01 / 21
3 . 1 4

Place Value
Read, Write, Compare, Round

Master the system that gives every digit its meaning: from whole numbers in the thousands to decimals in the thousandths.

Pre-Algebra

What Is Place Value?

Place value is the value of a digit based on its position within a number. The same digit can represent completely different amounts depending on where it sits.

Our number system is base-10: each place is \(10\) times the place to its right. This pattern extends in both directions: left for whole numbers, right for decimals.

The Place Value Chart

Hundred- Thousands Ten- Thousands Thousands Hundreds Tens Ones 100,000 10,000 1,000 100 10 1
\(\times 10\)
\(\times 10\)
\(\times 10\)
\(\times 10\)
\(\times 10\)
 ← Larger values Smaller values →

Extending to Decimals

The decimal point separates whole number places (left) from fractional places (right). The base-10 pattern continues: moving right, each place is worth \(\frac{1}{10}\) of the place to its left.

Ones
7
 
.
Tenths
3
Hundredths
0
Thousandths
5

The Base-10 Rule

. Ones
\(10^0 = 1\)
 Tens
\(10^1 = 10\)
 Tenths
\(10^{-1} = 0.1\)
 Hundredths
\(10^{-2} = 0.01\)
\(\text{Digit value} = \text{digit} \times \text{place value}\)
Example: \(4\) in hundreds place = \(4 \times 100 = 400\)

Reading and Writing Numbers

Standard Form
\(45{,}208.63\)
Written with digits and a decimal point.
Word Form
Forty-five thousand, two hundred eight and sixty-three hundredths.
Expanded Form
\(40{,}000 + 5{,}000 + 200 + 8 + 0.6 + 0.03\)

Tens vs. Tenths: a Critical Difference

Whole-Number Places Decimal Places
Name pattern Tens, Hundreds, Thousands Tenths, Hundredths, Thousandths
Ends with -s (plural) -ths (fractional)
Position Left of decimal Right of decimal
Value in \(305.07\) "Tens" digit = \(0\) "Tenths" digit = \(0\)
What \(3\) would be worth \(30\) \(0.3\)

Comparing Numbers with Place Value

1
Line up the decimal points so each digit sits in its correct place.
2
Compare from the largest place (leftmost) to the smallest (rightmost).
3
The first place where digits differ determines which number is greater.
4
Trailing zeros don't change value: \(3.50 = 3.5\). Append zeros to align columns if needed.

How to Round Any Number

1
Identify the rounding place. Underline or highlight that digit.
2
Look at the digit to the right of the rounding place (the "decision digit").
3
If the decision digit is \(5\) or greater: round up (add 1 to the rounding digit).
4
If the decision digit is less than \(5\): round down (keep the rounding digit).
5
Replace all digits to the right with zeros (whole numbers) or drop them (decimals).

Place Value Toolkit

Read
Identify each digit's place name. Say "and" for the decimal. End with the smallest place name.
Write
Convert words to digits. Use commas every 3 whole-number places. Place the decimal correctly.
Compare
Align decimals, scan left to right, and find the first differing digit. Use \(\lt\), \(\gt\), or \(=\).
Round
Find the rounding place, check the digit to its right, then round up or keep.

Example 1: Expanded Form

Write \(6{,}032.19\) in expanded form.

Th
6
H
0
T
3
O
2
 
.
Tenths
1
Hdths
9

Example 2: Comparing Decimals

Which is larger: \(12.639\) or \(12.7\)?

Tens Ones . Tenths Hdths Thths A: 1 2 . 6 3 9 B: 1 2 . 7 0 0
\(7 \gt 6\)
 First difference!

Example 3: Rounding to Hundredths

Round \(9.4738\) to the nearest hundredth.

9 . 4 7 3 8 Rounding place Decision digit
\(3 \lt 5 \rightarrow \text{Round down} \rightarrow 9.47\)

Example 4: Rounding with Carry-Over

Round \(3{,}982\) to the nearest hundred.

3 , 9 8 2 Hundreds Decision: 8 4,000
\(8 \ge 5 \rightarrow 9 \text{ rounds up to } 10 \rightarrow \text{ carry } 1 \text{ to thousands}\)

Common Mistakes

✕ Longer = Larger
Thinking \(0.125 \gt 0.3\) because it has more digits. Always compare place by place, not digit count.
✕ Mixing Up -s and -ths
Confusing "hundreds" with "hundredths." Remember: "-ths" is always the decimal (fractional) side.
✕ Forgetting the Carry
Rounding \(3{,}982\) to the nearest hundred and writing \(3{,}900\) instead of \(4{,}000\). The 9 rounds up and carries.

Place Value Summary

Place Value Power of 10 Example digit 5
Thousands \(1{,}000\) \(10^3\) \(5{,}000\)
Hundreds \(100\) \(10^2\) \(500\)
Tens \(10\) \(10^1\) \(50\)
Ones \(1\) \(10^0\) \(5\)
Tenths \(0.1\) \(10^{-1}\) \(0.5\)
Hundredths \(0.01\) \(10^{-2}\) \(0.05\)
Thousandths \(0.001\) \(10^{-3}\) \(0.005\)

Question 1 of 5

In the number \(74{,}586\), what is the value of the digit \(5\)?

Question 2 of 5

Which number is written in word form as "twelve and forty-five hundredths"?

Question 3 of 5

Which symbol correctly compares \(0.68\) and \(0.608\)?

Question 4 of 5

What is \(6.7851\) rounded to the nearest tenth?

Question 5 of 5

The expanded form \(30{,}000 + 400 + 6 + 0.02\) equals which number in standard form?