Decimal Place Value

Understanding Decimal Place Values with an Interactive Lesson

TENS
0
×10
ONES
0
×1
.
TENTHS
0
×0.1
HUNDRED THS
0
×0.01
THOUSAND THS
0
×0.001
TEN
THOUSAND THS
0
×0.0001
HUNDRED
THOUSAND THS
0
×0.00001
MILLION THS
0
×0.000001
Current number: 0.000000
Decimal places: 6

Understanding Decimal Place Value

Decimals extend the concept of place value from whole numbers to fractions of ten. Just as each digit in a whole number has a specific place value (units, tens, hundreds, etc.), each digit in a decimal number represents a fraction of ten (tenths, hundredths, thousandths, and so on). This lesson will help you grasp the similarities and differences between whole number place values and decimal place values.

Comparing Whole Numbers and Decimals

Whole Numbers:

  • Each place to the left of the decimal point represents a power of ten.
  • Example: In 5,432, the digit 4 is in the hundreds place, meaning 4 × 100 = 400.


Decimals:

  • Each place to the right of the decimal point represents a fraction of ten.
  • Example: In 15.43258, the digit 4 is in the tenths place, meaning 4 × 0.1 = 0.4.

Decimal Place Values

Here’s a breakdown of decimal places:

Place Name Value Fraction
Tenths 0.1 1/10
Hundredths 0.01 1/100
Thousandths 0.001 1/1,000
Ten-Thousandths 0.0001 1/10,000
Hundred-Thousandths 0.00001 1/100,000

Extracting Decimal Values

Method #1

To find the value of a specific decimal digit:

  1. Identify the Place: Determine the place value of the digit.
  2. Calculate the Value: Multiply the digit by its place value.

Method #2

  1. Isolate the Digit: Write down the digit.
  2. Replace Left Digits with Zeroes: Convert all digits to the left of the target digit to zero.
  3. Simplify: Remove unnecessary zeroes to find the decimal value.
Tens Ones Tenths Hundredths Thousandths Ten Thousandths Hundred Thousandths 1 5 . 4 3 2 5 8 10¹ 10⁰ 10⁻¹ 10⁻² 10⁻³ 10⁻⁴ 10⁻⁵ 10 1 0.1 0.01 0.001 0.0001 0.00001

Example showing how to extracting decimal values: 15.43258

Method #1

  • Identify the digit 2 in the thousandths place.
  • Multiply the digit by its place value.: 2 × 0.001 = 0.002

Method #2

  • Identify the digit 2 in the thousandths place.
  • Replace all digits to the left of 2 with zeroes: 00.002.
  • Simplify to 0.002.

More Examples Showing how to Find the Decimal Place Value

Example #1:

For the decimal number 756.45, find the name of the place of the underlined digit.

4 is in the tenths place.

Example #2:

For the decimal number 6214.265, find the name of the place of the underlined digit.

5 is in the thousandths place.

Example #3:

For the decimal number 32564.10477, find the name of the place of the underlined digit.

0 is in the hundredths place.

Example #4:

For the decimal number 50.00009014, find the name of the place of the underlined digit.

9 is in the hundred-thousandths place.


Now, try to find the value of each of the underlined digit above.

  • For 756.45, the value of 4 is 4 × 0.1 and that is equal to 0.4.
  • For 6214.265, the value of 5 is 5 × 0.001 and that is equal to 0.005.
  • For 50.00009014, the value of 9 is 9 × 0.00001 and that is equal to 0.00009.
  • For 32564.10477, the value of 0 is 0 × 0.01 and that is equal to 0.00.
0.00 is of course just 0!

Understanding decimals

Writing decimals in words