Decimals to Thousandths (Place Value)

Decimals let us write numbers smaller than 1 using place values to the right of the decimal point. The first three places after the point are tenths, hundredths, and thousandths. Each place is one tenth the size of the place before it.

The Decimal Place-Value Chart

• The decimal point separates the whole-number part from the fractional part.
• To the left of the point: ones, tens, hundreds, and so on (each place 10 times the next).
• To the right of the point: tenths (0.1), hundredths (0.01), thousandths (0.001).
• In 2.475 the 2 is ones, the 4 is tenths, the 7 is hundredths, and the 5 is thousandths.

Standard Form

• Write the digits in order with a decimal point separating ones from tenths.
• Use a leading zero when there are no ones: write 0.367 (not .367) for clarity.
• Trailing zeros after the last non-zero digit do not change the value: 0.5 = 0.50 = 0.500.

Word Form

• Read the whole-number part normally, then say "and" for the decimal point.
• Read the digits after the point as a whole number, then name the smallest place value used.
• 0.367 reads as "three hundred sixty-seven thousandths".
• 2.475 reads as "two and four hundred seventy-five thousandths".

Expanded Form

• Break the number into the value of each non-zero digit and add them.
• 2.475 becomes 2 + 0.4 + 0.07 + 0.005.
• 0.306 becomes 0.3 + 0.006 — skip any place whose digit is zero.