Decimals - Seventh Grade

Complete Notes & Formulas

1. Decimal Numbers Review

What is a Decimal?

A decimal is a number that has a

WHOLE NUMBER part and a FRACTIONAL part

separated by a DECIMAL POINT (.)

Example: 25.47 (25 is whole, 47 is fractional)

Decimal Place Value Chart

Thousands	Hundreds	Tens	Ones	•	Tenths	Hundredths	Thousandths
1000	100	10	1	.	1/10 or 0.1	1/100 or 0.01	1/1000 or 0.001
3	6	7	4	.	2	5	8

Example: 3674.258

Place Value Breakdown

For 3674.258:

3 = 3 thousands = 3000

6 = 6 hundreds = 600

7 = 7 tens = 70

4 = 4 ones = 4

2 = 2 tenths = 0.2 or 2/10

5 = 5 hundredths = 0.05 or 5/100

8 = 8 thousandths = 0.008 or 8/1000

Reading Decimals

25.6 → "twenty-five AND six tenths"

12.47 → "twelve AND forty-seven hundredths"

0.125 → "zero AND one hundred twenty-five thousandths"

8.003 → "eight AND three thousandths"

Remember: The word "AND" represents the decimal point!

2. Compare and Order Decimals

Steps to Compare Decimals

Step 1: ALIGN the decimal points vertically

Step 2: Add ZEROS to make equal decimal places (if needed)

Step 3: Compare from LEFT to RIGHT

Step 4: The FIRST different digit determines which is larger

Comparison Symbols

> greater than

< less than

= equal to

Example 1: Compare 2.45 and 2.47

Step 1: Align decimal points:

2.45

2.47

Step 2: Compare from left to right:

Ones place: 2 = 2 ✓

Tenths place: 4 = 4 ✓

Hundredths place: 5 < 7 ✗

Answer: 2.45 < 2.47

Example 2: Compare 5.3 and 5.28

Step 1: Align and add zeros:

5.30

5.28

Step 2: Compare:

Ones: 5 = 5 ✓

Tenths: 3 > 2 ✗

Answer: 5.3 > 5.28

Ordering Decimals

Ascending Order (Least to Greatest):

Start with the SMALLEST number

Descending Order (Greatest to Least):

Start with the LARGEST number

Example: Order 3.5, 3.15, 3.8, 3.05

Step 1: Align and add zeros:

3.50

3.15

3.80

3.05

Step 2: Compare tenths place: 0, 1, 5, 8

Ascending: 3.05, 3.15, 3.5, 3.8

Descending: 3.8, 3.5, 3.15, 3.05

3. Rounding Decimals

Rounding Rules

The "5 or More, Raise the Score" Rule:

Look at the digit to the RIGHT of the rounding place:

• If it's 5, 6, 7, 8, or 9 → ROUND UP

• If it's 0, 1, 2, 3, or 4 → ROUND DOWN (keep same)

Steps to Round Decimals

Step 1: IDENTIFY the place value to round to

Step 2: LOOK at the digit to its RIGHT

Step 3: DECIDE: Round up or keep the same

Step 4: DROP all digits to the right

Common Rounding Places

Round To	Look At	Example
Nearest whole number	Tenths place	7.6 → 8
Nearest tenth	Hundredths place	5.47 → 5.5
Nearest hundredth	Thousandths place	3.456 → 3.46

Example 1: Round 24.67 to the nearest whole number

Step 1: Identify ones place: 24.67

Step 2: Look at tenths place: 6

Step 3: 6 ≥ 5, so ROUND UP

Step 4: 24 + 1 = 25

Answer: 25

Example 2: Round 8.234 to the nearest tenth

Step 1: Identify tenths place: 8.234

Step 2: Look at hundredths place: 3

Step 3: 3 < 5, so KEEP THE SAME

Step 4: Drop everything after tenths

Answer: 8.2

Example 3: Round 12.895 to the nearest hundredth

Step 1: Identify hundredths place: 12.895

Step 2: Look at thousandths place: 5

Step 3: 5 ≥ 5, so ROUND UP

Step 4: 89 + 1 = 90, so 12.90

Answer: 12.90 or 12.9

Special Case: Rounding 9

Example: Round 4.97 to nearest tenth

Look at 7 → round up

9 + 1 = 10 (carry over to ones place)

Answer: 5.0 or 5

Quick Reference: Decimal Rules

Concept	Key Rule
Place Value	Tenths (0.1), Hundredths (0.01), Thousandths (0.001)
Reading Decimals	"AND" represents the decimal point
Comparing	Align decimals, compare left to right
Ordering	Add trailing zeros, compare place by place
Rounding	5+ round up, 0-4 round down