Decimal Place Value- 5th Grade Comprehensive Guide

What Decimal Place Value Actually Means

Decimals are just fractions in disguise. Instead of writing ½, you write 0.5. Instead of ¼, you write 0.25. The decimal point is the dividing line between whole numbers and parts of a whole.

In 5th grade, you're working with decimals to the tenths, hundredths, and thousandths places. If you can't visualize where each digit sits, you'll struggle with everything that comes next—adding, subtracting, comparing, rounding.

This guide cuts through the fluff and gives you exactly what you need to understand and work with decimal place values.

The Place Value System Explained

Every digit in a number has a specific position. Move one spot left of the decimal and you're in the ones place. Move one spot right and you're in the tenths place.

Breaking Down a Decimal Number

Take the number 347.529:

• 3 is in the hundreds place → 3 × 100 = 300
• 4 is in the tens place → 4 × 10 = 40
• 7 is in the ones place → 7 × 1 = 7
• 5 is in the tenths place → 5 × 0.1 = 0.5
• 2 is in the hundredths place → 2 × 0.01 = 0.02
• 9 is in the thousandths place → 9 × 0.001 = 0.009

Add them up: 300 + 40 + 7 + 0.5 + 0.02 + 0.009 = 347.529

Decimal Place Value Table

Each place value is 10 times smaller than the one to its left. Think of it like a ladder—going down means dividing by 10 each step.

How to Read Decimals Out Loud

Most students mess this up. The trick: read the whole number part, say "and" at the decimal point, then read the decimal part as if it were a whole number followed by the place value of the last digit.

Example: 12.47

• Read "twelve" (the whole number part)
• Say "and" at the decimal
• Read "forty-seven hundredths" (47 is read as a whole number, last digit is in hundredths)

So 12.47 = "twelve and forty-seven hundredths"

Another example: 5.083

Read as "five and eighty-three thousandths"

Comparing Decimals Without the Guesswork

Students often think 0.45 is bigger than 0.6 because 45 looks bigger than 6. It's not. Here's how to compare decimals correctly:

Step-by-Step Method

1. Line up the decimals vertically
2. Add zeros to the right so both numbers have the same length
3. Compare digit by digit from left to right

Compare 0.45 and 0.6:

• Write them as: 0.45 and 0.60
• Compare tenths: 4 vs 6 → 6 is bigger
• 0.6 is larger than 0.45

Compare 2.31 and 2.309:

• Write them as: 2.310 and 2.309
• Compare hundredths: 1 vs 0 → 1 is bigger
• 2.31 is larger than 2.309

Rounding Decimals: The Method That Sticks

Rounding decimals follows the same rules as rounding whole numbers, just with a decimal point.

The Rules

• Look at the digit to the right of your target place
• If it's 5 or greater, round up
• If it's 4 or less, round down

Example: Round 7.638 to the nearest tenth

• Target place: tenths (the 6)
• Digit to the right: 3
• 3 is less than 5, so round down
• Answer: 7.6

Example: Round 4.275 to the nearest hundredth

• Target place: hundredths (the 7)
• Digit to the right: 5
• 5 is 5 or greater, so round up
• The 7 becomes 8
• Answer: 4.28

Adding and Subtracting Decimals

This is where most 5th graders lose points. The decimal point doesn't disappear just because you're doing arithmetic.

The Golden Rule

Always line up the decimal points before you do anything else.

Getting Started: Adding 12.4 + 7.35

1. Line up the decimals:

  12.40
+  7.35
------

2. Add zeros where needed (12.4 becomes 12.40)
3. Add normally, starting from the right
4. Bring the decimal straight down

  12.40
+  7.35
------
  19.75

Answer: 19.75

Subtracting: 9.5 - 3.28

   9.50
-  3.28
------
   6.22

Answer: 6.22

Forgetting to line up the decimal is the fastest way to get these problems wrong. Don't do it.

Converting Fractions to Decimals

Some fractions convert neatly. Others don't. Know the difference.

Clean Conversions (Terminating Decimals)

When the denominator is 10, 100, or 1000, just move the decimal.

• 7/10 = 0.7 (move decimal 1 place left)
• 23/100 = 0.23 (move decimal 2 places left)
• 456/1000 = 0.456 (move decimal 3 places left)

Division Method

For anything else, divide the numerator by the denominator.

Convert 3/8 to a decimal:

• 3 ÷ 8 = 0.375
• Check: 0.375 × 8 = 3 ✓

Common Fraction-Decimal Equivalents to Memorize

Where Students Screw Up

• Misreading place values: Thinking the 5 in 0.25 means 0.5 instead of 0.05
• Forgetting zeros: 0.7 is not the same as 0.70, though they equal the same amount
• Not lining up decimals: Doing addition/subtraction with misaligned decimal points
• Comparing by length instead of value: 0.099 is less than 0.1, even though 099 looks longer than 1
• Rounding to the wrong digit: Looking at the wrong place when deciding to round up or down

Practice Problems

Work through these to check your understanding:

1. Write 4.072 in words
2. Compare 0.56 and 0.6 — which is bigger?
3. Round 8.749 to the nearest tenth
4. Add: 15.3 + 7.48
5. Convert 5/8 to a decimal

Answers:

1. Four and seventy-two thousandths
2. 0.6 (write 0.60 to compare: 6 tenths beats 5 tenths)
3. 8.7 (the 4 tells you to round down)
4. 22.78
5. 0.625