Place Value and Rounding — Charts, Rules, and Practice

By MathPal Editorial Team·Published Apr 17, 2026

Grade: 6 | Topic: Arithmetic

What You Will Learn

Understanding place value is the foundation for reading, writing, comparing, and rounding numbers. In this guide you will learn the place value chart from ones all the way up to millions (and down to thousandths on the decimal side), how to read and write large numbers, and the step-by-step rules for rounding both whole numbers and decimals.

Theory

The place value chart

Every digit in a number has a value determined by its position. Moving left, each place is 10 times larger. Moving right, each place is 10 times smaller.

Millions	Hundred-thousands	Ten-thousands	Thousands	Hundreds	Tens	Ones	.	Tenths	Hundredths	Thousandths
1,000,000	100,000	10,000	1,000	100	10	1	.	0.1	0.01	0.001

For the number 3,405,278:

• 3 is in the millions place: value = 3,000,000
• 4 is in the hundred-thousands place: value = 400,000
• 0 is in the ten-thousands place: value = 0
• 5 is in the thousands place: value = 5,000
• 2 is in the hundreds place: value = 200
• 7 is in the tens place: value = 70
• 8 is in the ones place: value = 8

Reading and writing large numbers

To read a large number, break it into groups of three digits separated by commas, reading each group with its period name:

• $3,405,278$ is read as "three million, four hundred five thousand, two hundred seventy-eight."

Expanded form writes each digit multiplied by its place value:

$3,405,278 = 3,000,000 + 400,000 + 5,000 + 200 + 70 + 8$

Decimal place values

The decimal point separates the whole-number part from the fractional part. Digits to the right of the decimal point represent fractions of one:

For 6.394:

• 6 is in the ones place
• 3 is in the tenths place: $\frac{3}{10} = 0.3$
• 9 is in the hundredths place: $\frac{9}{100} = 0.09$
• 4 is in the thousandths place: $\frac{4}{1000} = 0.004$

Rounding rules

Rounding replaces a number with a simpler nearby value. The steps are always the same:

1. Identify the place you are rounding to (the "rounding place").
2. Look at the digit one place to the right (the "decision digit").
3. Apply the rule:
   • If the decision digit is 0, 1, 2, 3, or 4, the rounding-place digit stays the same (round down).
   • If the decision digit is 5, 6, 7, 8, or 9, the rounding-place digit goes up by 1 (round up).
4. Replace all digits to the right of the rounding place with zeros (for whole numbers) or drop them (for decimals).

Worked Examples

Example 1 — Identifying place value

What is the value of the digit 6 in $462,019$?

Step 1: The digit 6 is in the ten-thousands place.

Step 2: Its value is $6 \times 10,000 = 60,000$.

Answer: 60,000.

Example 2 — Rounding a whole number to the nearest hundred

Round $3,847$ to the nearest hundred.

Step 1: The rounding place is the hundreds digit, which is $8$.

Step 2: The decision digit (one place to the right) is $4$.

Step 3: Since $4 < 5$, the hundreds digit stays at $8$.

Step 4: Replace digits to the right with zeros: $3,800$.

Answer: $3,847$ rounded to the nearest hundred is $3,800$.

Example 3 — Rounding when the digit rounds up past 9

Round $6,972$ to the nearest hundred.

Step 1: The hundreds digit is $9$. The decision digit is $7$.

Step 2: Since $7 \geq 5$, round up. But $9 + 1 = 10$, so the hundreds digit becomes $0$ and you carry $1$ to the thousands place.

Step 3: The thousands digit was $6$, now becomes $7$.

Answer: $6,972$ rounds to $7,000$.

Example 4 — Rounding a decimal

Round $14.368$ to the nearest tenth.

Step 1: The tenths digit is $3$. The decision digit (hundredths place) is $6$.

Step 2: Since $6 \geq 5$, round up: $3$ becomes $4$.

Step 3: Drop everything after the tenths place.

Answer: $14.368$ rounded to the nearest tenth is $14.4$.

Common Mistakes

Mistake 1 — Looking at the wrong digit

❌ To round $4,362$ to the nearest hundred, looking at the digit $4$ (thousands) instead of $6$ (tens).

✅ Always look at the digit one place to the right of the rounding place. The hundreds digit is $3$, and the decision digit is $6$ (in the tens place). Since $6 \geq 5$, round up to $4,400$.

Mistake 2 — Forgetting to carry when rounding up past 9

❌ Rounding $2,950$ to the nearest hundred gives $2,900$ (keeping 9 unchanged because "it is already big").

✅ The decision digit is $5$, so round up: $9 + 1 = 10$. Carry the $1$, giving $3,000$.

Mistake 3 — Adding zeros after a decimal round

❌ Rounding $7.849$ to the nearest tenth gives $7.900$.

✅ After rounding the tenths digit up to $9$, simply write $7.9$. Do not pad with unnecessary trailing zeros (though $7.90$ and $7.900$ are technically equal, the clean form is $7.9$).

Practice Problems

Problem 1: What is the place value of the digit 5 in $2,508,314$?

Show Answer

The digit 5 is in the hundred-thousands place. Its value is $500,000$.

Problem 2: Write $7,030,006$ in words.

Show Answer

Seven million, thirty thousand, six.

Problem 3: Round $8,465$ to the nearest thousand.

Show Answer

The thousands digit is $8$. The decision digit is $4$. Since $4 < 5$, round down.

$8,465$ rounds to $8,000$.

Problem 4: Round $0.7849$ to the nearest hundredth.

Show Answer

The hundredths digit is $8$. The decision digit is $4$. Since $4 < 5$, round down.

$0.7849$ rounds to $0.78$.

Problem 5: Round $9,985$ to the nearest ten.

Show Answer

The tens digit is $8$. The decision digit is $5$. Since $5 \geq 5$, round up: $8$ becomes $9$, but that makes the ones place $0$, giving $9,990$.

Wait — let us recheck. The tens digit is $8$, decision digit is $5$. Round up: tens becomes $9$, ones become $0$. Result: $9,990$.

Summary

• Place value tells you how much each digit is worth based on its position — each place is 10 times the place to its right.
• Read large numbers by breaking them into groups of three digits (millions, thousands, ones).
• Rounding rule: look at the digit one place to the right. If it is 5 or more, round up; if it is 4 or less, round down.
• When rounding causes a digit to pass 9, carry over to the next place.
• Rounding decimals follows the same rule — just drop digits instead of replacing with zeros.

Related Topics

• Integers — positive and negative whole numbers
• Decimal Operations — add, subtract, multiply, and divide decimals
• Comparing and Ordering Integers — use place value to compare numbers

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