Unit 4 Study Guide — Decimals & Percents

4.1 — Decimal Place Value & Operations

Place value to thousandths, and how to add and subtract decimals by lining up the decimal points.

Key Ideas

Each place in a decimal has a value that is ten times the place to its right:

ones . tenths hundredths thousandths
1 . 1 0 1 = 1.101

To add or subtract decimals, line up the decimal points and fill in zeros as placeholders so each number has the same number of decimal places. Then add or subtract as with whole numbers.

Example: 3.45 + 2.70 — line up the decimals, add column by column: 3.45 + 2.70 = 6.15

Example: 5.3 − 2.18 — rewrite as 5.30 − 2.18 = 3.12

Practice

What is 4.56 + 3.7?

7.93

8.26

8.63

What is 9.04 − 3.6?

5.44

5.64

6.44

In the number 7.835, what is the value of the digit 3?

3 tenths (0.3)

3 thousandths (0.003)

3 hundredths (0.03)

Score

0/3

4.2 — Multiply Decimals

Multiply decimals by counting the total decimal places in the factors to place the decimal point in the product.

Key Ideas

Step 1: Multiply as if there are no decimal points (treat the numbers as whole numbers).

Step 2: Count the total number of decimal places in both factors.

Step 3: Place the decimal point in the product so it has that many decimal places.

Example: 2.3 × 1.4
Multiply: 23 × 14 = 322
Decimal places: 1 + 1 = 2
Product: 3.22

Example: 0.6 × 0.03
Multiply: 6 × 3 = 18
Decimal places: 1 + 2 = 3
Product: 0.018

Practice

What is 3.5 × 2.4?

8.40

8.04

84.0

What is 0.7 × 0.05?

0.35

0.035

How many decimal places does the product of 4.12 × 3.5 have?

2

3

4

Score

0/3

4.3 — Divide Decimals

Divide decimals by whole numbers and by other decimals using long division strategies.

Dividing a Decimal by a Whole Number

Place the decimal point in the quotient directly above the decimal point in the dividend. Then divide as normal.

Example: 8.4 ÷ 3 = 2.8

Dividing by a Decimal

Make the divisor a whole number by multiplying both the divisor and dividend by the same power of 10. Then divide.

Example: 7.2 ÷ 0.6
Multiply both by 10: 72 ÷ 6 = 12

Example: 0.325 ÷ 0.05
Multiply both by 100: 32.5 ÷ 5 = 6.5

Practice

What is 9.6 ÷ 4?

2.2

2.4

2.6

What is 4.5 ÷ 0.9?

5

0.5

50

What is 0.72 ÷ 0.08?

0.9

90

9

Score

0/3

4.4 — Fraction, Decimal, Percent Conversions

Convert between fractions, decimals, and percents fluently.

Conversion Methods

Fraction to Decimal: Divide the numerator by the denominator. Example: 3/8 = 3 ÷ 8 = 0.375

Decimal to Percent: Multiply by 100 (move the decimal point two places right). Example: 0.25 = 25%

Percent to Decimal: Divide by 100 (move the decimal point two places left). Example: 60% = 0.60

Percent to Fraction: Write the percent over 100 and simplify. Example: 75% = 75/100 = 3/4

Full conversion: 1/4 = 0.25 = 25%

Full conversion: 2/5 = 0.4 = 40%

Practice

What is 3/5 written as a percent?

35%

53%

60%

What is 0.125 written as a fraction in simplest form?

1/8

1/5

1/4

What is 45% written as a decimal?

4.5

0.45

0.045

Score

0/3

4.5 — Percent of a Number

Find the percent of a quantity using multiplication, with real-world applications like tax, tip, and discount.

Key Ideas

To find the percent of a number, convert the percent to a decimal and multiply.

Example: 20% of 150
0.20 × 150 = 30

Real-World Applications

Tax/Tip: Add the percent amount to the original price.
Discount: Subtract the percent amount from the original price.

Tip example: A meal costs $45 and you leave a 15% tip.
0.15 × 45 = $6.75 tip. Total = $45 + $6.75 = $51.75

Discount example: A $60 shirt is 25% off.
0.25 × 60 = $15 discount. Sale price = $60 − $15 = $45

Practice

What is 30% of 200?

30

60

600

A jacket costs $80 and is 15% off. What is the sale price?

$68

$65

$12

You leave a 20% tip on a $35 meal. How much is the tip?

$3.50

$5.00

$7.00

Score

0/3

Vocabulary

Tap a card to reveal the definition.

Decimal

A number written using a decimal point to show values less than one (tenths, hundredths, etc.).

Place Value

The value of a digit based on its position in a number. Each place is 10 times the place to its right.

Tenths

The first decimal place to the right of the decimal point. One tenth = 0.1 = 1/10.

Hundredths

The second decimal place to the right of the decimal point. One hundredth = 0.01 = 1/100.

Thousandths

The third decimal place to the right of the decimal point. One thousandth = 0.001 = 1/1000.

Product

The result of multiplying two or more numbers. Example: 3 × 4 = 12, so 12 is the product.

Quotient

The result of dividing one number by another. Example: 12 ÷ 4 = 3, so 3 is the quotient.

Dividend

The number being divided. In 12 ÷ 4, the dividend is 12.

Divisor

The number you divide by. In 12 ÷ 4, the divisor is 4.

Percent

A ratio that compares a number to 100. The symbol % means "per hundred." Example: 50% = 50/100 = 0.5.

Fraction

A number that represents part of a whole, written as a numerator over a denominator. Example: 3/4.

Equivalent

Having the same value in different forms. Example: 1/2, 0.5, and 50% are all equivalent.