SME
Grade 5 Math · Problem type
Estimate differences of decimals
Use this for “About how much is 12.65 − 8.3?” by rounding each to the nearest whole number.
Diagram
13 − 8 = 5
This is an example. Type your own values to start a new problem.
Start
−
Take away
≈
Start rounded
−
Second number rounded
=
Estimated difference
Formulas
12.65 rounded to the ones: 13
The start rounded to the nearest whole = start rounded
8.3 rounded to the ones: 8
The take-away rounded to the nearest whole = second number rounded
13 − 8 = 5
Start rounded − second number rounded = estimated difference
Assumptions
•
Round each decimal to the nearest whole number: 5 tenths or more rounds up.
•
Subtract the rounded numbers. The estimate is close to the exact difference.
•
Use the estimate to check that an exact answer makes sense. Numbers from 1 to 999.99.
Step-by-step
WE KNOW
Start: 12.65
Take away: 8.3
FIND
start rounded, second number rounded, estimated difference
Step 1 · Find start rounded
12.65 rounded to the ones: ?
The start rounded to the nearest whole = start rounded
Look at the tenths digit. 5 or more rounds up to the next whole number.
12.65 is between 12 and 13 → 13
Start rounded = 13
Step 2 · Find second number rounded
8.3 rounded to the ones: ?
The take-away rounded to the nearest whole = second number rounded
Round the take-away the same way.
8.3 is between 8 and 9 → 8
Second number rounded = 8
Step 3 · Find estimated difference
13 − 8 = ?
Start rounded − second number rounded = estimated difference
Subtract the whole numbers in your head.
Estimated difference = 5 (the exact difference is 4.35)
Check
Put the numbers back in. Both sides should match.
12.65 rounded to the ones: 13 ✓
8.3 rounded to the ones: 8 ✓
13 − 8 = 5 ✓
Topic check
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