SME
Grade 5 Math · Problem type
Place value patterns with decimals
Use this for “Write a multiplication equation relating 0.8 and 0.08,” or 3.45 × 10².
Chart
Before
hundreds
0
tens
0
ones
3
.
tenths
4
hundredths
5
thousandths
0
After
hundreds
3
tens
4
ones
5
.
tenths
0
hundredths
0
thousandths
0
3 hundreds + 4 tens + 5 ones.
Each digit moves 2 places to the left: 3.45 × 100 = 345.
This is an example. Type your own values to start a new problem.
Decimal
×
10
=
Product
Power of 10
calculated
Formulas
10
2
=
100
10exponent = power of 10
3.45 × 100 = 345
Decimal × power of 10 = product
Assumptions
•
Multiplying by 10 moves every digit one place left. The point stays where it is.
•
Times 10² moves every digit 2 places left. Dividing moves every digit right.
•
Decimals to thousandths, exponents to 3.
Step-by-step
WE KNOW
Decimal: 3.45
Exponent: 2
FIND
power of 10, product
Step 1 · Find power of 10
10
2
=
?
10ᵉˣᵖᵒⁿᵉⁿᵗ = power of 10
Multiply that many tens together. The exponent is also the number of zeros.
10
2
=
10
×
10
=
100
Power of 10 = 100
Step 2 · Find product
3.45 × 100 = ?
Decimal × power of 10 = product
Every digit moves one place left for each ten. Fill any empty places with zeros.
Every digit moves 2 places left: 3.45 → 345
Product = 345
Check
Put the numbers back in. Both sides should match.
10
2
=
100
✓
3.45 × 100 = 345 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Place value patterns and powers of 10
Main lesson
Decimals to thousandths
Use this for “What is the value of the 3 in 4.263?”
Compare decimals
Use this for “Which is greater, 0.307 or 0.37?” with >, < or =.
Round decimals
Use this for “Round 4.268 to the nearest hundredth.”
Convert metric units
Use this for “A trail is 12 kilometers long. How many meters is that?”