5.NBT.2 — Multiplying by Powers of Ten
Practice multiplying whole numbers and decimals by powers of ten using exponent notation, and identify patterns in zeros and decimal point movement to build place value fluency.
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Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
Solve each problem by applying patterns in zeros and decimal placement when multiplying by powers of 10.
- 1.3 × 10^1 =
- 2.7 × 10^2 =
- 3.5 × 10^3 =
- 4.4 × 10^4 =
- 5.12 × 10^2 =
- 6.25 × 10^3 =
- 7.0.6 × 10^1 =
- 8.0.6 × 10^2 =
- 9.0.6 × 10^3 =
- 10.3.4 × 10^2 =
- 11.7.52 × 10^2 =
- 12.0.04 × 10^3 =
- 13.1.8 × 10^4 =
- 14.0.009 × 10^3 =
- 15.45 × 10^4 =
- 16.2.75 × 10^3 =
- 17.0.37 × 10^4 =
- 18.100 × 10^3 =
- 19.6.1 × 10^4 =
- 20.0.008 × 10^4 =
- 21.53.2 × 10^2 =
- 22.0.001 × 10^4 =
What this worksheet covers
Set A of this grade 5 drill sheet holds 22 place value problems on one printable page, with the answer key on the page behind it. What makes this set particular: the expressions carry exponents, so the order of operations decides the answer and operands run to three decimal places, so the decimal points have to be lined up rather than the right-hand digits. Two problems from the middle of the page — "0.6 × 10^2" and "45 × 10^4" — show the range. Common Core 5.NBT.2 is the slot this page fills.
Skills practised
At grade 5, place value is about decimal place value to thousandths, powers of ten, and rounding decimals, and this sheet takes one slice of that. What a student is asked to do here is multiplying by Powers of Ten. Concretely, the sheet tests whether a student can keep the decimal points aligned and apply the order of operations to powers.
About the drill format
This drill runs 22 problems in a steady layout, so the eye never has to hunt for the next one; problem 8, "0.6 × 10^2" shows the level it holds. Repeating one question shape — which digit, what value, round to which place — is how the vocabulary of place value becomes automatic.
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 12 is "0.04 × 10^3", Set B's is "0.48 × 10^2".
How to use this worksheet
By grade 5 a student should take all 22 place value problems in one sitting. If the page takes more than about fifteen minutes, the underlying facts are probably not automatic yet, and that is worth fixing before more place value practice piles on. If more than a third of the 22 problems come back wrong, stop and step back a grade in place value rather than assigning Set B.
One mistake to watch for
The value of a digit is given as the digit itself: the 4 in 4,371 is "4". On this grade 5 drill, problem 15 ("45 × 10^4") is the kind of item where it shows.
The digit is being read as a symbol rather than as a count of a unit.
Ask "four what?" every time and have the student answer with the unit — four thousands — before writing the number.
Other grade 5 place value formats
The same skill in the other formats available at this grade.
- Timed Drill — Grade 5 Place Value Timed Drill, 72 problems
- Missing Number — Grade 5 Place Value Missing Number, 24 problems
- Mixed Review — Grade 5 Place Value Mixed Review, 30 problems
- Word Problems — Grade 5 Place Value Word Problems, 10 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 4 Place Value Drill — grade 4, 30 problems
Drill sheets in other grade 5 topics
Free to download, print and photocopy for a whole class: three drill sheets of grade 5 place value, 22 problems each, keys included.