Decimal Rounding Reference Sheet
Math & Science Reference Place Value & Decimals
The Golden Rule of Rounding
Mastering the "5 or More" principle when rounding mileage and decimal figures
5 or More? Round UP (+1)
If the digit directly to the right is 5, 6, 7, 8, or 9, increase the target digit by 1.
5 6 7 8 9
4 or Less? Let It Rest
If the digit directly to the right is 0, 1, 2, 3, or 4, keep the target digit the same.
0 1 2 3 4
Why does 5 round up? In base-10, there are 10 single digits: {0, 1, 2, 3, 4} (5 lower digits) and {5, 6, 7, 8, 9} (5 upper digits). Since 5 sits exactly at the halfway mark, the universal standard rounds it up.
Case Study: Rounding Mileage of 8.7875
Value: 8.7875 miles
Ones
8
Tenths
.7
Hundredths
8
Thousandths
7
Ten-Thousandths
5
| Target Place | Target Digit | Look Right (Test Digit) | Decision Rule | Rounded Mileage |
|---|
| Nearest Whole Mile | 8 | 7 (tenths) | 7 ≥ 5 → Round up (+1) | 9 miles |
| Nearest Tenth | 7 | 8 (hundredths) | 8 ≥ 5 → Round up (+1) | 8.8 miles |
| Nearest Hundredth | 8 | 7 (thousandths) | 7 ≥ 5 → Round up (+1) | 8.79 miles |
| Nearest Thousandth | 7 | 5 (ten-thousandths) | 5 ≥ 5 → Round up (+1) | 8.788 miles |
Avoid "Double Rounding": Always look only at the single digit directly to the right of your target place. Never chain-round from digits further down the line!
Test Your Understanding: Quick Mileage Check
Apply the rule
Trip A: 12.43 miles
Round to nearest tenth:
4 next to 3 (<5) 12.4
Trip B: 45.685 miles
Round to nearest hundredth:
8 next to 5 (≥5) 45.69
Trip C: 19.51 miles
Round to nearest whole mile:
19 next to 5 (≥5) 20
Rule of thumb: 5, 6, 7, 8, 9 rounds UP (+1) • 0, 1, 2, 3, 4 stays the SAME
