Chart for Decimal Places

Every digit after a decimal point has a place and a value: tenths, hundredths, thousandths and beyond. Type a number and this chart puts each digit in its column, writes the number in words and in expanded form, rounds it to any number of decimal places, compares it with another decimal and converts it to a fraction — making place value visible at a glance.

The decimal places

Each place to the right is worth one-tenth of the place before it. Notice the names: tens and tenths, hundreds and hundredths — the “th” marks the decimal side.

Reading and writing decimals

1. Read the whole-number part normally.
2. Say “and” for the decimal point.
3. Read the digits after the point as a whole number.
4. Finish with the place name of the last digit: 3.27 is “three and twenty-seven hundredths”.
5. In everyday speech people often say “three point two seven”, which is also correct.

Worked example

For 3,406.2758: the 2 is in the tenths place (0.2), 7 in the hundredths (0.07), 5 in the thousandths (0.005) and 8 in the ten-thousandths (0.0008). In words it is “three thousand four hundred six and two thousand seven hundred fifty-eight ten-thousandths”. Rounded to two decimal places it is 3,406.28, because the thousandths digit (5) rounds the hundredths up. As a fraction it is 34,062,758/10,000, which simplifies to 17,031,379/5,000.

Rounding decimals

1. Find the place you’re rounding to.
2. Look at the digit immediately to its right.
3. If it is 5 or more, add one to the rounding digit; if it is 4 or less, leave it.
4. Drop all the digits to the right.

Round 2.346 to one decimal place: the tenths digit is 3 and the next digit is 4, so it stays 2.3. Round it to two places: the next digit is 6, so 2.346 becomes 2.35.

Comparing decimals

• Line up the decimal points.
• Compare digits from left to right; the first place where they differ decides.
• Add zeros to make the numbers the same length if it helps: 0.5 = 0.50 > 0.45.
• A longer decimal isn’t necessarily bigger: 0.4 is greater than 0.3999.

Decimals and fractions

To turn a terminating decimal into a fraction, write the digits over 10, 100, 1,000… (by the number of decimal places) and simplify: 0.375 = 375/1000 = 3/8.

Decimals in everyday life

Knowing which place a digit is in tells you how much it matters: a change in the tenths place of a price is ten cents; a change in the thousandths is a tenth of a cent.

Adding and subtracting decimals

1. Write the numbers in a column with the decimal points lined up.
2. Fill empty places with zeros so every number has the same number of decimal places.
3. Add or subtract as with whole numbers, regrouping as needed.
4. Put the decimal point in the answer directly below the others.

Example: 12.5 + 3.47 → 12.50 + 3.47 = 15.97. Lining up the points keeps tenths with tenths and hundredths with hundredths — the place value chart makes this visible.

Multiplying and dividing by 10, 100 and 1,000

Multiplying by 10 moves every digit one place to the left — 3.47 × 10 = 34.7; by 100 two places — 347; by 1,000 three places — 3,470. Dividing moves digits to the right: 3.47 ÷ 10 = 0.347. Thinking of digits moving (rather than the decimal point jumping) matches how the place value chart works.

Common mistakes

• Thinking 0.25 is bigger than 0.3 because 25 > 3.
• Reading 0.07 as “seven tenths” instead of seven hundredths.
• Forgetting to regroup when rounding 2.97 to one place (it becomes 3.0).
• Losing place value when adding: line up the decimal points first.

Printable place value pack

The optional pack includes printable decimal place value charts (to thousandths and ten-thousandths), blank charts, rounding and comparing worksheets with answers and a fraction–decimal conversion card. The interactive chart above is free.

AI-assisted content

This page was drafted with AI assistance and reviewed by Kedop.