A percent is a ratio that compares a number to 100

%

The symbol % means "per hundred" or "out of 100"

Example: 50% means 50 out of 100

• 100% = whole or all

• 50% = half

• 25% = quarter (one-fourth)

• 75% = three-quarters

Percent ÷ 100 = Decimal

Move decimal point 2 places LEFT

Example: 75% = 75 ÷ 100 = 0.75

Decimal × 100 = Percent

Move decimal point 2 places RIGHT

Example: 0.65 = 0.65 × 100 = 65%

Percent/100 = Fraction

Then simplify

Example: 25% = 25/100 = 1/4

(Fraction × 100)%

or divide numerator by denominator, then × 100

Example: 3/4 = 0.75 = 0.75 × 100 = 75%

Step 1: Convert all values to the same form (all decimals OR all percents)

Step 2: Compare the values

Percent of Number = (Percent/100) × Number

or

Decimal × Number

Example 1: Find 30% of 80

Example 2: Find 15% of $60

Use benchmark percents:

• 10% = divide by 10

• 25% = divide by 4

• 50% = divide by 2

• 1% = divide by 100

Type 1: Find the percent

What percent of 50 is 15?

Formula: (Part/Whole) × 100 = Percent

Type 2: Find the part

What is 30% of 80?

Formula: (Percent/100) × Whole = Part

Type 3: Find the whole

20 is 25% of what number?

Formula: Part ÷ (Percent/100) = Whole

Part/Whole = Percent/100

Example 1: What percent of 50 is 15?

Example 2: 20 is 25% of what number?

Percent of Change = (New - Old)/Old × 100

or

Change/Original × 100

Percent Increase: If result is POSITIVE (+)

New value is greater than old value

Percent Decrease: If result is NEGATIVE (−)

New value is less than old value

Step 1: Find the change (New − Old)

Step 2: Divide by original value

Step 3: Multiply by 100

Step 4: Determine if increase or decrease

Problem: A shirt cost $40. Now it costs $50. Find the percent of change.

Problem: A population decreased from 200 to 150. Find the percent of change.

If you know the new amount and percent change:

For increase: Original = New ÷ (1 + rate)

For decrease: Original = New ÷ (1 − rate)

Percent error measures the accuracy of an

estimated or measured value compared to the exact value

Percent Error = |Approximate − Exact|/Exact × 100

Always use ABSOLUTE VALUE (positive)

Step 1: Find difference (Approximate − Exact)

Step 2: Take absolute value |difference|

Step 3: Divide by exact value

Step 4: Multiply by 100

Problem: You estimated the distance as 45 miles. The actual distance is 50 miles. Find the percent error.

✓ Percent means "per hundred" or "out of 100"

✓ To convert percent to decimal: move decimal 2 places left

✓ To convert decimal to percent: move decimal 2 places right

✓ 100% = 1 whole; more than 100% means more than one whole

✓ Percent of a number: multiply by the decimal form

✓ Part/Whole = Percent/100 is the key relationship

✓ Percent increase: result is positive

✓ Percent decrease: result is negative (report as positive)

✓ Percent error: ALWAYS use absolute value (positive)

✓ Always use the ORIGINAL value as denominator in percent change

Converting Percents:

"Percent to decimal? Divide by 100, it's quite simple! Decimal to percent? Multiply by 100, don't be resentful!"

Finding Percent of Number:

"Of means multiply, so take the decimal and multiply!"

Percent Equation:

"Part over Whole equals Percent over 100 - remember this rule!"

Percent of Change:

"New minus old, divide by old, times 100 - percent change is told!"

"Positive means increase, negative means decrease!"

Percent Error:

"Error is absolute - always positive, don't debate!"

"Approximate minus exact, absolute it, divide by exact!"

Benchmark Percents:

"50% is half, 25% is quarter, 10% is tenth - use them for order!"