Scientific Notation: Grade 8 Math Worksheet Answer Key – PDF Download

Problem 1: Thousands

Move the decimal point 3 places left to get 5. So 5,000 is 5 times \(10^{3}\).

\(5\times 10^{3}\)

Problem 2: Ten thousands

Move the point 4 places left to get 7.2. Check: 7.2 times 10,000 is 72,000.

\(7.2\times 10^{4}\)

Problem 3: A very large number

Place the point after the 3: 3.8. Count the places from the end of the number: 8.

\(3.8\times 10^{8}\)

Problem 4: A small number

Move the point 4 places right to get 4. The number is less than 1, so the exponent is negative.

\(4\times 10^{-4}\)

Problem 5: Small number with two digits

The point moves 4 places right to sit after the 6, giving 6.2. The number is less than 1, so the exponent is \(-4\).

\(6.2\times 10^{-4}\)

Problem 6: Standard form

The exponent 5 moves the point 5 places right: 3.5 becomes 350000 after filling with zeros.

350,000

Problem 7: Negative exponent to decimal

The exponent \(-3\) moves the point 3 places left: 0.0081.

0.0081

Problem 8: Millions

Move the point 6 places right: 2.04 becomes 2,040,000.

2,040,000

Problem 9: Tiny decimal

The first nonzero digit, 7, is in the seventh decimal place. Move the point 7 places right to get 7.05.

\(7.05\times 10^{-7}\)

Problem 10: Compare two numbers

The exponents are 5 and 6. The larger exponent gives the larger number. Check: 420,000 is less than 3,900,000.

\(4.2\times 10^{5}<3.9\times 10^{6}\)

Problem 11: Order small numbers

Compare exponents: \(-4<-3<-2\). The values are 0.00099, 0.0061 and 0.025.

\(9.9\times 10^{-4},\ 6.1\times 10^{-3},\ 2.5\times 10^{-2}\)

Problem 12: How many times as much?

Divide: \(\frac{6\times 10^{8}}{3\times 10^{5}}=\frac{6}{3}\times 10^{8-5}=2\times 10^{3}\).

2,000 times as large (\(2\times 10^{3}\))

Problem 13: Small numbers: how many times

\(\frac{9\times 10^{-2}}{3\times 10^{-5}}=3\times 10^{-2-(-5)}=3\times 10^{3}\). Check: 0.09 divided by 0.00003 is 3,000.

3,000 times as large

Problem 14: Multiply

Multiply the coefficients: \(3\cdot2=6\). Add the exponents: \(4+3=7\).

\(6\times 10^{7}\)

Problem 15: Multiply and fix

\(4\cdot5=20\) and \(5+(-2)=3\), so the product is \(20\times 10^{3}\). The coefficient must be less than 10: \(20\times 10^{3}=2\times 10^{4}\). Check: 400,000 times 0.05 is 20,000.

\(2\times 10^{4}\)

Problem 16: Divide

\(8.4: 2.1=4\) and \(7-3=4\).

\(4\times 10^{4}\)

Problem 17: Add

Rewrite \(4.8\times 10^{5}\) as \(0.48\times 10^{6}\). Then \(0.48+3.7=4.18\).

\(4.18\times 10^{6}\)

Problem 18: Calculator notation

3.2E5 means \(3.2\times 10^{5}\): move the point 5 places right to get 320,000. 7.5E-3 means \(7.5\times 10^{-3}\): move the point 3 places left to get 0.0075.

320,000 = \(3.2\times 10^{5}\); 0.0075 = \(7.5\times 10^{-3}\)

Problem 19: Miles to feet

Multiply: \(2450\cdot5280=12936000\) ft, or 12,936,000 ft. Move the point 7 places left: 1.2936.

\(1.2936\times 10^{7}\) feet

Problem 20: Population comparison

Divide: \(\frac{3\times 10^{8}}{2.5\times 10^{5}}=1.2\times 10^{3}\) because \(3: 2.5=1.2\) and \(8-5=3\).

1,200 times as large

Problem 21: Sunlight to Earth

Time = distance \(: \) speed: \(\frac{9.3\times 10^{7}}{1.86\times 10^{5}}=5\times 10^{2}\) seconds, since \(9.3: 1.86=5\).

500 seconds is 8 minutes and 20 seconds.

\(5\times 10^{2}\) seconds, or 8 min 20 s

Problem 22: Stack of paper

Multiply: \((4\times 10^{-3})(5\times 10^{3})=20\times 10^{0}=2\times 10^{1}\). Check: 5,000 sheets at 0.004 inch each is 20 inches.

\(2\times 10^{1}\) inches

Problem 23: Photos on a tablet

Divide: \(\frac{6.4\times 10^{10}}{4\times 10^{6}}=1.6\times 10^{4}\), because \(6.4: 4=1.6\) and \(10-6=4\).

\(1.6\times 10^{4}\) photos (16,000)

Problem 24: Snail on a trail

Distance = rate \(\times \) time: \((2\times 10^{-3})(4\times 10^{2})=8\times 10^{-1}\).

\(8\times 10^{-1}\) mile, which is 0.8 mile

Problem 25: Earth and Moon

\(\frac{1.3\times 10^{25}}{1.6\times 10^{23}}=0.8125\times 10^{2}=81.25\). Rounded, that is 81.

About 81 times as heavy

See every chapter on the Grade 8 math page.