This grade 8 scientific worksheet answer key solves all 25 problems of the scientific notation worksheet step by step.
This answer key gives every step for the 25 problems on the scientific notation worksheet (8.EE.A.3 and 8.EE.A.4). Use it to check the exponent, the coefficient and the units in each answer, and to see how a coefficient of 10 or more is fixed.
Grade 8 Scientific Worksheet Answer Key: problems 1–5
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 \(-4\).
\(6.2\times 10^{-4}\)
Grade 8 Scientific Worksheet Answer Key: problems 6–10
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.
\(4.2\times 10^{5}<3.9\times 10^{6}\)
Grade 8 Scientific Worksheet Answer Key: problems 11–15
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.
\(2\times 10^{4}\)
Grade 8 Scientific Worksheet Answer Key: problems 16–20
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
Grade 8 Scientific Worksheet Answer Key: problems 21–25
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
How to use this grade 8 scientific worksheet answer key
Read this grade 8 scientific worksheet answer key after trying each problem yourself, and redo any problem you missed.
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Grade 8 Scientific Notation worksheet answer key
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