Decimal Place Value Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Decimal Place Value.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The value assigned to each digit's position to the right of the decimal point: the first position is tenths ( $\frac{1}{10}$ ), the second is hundredths ( $\frac{1}{100}$ ), the third is thousandths ( $\frac{1}{1000}$ ), and so on.

Just as moving left of the decimal point makes each place 10 times bigger (ones, tens, hundreds), moving right makes each place 10 times smaller (tenths, hundredths, thousandths). It's like zooming in—each step splits things into 10 equal pieces.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Decimal place value is base-ten place value continuing past ones.

Common stuck point: The procedure for decimal place value is the easy part; the trap is saying the 6 in $0.46$ is six tenths. Asking "Can I name the place of the digit I am using?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Can I name the place of the digit I am using?

Worked Examples

Example 1

easy

In the number 4.73, identify the value of each digit.

Answer

4 ones, 7 tenths, 3 hundredths

First step

4 is in the ones place: value = 4.

Full solution

2
7 is in the tenths place: value = $\frac{7}{10} = 0.7$ .
3
3 is in the hundredths place: value = $\frac{3}{100} = 0.03$ .
4
Total: $4 + 0.7 + 0.03 = 4.73$ .

Place value tells us what a digit is worth. Moving right of the decimal point: tenths (÷10), hundredths (÷100), thousandths (÷1000), etc.

Example 2

medium

Write 3 hundredths, 5 tenths, and 2 ones as a single decimal number.

Example 3

medium

In the number

45.0372

, what is the place value of the digit 3?

Example 4

medium

Write

0.358

in expanded form using place-value fractions.

Example 5

medium

7.108

, name the place of each nonzero digit and its value.

Example 6

medium

Convert

\frac{17}{100}

to a decimal.

Example 7

hard

Express

0.275

as a fraction in simplest form.

Example 8

hard

A runner's time is recorded as

12.084

seconds. By what amount would the time change if the digit in the hundredths place increased by

3

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

What is the value of the digit 6 in the number 1.63?

Example 2

medium

Order these decimals from least to greatest: 0.8, 0.08, 0.80, 0.008.

Example 3

easy

0.46

, what is the place value of the

6

Example 4

easy

What is the place value of the

7

3.7

Example 5

easy

Write 'three tenths' as a decimal.

Example 6

easy

Write 'five hundredths' as a decimal.

Example 7

easy

Which is larger,

0.5

0.46

Example 8

easy

What digit is in the thousandths place of

2.184

Example 9

easy

0.7

equal to

0.70

Example 10

easy

Write

\frac{1}{100}

as a decimal.

Example 11

medium

Write

3.205

in expanded form using place values.

Example 12

medium

Order from least to greatest:

0.3,\ 0.29,\ 0.301,\ 0.31

Example 13

medium

How many times larger is the

4

0.4

than the

4

0.04

Example 14

medium

Round

4.768

to the nearest hundredth.

Example 15

medium

Write 'two and thirty-five hundredths' as a decimal.

Example 16

medium

What is

10

times

0.07

? Explain via place value.

Example 17

medium

Which is greater:

0.108

0.11

? Justify by place value.

Example 18

medium

Convert

0.250

to a simplified fraction.

Example 19

medium

7.083

, what is the value of the

8

, written as a decimal?

Example 20

challenge

A digit

d

is in the tenths place and the same digit is in the thousandths place of a number; the two are worth

0.404

together. What is

d

, and what is the number (with

0

hundredths)?

Example 21

challenge

Between

0.2

and

0.3

, list three decimals and explain why infinitely many exist.

Example 22

challenge

Order these by value:

0.6,\ \frac{5}{8},\ 0.625,\ \frac{3}{5}

. Explain using decimals.

Example 23

easy

What digit is in the tenths place of

8.392

Example 24

easy

Write

0.6

as a fraction.

Example 25

easy

Write 'two and four tenths' as a decimal.

Example 26

easy

What is the value of the digit

9

5.09

Example 27

easy

Compare:

0.3

___

0.30

Example 28

medium

Which is greater,

0.27

0.3

Example 29

medium

Order from least to greatest:

0.5, 0.45, 0.504, 0.54

Example 30

medium

What number is

\frac{1}{100}

more than

4.29

Example 31

medium

Round

3.476

to the nearest tenth.

Example 32

medium

Round

0.0834

to the nearest hundredth.

Example 33

medium

What is

0.4 + 0.05

Example 34

medium

What is the difference between the place values of the two

5

s in

5.05

Example 35

hard

Write the decimal that has

3

tenths,

0

hundredths,

4

thousandths, and

6

ten-thousandths.

Example 36

hard

A number rounds to

4.7

when rounded to the nearest tenth. What is the smallest possible such number with two decimal places?

Example 37

hard

What value of digit

d

makes

2.d8 > 2.31

but

2.d8 < 2.51

Example 38

hard

How many times greater is the value of the

7

7.0

than the value of the

7

0.07

Example 39

challenge

Find the smallest decimal greater than

0.5

that uses each of the digits

0

through

5

exactly once after the decimal point.

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Related Concepts

Place Value Adding and Subtracting Decimals Multiplying Decimals Dividing Decimals Rounding

Background Knowledge

These ideas may be useful before you work through the harder examples.

place value