Working with Percents

Lesson 2: Decimals and Benchmark Percents

Learning Objectives:

• Convert between percents and decimals
• Recognize equivalent representations
• Memorize common benchmark percents

Quick Review

From Lesson 1:

• Percent means "per hundred"
• 45% = 45/100

Today we'll add:

• 45% = 45/100 = 0.45

Percents and Decimals: The Connection

Since percent means "÷ 100":

45% = 45 ÷ 100 = 0.45

The percent symbol tells you to divide by 100.

Converting Percent to Decimal

Method: Divide by 100 (move decimal 2 places LEFT)

The Shortcut: Move Decimal 2 Places Left

45% → 0.45

Remove the % symbol, move decimal 2 places left.

Watch the Tricky Cases

Single digits need a placeholder zero:

8% = 0.08 (not 0.8!)

Percents Over 100%

Percents can be greater than 100%.

200% of your money = double your money

Percents Less Than 1%

Very small percents exist too:

0.5% is NOT the same as 50%!

Converting Decimal to Percent

Method: Multiply by 100 (move decimal 2 places RIGHT)

Practice: Percent to Decimal

Convert each percent to a decimal:

1. 35% = ?
2. 6% = ?
3. 150% = ?
4. 0.4% = ?

Move decimal 2 places LEFT

Answers: Percent to Decimal

1. 35% = 0.35
2. 6% = 0.06 (not 0.6)
3. 150% = 1.50 or 1.5
4. 0.4% = 0.004

Practice: Decimal to Percent

Convert each decimal to a percent:

1. 0.72 = ?%
2. 0.05 = ?%
3. 2.0 = ?%
4. 0.125 = ?%

Move decimal 2 places RIGHT

Answers: Decimal to Percent

1. 0.72 = 72%
2. 0.05 = 5%
3. 2.0 = 200%
4. 0.125 = 12.5%

The Percent-Fraction-Decimal Triangle

Every value can be written three ways:

25% = 1/4 = 0.25

All three represent the same amount!

Benchmark Percents to Memorize

More Benchmarks

Using Benchmarks for Mental Math

"The shirt is 50% off the $40 price"

50% = 1/2

Half of $40 = $20

Benchmarks make estimation fast!

Another Example

"About 25% of students passed"

If there are 80 students:

• 25% = 1/4
• 1/4 of 80 = 80 ÷ 4 = 20 students

Quick Match Practice

Match each percent to its equivalent:

Answers

Key Takeaways

• Percent to decimal: divide by 100 (2 places LEFT)
• Decimal to percent: multiply by 100 (2 places RIGHT)
• Percents can exceed 100% (200% = double)
• Percents can be tiny (0.5% ≠ 50%)
• Memorize benchmarks for fast mental math

Common Mistakes to Avoid

Always check: does my answer make sense?

The Complete Picture

25% = 25/100 = 1/4 = 0.25

You can now move fluently between all three forms.

What's Next?

Future lessons will cover:

• Finding percent of a quantity (What is 30% of 80?)
• Finding the whole from a part
• Percent increase and decrease

Practice your conversions and benchmarks!