Place Value — Grade 5 Mathematics
In Grade 5, we extend our place value knowledge to numbers up to 1 million and decimal thousandths. We write numbers in full expanded decimal notation and connect place value understanding to rounding and ordering.
Full Place Value Chart — Millions to Thousandths
Millions
1
H. Thousands
4
T. Thousands
0
Thousands
6
Hundreds
3
Tens
5
Ones
2
·
.
Tenths
7
Hundredths
0
Thousandths
4
This number is 1,406,352.704
Read as: one million, four hundred and six thousand, three hundred and fifty-two point seven zero four
Decimal Expanded Notation
Thousandths
One thousandth = 1 ÷ 1,000 = 0.001
- 0.007 = 7 thousandths
- 0.042 = 4 hundredths + 2 thousandths
- 1.305 = 1 one + 3 tenths + 0 hundredths + 5 thousandths
Place Value and Rounding
Knowing the place value of each digit tells you exactly which digit to look at when rounding.
Rounding 3.867 to 2 decimal places (hundredths):
Look at the thousandths digit: 7 ≥ 5 → round up the hundredths digit: 6 → 7
Result: 3.87
Rounding 3.867 to 2 decimal places (hundredths):
Look at the thousandths digit: 7 ≥ 5 → round up the hundredths digit: 6 → 7
Result: 3.87
Worked Examples
Example 1 — Read and Write a 7-digit Number
Write 2,053,809 in words and expanded form.
- Words: two million, fifty-three thousand, eight hundred and nine
- Expanded: 2,000,000 + 50,000 + 3,000 + 800 + 9
Example 2 — Thousandths Place Value
What is the value of the digit 3 in 7.039?
- 7 → ones, 0 → tenths, 3 → hundredths, 9 → thousandths
- The digit 3 is in the hundredths place
- Its value is 0.03
Example 3 — Comparing Decimals by Place Value
Which is greater: 4.082 or 4.089?
- Ones: both 4 — equal
- Tenths: both 0 — equal
- Hundredths: both 8 — equal
- Thousandths: 2 < 9 → 4.089 is greater
Practice Questions
1. Write the value of the digit 5 in 3,500,217.
✅ The digit 5 is in the hundred-thousands place. Value = 500,000.
2. Write 0.509 in words.
✅ Five tenths and nine thousandths (or zero point five zero nine).
3. In the number 12.307, what is the value of the digit 7?
✅ The digit 7 is in the thousandths place. Value = 0.007.
4. Order from smallest to largest: 5.203 / 5.032 / 5.320
✅ All have 5 ones. Compare tenths: 0 < 2 < 3. Order: 5.032 → 5.203 → 5.320
5. Write 4,060,008.25 in expanded form.
✅ 4,000,000 + 60,000 + 8 + 0.2 + 0.05
Key Points to Remember
- Numbers to 1 million have 7 digits: Millions | H.Th | T.Th | Th | H | T | O.
- Decimal columns to the right of the point: Tenths (÷10) | Hundredths (÷100) | Thousandths (÷1,000).
- 1 thousandth = 0.001; 1 hundredth = 0.01; 1 tenth = 0.1.
- To compare decimals, work left to right column by column.
- Place value underpins rounding — the digit to the right of the rounding place decides whether to round up or keep.