8th Grade Scientific Notation Worksheet Solutions (PDF)

8th Grade math worksheet solutions: Scientific Notation – Maths PDF

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This scientific notation answers for 8th Grade covers scientific notation (Common Core 8.EE.A.3, 8.EE.A.4), with a free PDF to print.

This answer key gives a full worked solution for each of the 20 problems on the scientific notation worksheet (Common Core 8.EE.A.3 and 8.EE.A.4). Compare each step with your own work, not only the final answer, and note any step where your method differed.

Grade 8 · Common Core State Standards: 8.EE.A.3, 8.EE.A.4

Scientific notation answers: exercises 1 to 10

Exercise 1 – Large number

4,500 = 4.5 × 10³

Move the decimal point 3 places left to get 4.5.

\(4.5 \times 10^{3}\)

Exercise 2 – Small number

Move the decimal point 4 places right to get 3.2. Moving right makes the exponent negative.

\(3.2 \times 10^{-4}\)

Exercise 3 – Standard form 1

Move the decimal point 5 places right: 620,000.

\(620{,}000\)

Exercise 4 – Standard form 2

Move the decimal point 3 places left: 0.0071.

\(0.0071\)

Exercise 5 – Distance to the Sun

Move the decimal point 7 places left: 9.3.

\(9.3 \times 10^{7}\) miles

Exercise 6 – Tiny length

Move the decimal point 8 places right: 2.5.

\(2.5 \times 10^{-8}\) meter

Exercise 7 – Which is larger

Compare exponents first: 5 is greater than 4.

Standard form: 320,000 and 41,000.

\(3.2 \times 10^{5}\) is greater

Exercise 8 – How many times

\(\frac{8 \times 10^{9}}{4 \times 10^{6}} = 2 \times 10^{3}\).

2,000 times as massive

Exercise 9 – Multiply

\(5 \cdot 1.2 = 6\) and \(10^{3} \cdot 10^{2} = 10^{5}\).

\(6 \times 10^{5}\)

Exercise 10 – Multiply and adjust

\(4 \cdot 5 = 20\) and \(10^{5} \cdot 10^{3} = 10^{8}\), so \(20 \times 10^{8}\).

20 is too large, so write \(2 \times 10^{9}\).

\(2 \times 10^{9}\)

Exercises 11 and up

Exercise 11 – Divide

\(8.4 \div 2.1 = 4\) and \(10^{6} \div 10^{2} = 10^{4}\).

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

Exercise 12 – Add

\(4.2 \times 10^{3} = 0.42 \times 10^{4}\).

\(3.5 + 0.42 = 3.92\).

\(3.92 \times 10^{4}\)

Exercise 13 – Subtract

The powers match, so subtract the front numbers: \(5.6 – 2.1 = 3.5\).

\(3.5 \times 10^{-3}\)

Exercise 14 – Order

Compare exponents: B has -2, D has 2, A has 3, C has 4.

From left to right: B, D, A, C.

B, D, A, C: \(3 \times 10^{-2},\ 9 \times 10^{2},\ 2.5 \times 10^{3},\ 1.2 \times 10^{4}\)

Exercise 15 – Population comparison

\(\frac{3.3 \times 10^{8}}{5.8 \times 10^{5}} = 0.569 \times 10^{3} = 5.69 \times 10^{2}\).

about \(5.7 \times 10^{2}\) times, or 570 times

Exercise 16 – Red blood cells

\(\frac{1 \times 10^{-3}}{7 \times 10^{-6}} = 0.1428… \times 10^{3} \approx 1.4 \times 10^{2}\).

about 143 cells

Exercise 17 – Light from the Sun

Distance \(= (1.86 \times 10^{5})(5 \times 10^{2}) = 9.3 \times 10^{7}\).

About 9.3 x 10^7 miles.

\(9.3 \times 10^{7}\) miles

Exercise 18 – Movie downloads

\(\frac{6.4 \times 10^{10}}{2.4 \times 10^{9}} = 2.666… \times 10^{1} \approx 26.7\).

26 movies

Exercise 19 – Earth and Moon

\(\frac{5.97 \times 10^{24}}{7.35 \times 10^{22}} = 0.812… \times 10^{2} \approx 81\).

about 81 times

Exercise 20 – Find the error

The front number must be at least 1 and less than 10; 45 is too large. \(45 = 4.5 \times 10^{1}\), so \(45 \times 10^{3} = 4.5 \times 10^{4}\).

\(4.5 \times 10^{4}\)

Key facts behind this scientific notation answers

Key facts

Form: \(a \times 10^{n}\) with \(1 \le a < 10\).
\(93{,}000{,}000 = 9.3 \times 10^{7}\) and \(0.00032 = 3.2 \times 10^{-4}\).
To multiply, multiply the front numbers and add the exponents; to divide, subtract the exponents.
To add or subtract, first write both numbers with the same power of 10.
To tell how many times as large one value is, divide the two values.

How to use this scientific notation answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the scientific notation answers as a PDF with the button below and keep it with your notes.

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