Decimal Place Value
Grade 5 · Math · Study Guide
Understand the value of digits in decimal numbers from hundredths to thousandths and beyond.
Every digit in a number has a place value. To the left of the decimal point are ones, tens, hundreds, and so on. To the right of the decimal point are tenths, hundredths, thousandths, and beyond — each position is 10 times smaller than the one to its left.
Reading a decimal correctly means naming the whole number part, saying 'and' for the decimal point, then reading the digits to the right as a number followed by the place of the last digit. For example, 3.47 is read as 'three and forty-seven hundredths.'
Comparing decimals requires lining up the decimal points and comparing digit by digit from left to right, adding zeros as placeholders if needed to make the decimals the same length.
| Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 3 | . | 4 | 7 | |||
| 1 | 2 | . | 0 | 5 | 3 | |
| 2 | 0 | 0 | . | 1 | 0 | 6 |
| Decimal A | Decimal B | Comparison | Reason |
|---|---|---|---|
| 0.5 | 0.50 | = | Same value; trailing zero doesn't change value |
| 0.3 | 0.29 | > | 3 tenths is greater than 2 tenths |
| 1.045 | 1.05 | < | 4 hundredths < 5 hundredths |
Key terms
- Decimal Point
- The dot separating the whole number part from the fractional part of a number.
- Tenths
- The first place to the right of the decimal point; represents 1/10.
- Hundredths
- The second place to the right of the decimal point; represents 1/100.
- Thousandths
- The third place to the right of the decimal point; represents 1/1000.
Practice questions
What is the value of the digit 7 in 3.472?
- 7 ones
- 7 tenths
- 7 hundredths
- 7 thousandths
Show answer
Answer: 7 hundredths
In 3.472, the digits after the decimal are 4 (tenths), 7 (hundredths), 2 (thousandths).
Which number is greatest: 0.4, 0.39, 0.405, 0.41?
- 0.39
- 0.405
- 0.41
- 0.4
Show answer
Answer: 0.41
0.41 = 41 hundredths, which is greater than 40.5 hundredths (0.405) and 40 hundredths (0.4).
Write 'five and thirty-two thousandths' as a decimal: ___
Show answer
Answer: 5.032
Five is the whole number, and 32 thousandths = 0.032, so the answer is 5.032.
What digit is in the tenths place of 12.675? ___
Show answer
Answer: 6
After the decimal point: 6 is tenths, 7 is hundredths, 5 is thousandths.
Which correctly compares 0.60 and 0.6?
- 0.60 > 0.6
- 0.60 < 0.6
- 0.60 = 0.6
- Cannot compare
Show answer
Answer: 0.60 = 0.6
Trailing zeros after the last significant decimal digit do not change the value; 0.60 = 0.6.
Fun facts
- Money is the most common real-world use of decimals — $1.25 means 1 dollar, 2 dimes, and 5 pennies!
- The metric system uses decimals for everything from millimeters (0.001 m) to kilometers (1000 m).
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