Read, Write, and Compare Decimals to Thousandths

In this lesson:

• Read and write decimals using numerals, number names, and expanded form
• Compare two decimals to thousandths using >, =, and <

Goals for Reading, Writing, and Comparing

By the end of this lesson, you will:

1. Read and write decimals to thousandths
2. Express decimals in expanded form
3. Translate among numerals, names, and expanded form
4. Compare two decimals place by place using >, =, <

Review the Place Value Pattern

Each place is 10 times the place to its right:

Each place is also of its left neighbor.

Three Forms of Every Decimal

Every decimal can be written three ways:

All three forms represent the same number.

Building Three Forms of 347.392

Base-ten numeral: 347.392

Number name: three hundred forty-seven and three hundred ninety-two thousandths

• "And" marks the decimal point
• The decimal part is read as a whole number (392) plus the smallest place name (thousandths)

The Word "And" Marks the Decimal Point

In math, "and" means the decimal point — nowhere else.

• 347 → "three hundred forty-seven" (no "and")
• 347.5 → "three hundred forty-seven and five tenths"
• 500.08 → "five hundred and eight hundredths"

Read decimal digits as a whole number, then say the smallest place name.

Expanded Form Breaks Down Each Digit

Each digit is multiplied by its place value:

Every digit maps to one term in the sum.

Check: Write the Number Name

What is the number name for 52.7?

Think about it before the next slide...

Answer: fifty-two and seven tenths

• "And" goes at the decimal point
• The smallest place is tenths

Zeros Hold Their Place in Decimals

The number 40.206 has zeros in the ones and hundredths places.

Name: forty and two hundred six thousandths

Zeros are silent in the name but hold their place in the numeral.

Your Turn: Expanded Form to Numeral

Write the base-ten numeral for:

Which place has no term? What digit goes there?

Answer: 8.051 — the tenths place has no term, so a 0 fills that place.

Translate Each Decimal Into Two Forms

1. 9.030 → Name: ? → Expanded: ?
2. "twelve and three hundred four thousandths" → Numeral: ?
3. → Numeral: ? → Name: ?

Try all three before the next slide.

Answers for the Three Forms Practice

1. 9.030 → "nine and thirty thousandths" →
2. 12.304 →
3. 7.004 → "seven and four thousandths"

Compare Decimals Digit by Digit from Left

Compare digits left to right — the first difference decides:

• Line up decimal points
• Compare place by place from left
• First different digit determines the result

Worked Example: Comparing 6.472 and 6.438

Compare place by place:

The hundredths differ first: 7 > 3

Longer Does Not Mean Larger

Does 0.45 have more than 0.6 just because 45 > 6?

No. The tenths place decides: 6 tenths > 4 tenths.

Trailing Zeros Make It Clear

Rewrite 0.6 as 0.60 — the value does not change:

• 0.60 vs 0.45
• 60 hundredths vs 45 hundredths
• 0.6 > 0.45

Strategy: When decimals have different lengths, add trailing zeros to equalize, then compare.

Check: Compare 0.125 and 0.2

Which is greater: 0.125 or 0.2?

Use the place-by-place strategy before checking...

Answer: Compare tenths first: 1 vs 2. Since 2 > 1:

The three digits in 0.125 do not make it larger.

Practice Comparing Decimals with Symbols

Write >, =, or < for each pair:

1. 3.872 ___ 3.878
2. 0.5 ___ 0.41
3. 0.700 ___ 0.7
4. 12.09 ___ 12.1

Work through all four, then check.

Answers for the Decimal Comparison Practice

1. 3.872 < 3.878 — thousandths differ: 2 < 8
2. 0.5 > 0.41 — tenths differ: 5 > 4
3. 0.700 = 0.7 — trailing zeros do not change value
4. 12.09 < 12.1 — tenths differ: 0 < 1

Translate to Numerals, Then Compare Them

Number A: eight and forty-five thousandths
Number B:

Step 1: Convert both to numerals

• A = 8.045, B = 8.402

Step 2: Compare tenths: 0 vs 4 → B > A

Order from Least to Greatest

Arrange: 2.15, 2.105, 2.5, 2.051

Step 1: Equalize decimal places — write all with three places:
2.150, 2.105, 2.500, 2.051

Step 2: Compare tenths, then hundredths, then thousandths

Answer: 2.051 < 2.105 < 2.15 < 2.5

Mixed Practice Combining All Decimal Skills

1. Write "twenty and thirty-six thousandths" as a numeral. Is it greater than 20.4?
2. Which is greatest: , or 5.29, or 5.3?
3. Put in order: 0.8, 0.08, 0.800, 0.088

Solve all three before checking.

Answers for the Mixed Practice Problems

1. 20.036 — tenths: 0 < 4, so 20.036 < 20.4
2. = 5.3 and 5.3 = 5.3, both > 5.29. Two are tied for greatest.
3. 0.08 < 0.088 < 0.8 = 0.800

Summary of Key Decimal Place Value Ideas

✓ Three forms — numeral, name, expanded — all equivalent
✓ "And" marks the decimal point, exactly once
✓ Fill empty places with zero
✓ Compare left to right — first difference decides

More digits does not mean larger
Trailing zeros do not change value

Next Up: Rounding Decimals to Any Place

Next lesson: 5.NBT.A.4 — Rounding decimals

You will use today's place value skills to:

• Identify which digit to round
• Determine whether to round up or down
• Apply rounding in real-world contexts