Math Rules & Formulas
Complete guide to significant figures, standard form, and decimal places
Significant Figures Rules
Essential rules for counting and working with significant figures
Counting Rules
Non-zero digits
Always significant (1, 2, 3, 4, 5, 6, 7, 8, 9)
Zeros between digits
Always significant (101, 2003)
Trailing zeros
Significant only with decimal point (100.0)
Rounding Rules
Round up if ≥5
2.456 → 2.46 (2 SF)
Round down if <5
2.454 → 2.45 (2 SF)
Exact 5 rule
Round to even number (2.455 → 2.46)
Examples
123.45
5 significant figures
0.00123
3 significant figures
100.0
4 significant figures
Standard Form Rules
Essential rules for scientific notation and decimal movement
Large Numbers (>10)
1234.567 → 1.234567 × 10³
Move decimal LEFT, exponent is POSITIVE
Step 1:
Count decimal places moved left
Step 2:
Exponent = number of places moved
Step 3:
Coefficient must be 1 ≤ a < 10
Small Numbers (<1)
0.001234 → 1.234 × 10⁻³
Move decimal RIGHT, exponent is NEGATIVE
Step 1:
Count decimal places moved right
Step 2:
Exponent = negative number of places
Step 3:
Coefficient must be 1 ≤ a < 10
Key Rules Summary
1 ≤ coefficient < 10
Coefficient must be at least 1 and less than 10
a × 10^n
Standard form format
Count decimal places
Exponent = number of places moved
Decimal Places Rules
Essential rules for working with decimal places
Rounding to Decimal Places
Identify the position
Find the digit at the specified decimal place
Look at the next digit
Check the digit immediately to the right
Round up or down
≥5 round up, <5 round down
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