Grade 8 Multiplying Numbers in Scientific Notation
Multiplying in scientific notation for grade 8: multiply the coefficients, add the exponents, then rewrite the result. Sixteen problems with answers.
Multiply the coefficients, add the exponents, then rewrite the answer in scientific notation.
- 1.(2.0 x 10^8) × (6.9 x 10^5) =
- 2.(8.8 x 10^4) × (4.5 x 10^2) =
- 3.(1.8 x 10^4) × (2.4 x 10^2) =
- 4.(4.0 x 10^4) × (8.8 x 10^6) =
- 5.(9.8 x 10^7) × (3.0 x 10^2) =
- 6.(6.5 x 10^4) × (2.4 x 10^2) =
- 7.(4.4 x 10^4) × (1.9 x 10^2) =
- 8.(9.9 x 10^3) × (2.0 x 10^2) =
- 9.(3.2 x 10^2) × (3.1 x 10^3) =
- 10.(3.9 x 10^6) × (7.0 x 10^4) =
- 11.(4.1 x 10^4) × (6.0 x 10^6) =
- 12.(3.0 x 10^3) × (5.1 x 10^5) =
- 13.(2.4 x 10^6) × (4.5 x 10^4) =
- 14.(2.1 x 10^6) × (3.6 x 10^4) =
- 15.(3.5 x 10^5) × (1.8 x 10^5) =
- 16.(4.5 x 10^8) × (3.2 x 10^2) =
What this worksheet covers
There are sixteen multiplication problems here, on one printable page, with the worked answer key on the second. What makes this set particular: the expressions carry exponents, including the zero and negative cases that break the "repeated multiplication" reading; the operands are decimals rather than whole numbers. The whole sheet sits inside Common Core 8.EE.4, in the grade 8 Expressions & Equations strand.
Skills practiced
At this point in the sequence, work in multiplication is really about signed rational numbers, integer exponents, scientific notation. Working the page asks a student to keep decimal points aligned rather than right-aligning digits out of habit; apply exponent properties instead of expanding every term. The sheet is doing its job when the student can work it without hesitating.
How to use this worksheet
Work it without a calculator. Every problem on this sheet is designed to be done by hand, and reaching for a calculator at grade 8 skips exactly the reasoning being built. If more than a third of the page comes back wrong, stop and go back a step rather than assigning another sheet like it.
One mistake to watch for
Exponents are multiplied by the base: 3^4 is answered as 12.
The notation is being read as a product of the two visible numbers rather than as repeated multiplication.
Write it out longhand as 3 × 3 × 3 × 3 for a week. Then introduce 3^4 × 3^2 and let the student count the factors rather than apply a rule.
Related worksheets
Also aligned to 8.EE.4
Other sheets covering 8.EE.4. Same target, different problems, so a student who has seen this page has not seen these.
- Grade 8 Adding Numbers in Scientific Notation — grade 8, 16 problems
- Grade 8 Subtracting Numbers in Scientific Notation — grade 8, 16 problems
A step either side
Where this skill comes from and where it goes next. Drop back a grade when the page stalls; move up when it does not.
- Grade 7 Multiplying Rational Numbers — grade 7, 20 problems
One PDF, sixteen problems, and a full key: this is grade 8 multiplication practice for signed rational numbers, integer exponents, scientific notation, free for home and classroom use.