Place Value Chart: Decimals, Words, Rounding and Blocks

What place value means

In our number system the position of a digit decides what it is worth. In 4,508,092 the 5 is in the hundred thousands place, so it is worth 500,000, not 5. Each place is ten times the place to its right and one tenth of the place to its left. That one rule works in both directions across the decimal point, from hundred trillions down to trillionths.

How to read the chart

1. The big headings (Ones, Thousands, Millions, Billions, Trillions) are periods. Digits are read in groups of three, and the comma in a number marks the break between periods.
2. Under each period are the hundreds, tens and ones places of that period.
3. The decimal point sits between the ones and the tenths. Decimal places end in “ths”: tenths, hundredths, thousandths and so on.
4. Zeros are placeholders. In 4,508,092 the zero in the ten thousands place holds that place open so the 5 lands in the hundred thousands.

Digit, place and value

The digit is the symbol 0 to 9. The place is where it sits. The value is the digit times the place value. In 325.67, the 6 is in the tenths place, so its value is 6 × 0.1 = 0.6, and the 7 in the hundredths place is worth 0.07.

Expanded form

Expanded form writes a number as the sum of the values of its digits: 325.67 = 300 + 20 + 5 + 0.6 + 0.07. Zero digits are skipped because they add nothing. You can also show the multiplication (3 × 100 + 2 × 10 + 5 × 1 + 6 × 0.1 + 7 × 0.01) or use fractions for the decimal places.

How rounding works

To round to a place, look at the digit one place to the right. If it is 5 or more, round up; if it is 4 or less, round down. Then replace every digit to the right of the rounding place with zero, and drop zeros that fall after the decimal point. For example, 325.67 rounded to the nearest tenth is 325.7, and to the nearest ten is 330. This tool rounds half away from zero, which is how most classrooms teach it.

Reading decimals in words

Read the whole-number part, say “and” for the decimal point, then read the digits after the point as a whole number and finish with the name of the last place. So 325.67 is “three hundred twenty-five and sixty-seven hundredths”. The alternative is to say “point” and read each digit: “three hundred twenty-five point six seven”. Both are shown in the tool.

For teachers and parents

Switch to Teacher worksheet mode to print a blank chart, or to make a worksheet with a new set of numbers each time and an answer key. Student practice mode asks about the value of a digit, which place it is in, rounding, and writing a number from words. Base-ten blocks show whole numbers up to 9,999 and decimals up to 9.99 with a flat standing for one.

Practice questions

Sources

• Common Core State Standards: Number and Operations in Base Ten (grades K to 5)
• Common Core State Standards, Grade 5: Understand the place value system