconds too.
Problem 22: Stack of paper
One sheet of paper is \(4\times 10^{-3}\) inch thick. Jamal stacks \(5\times 10^{3}\) sheets. How tall is the stack? Write the answer in scientific notation.
Problem 23: Photos on a tablet
A tablet stores \(6.4\times 10^{10}\) bytes. Each photo uses \(4\times 10^{6}\) bytes. How many photos fit? Write the answer in scientific notation.
Problem 24: Snail on a trail
A garden snail crawls \(2\times 10^{-3}\) mile per hour. How far does it go in \(4\times 10^{2}\) hours? Write the answer in scientific notation and in standard form.
Problem 25: Earth and Moon
Earth weighs about \(1.3\times 10^{25}\) pounds. The Moon weighs about \(1.6\times 10^{23}\) pounds. About how many times as heavy is Earth as the Moon? Round to the nearest whole number.
See every chapter on the Grade 8 math page.