Grade 8 Subtracting Numbers in Scientific Notation
Subtracting in scientific notation for grade 8 — give both numbers the same power of ten, then subtract the coefficients. Sixteen problems with key.
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Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
Subtract. Give both numbers the same power of 10 first, then write the answer in scientific notation.
- 1.(3.3 x 10^3) - (2.6 x 10^3) =
- 2.(8.3 x 10^6) - (3.0 x 10^5) =
- 3.(7.4 x 10^6) - (3.9 x 10^5) =
- 4.(7.2 x 10^9) - (5.6 x 10^8) =
- 5.(7.2 x 10^3) - (3.4 x 10^2) =
- 6.(6.5 x 10^4) - (7.0 x 10^3) =
- 7.(1.8 x 10^3) - (3.6 x 10^2) =
- 8.(7.2 x 10^9) - (1.4 x 10^9) =
- 9.(7.9 x 10^9) - (8.7 x 10^8) =
- 10.(1.4 x 10^5) - (3.9 x 10^4) =
- 11.(6.6 x 10^4) - (8.8 x 10^3) =
- 12.(8.7 x 10^4) - (1.9 x 10^4) =
- 13.(8.1 x 10^7) - (6.4 x 10^6) =
- 14.(9.5 x 10^2) - (8.0 x 10^2) =
- 15.(3.8 x 10^7) - (2.7 x 10^6) =
- 16.(5.0 x 10^9) - (1.2 x 10^8) =
What this worksheet covers
Sixteen expressions and equations problems fill this mixed review page; problem 6 asks "(6.5 x 10^4) - (7.0 x 10^3)", and the sheet stays at that level throughout. The expressions carry exponents, so the order of operations decides the answer and some operands are decimals rather than whole numbers. Further down, problem 11 asks "(6.6 x 10^4) - (8.8 x 10^3)". Common Core 8.EE.4 is the slot this page fills.
Skills practised
The grade 8 expressions and equations sequence covers multi-step linear equations, operations in scientific notation and integer exponent rules; this page sits inside it. What a student is asked to do here is grade 8 Subtracting Numbers in Scientific Notation. Concretely, the sheet tests whether a student can keep the decimal points aligned and apply the order of operations to powers.
About the mixed review format
The 16 problems are deliberately assorted — problem 6, "(6.5 x 10^4) - (7.0 x 10^3)" is followed by something of another shape — so the student has to read each one rather than run the last method again. Evaluating, simplifying and solving on one page keep the student reading the instruction rather than assuming one.
Set A, Set B and Set C
Set A is the original MathSheetLab worksheet; Sets B and C keep its structure and redraw the numbers, with each answer recomputed rather than copied. Where Set A's problem 9 is "(7.9 x 10^9) - (8.7 x 10^8)", Set B's is "(6.1 x 10^4) - (6.7 x 10^3)".
How to use this worksheet
Work it without a calculator. Every one of the sixteen expressions and equations problems is designed to be done by hand, and reaching for a calculator at grade 8 skips exactly the reasoning being built. Use the key as a check, not as a grade; none of the sixteen problems needs a score attached to be useful.
One mistake to watch for
The distributive property only reaches the first term: 3(x + 4) becomes 3x + 4. Watch problem 11 of this mixed review — "(6.6 x 10^4) - (8.8 x 10^3)" — for this one.
The multiplier is being attached to the nearest term only.
Draw arrows from the multiplier to each term inside the bracket before writing anything.
Other grade 8 expressions and equations formats
The same skill in the other formats available at this grade.
- Drill — Grade 8 Adding Numbers in Scientific Notation, 16 problems
- Timed Drill — 8.EE.3 — Scientific Notation Division Practice, 22 problems
- Missing Number — Grade 8 Expressions & Equations Missing Number, 24 problems
- Word Problems — Grade 8 Word Problems: Writing and Solving Linear Equations, 14 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- Grade 7 Expressions & Equations Mixed Review — grade 7, 30 problems
Mixed Review sheets in other grade 8 topics
Six PDFs, no sign-up: three versions of this grade 8 expressions and equations mixed review and three answer keys, each sixteen problems long.