SME
Grade 5 Math · Number & Base Ten
Place value patterns and powers of 10
Use this for “What is 34 × 10³?” and why the digits move three places.
Chart
Before
ten thousands
0
thousands
0
hundreds
0
tens
3
ones
4
After
ten thousands
3
thousands
4
hundreds
0
tens
0
ones
0
3 ten thousands + 4 thousands.
Each digit moves 3 places to the left: 34 × 1,000 = 34,000.
This is an example. Type your own values to start a new problem.
Number
×
10
=
Product
Power of 10
worked out (not typed)
Formulas
10
3
=
1,000
10exponent = power of 10
34 × 1,000 = 34,000
Number × power of 10 = product
Assumptions
•
The exponent counts how many tens are multiplied: 10³ = 10 × 10 × 10 = 1,000.
•
Multiplying by 10 moves every digit one place to the left. The chart shows the places.
•
Multiplying by 10³ moves the digits three places: write three zeros after the number.
•
Numbers to 999, exponents to 9 (10⁹ = 1,000,000,000): past millions the chart groups the places in periods.
Step-by-step
WE KNOW
Number: 34
Exponent: 3
FIND
power of 10, product
Step 1 · Find power of 10
10
3
=
?
10ᵉˣᵖᵒⁿᵉⁿᵗ = power of 10
Multiply that many tens together. The exponent is also the number of zeros.
10
3
=
10
×
10
×
10
=
1,000
Power of 10 = 1,000
Step 2 · Find product
34 × 1,000 = ?
Number × power of 10 = product
Every digit moves left one place for each ten. Write the zeros after the number.
34 with 3 zeros after it: 34,000
Product = 34,000
Check
Put the numbers back in. Both sides should match.
10
3
=
1,000
✓
34 × 1,000 = 34,000 ✓
Topic check
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