Place value in integers and decimals

Before this page: be able to read and write whole numbers and say which digit is which.

What a digit is worth

The same digit can stand for a few hundredths or several million. Its position tells us which. Reading that position is what lets us compare prices, write measurements and keep a calculation in order.

Place value chart
number millions hundred thousands ten thousands thousands hundreds tens ones decimal point tenths hundredths thousandths
worth 1,000,000 100,000 10,000 1,000 100 10 1 point 0.1 0.01 0.001
4,582.307 4 5 8 2 point 3 0 7
6,040 6 0 4 0
470 4 7 0
0.007 0 point 0 0 7
6,312,047.86 6 3 1 2 0 4 7 point 8 6

500 = 5 × 100

  1. The digit 5 says how many.
  2. The hundreds place says what they are: hundreds, each worth 100.

In 4,582.307, the 7 is in the thousandths place. It is worth 7 × 0.001 = 0.007, or seven thousandths.

Now compare the two numbers beginning with 6. In 6,040 it represents six thousand; in 6,312,047.86 it represents six million. The digit is the same, but its value is a thousand times as large.

Digits to the left of the point make the whole-number part, and digits to the right make the decimal part. Each step to the left multiplies the place by 10 and each step to the right divides it by 10.

The commas mark off the whole-number digits in threes from the right: 6,312,047 is 6 million, 312 thousand and 47.

The ones place is the centre

The place names pair outward from ones: tens with tenths, and hundreds with hundredths. The decimal point separates ones from tenths, so the first place to its right is tenths and there is no oneths place.

Zeros that hold a place

Six thousand and forty has no hundreds, so a zero holds the hundreds place open:

6040

six thousand and forty

The 6 is 6 thousands.

640

six hundred and forty

Without that zero the 6 drops into the hundreds place, and the number is 5,400 smaller.

After the point too: seven thousandths is 0.007, with zeros holding the tenths and hundredths places open, while 0.7 is seven tenths, a hundred times as much.

A zero written after the last decimal digit behaves differently: 0.860 and 0.86 are the same number, because the extra zero adds no thousandths. A zero after the last whole-number digit is not spare: 470 is ten times 47.

Reading decimals

4,582.307 is 4,000 + 500 + 80 + 2 + 0.3 + 0.007; the 0 in the hundredths place adds nothing:

The place values in 4,582.307 The number four thousand five hundred and eighty-two point three zero seven. Each digit is labelled with its place and what it is worth: 4 thousands is 4,000, 5 hundreds is 500, 8 tens is 80, 2 ones is 2, 3 tenths is 0.3, 0 hundredths is 0, and 7 thousandths is 0.007. 4 5 8 2 . 3 0 7 thousands 4,000 hundreds 500 tens 80 ones 2 tenths 0.3 hundredths 0 thousandths 0.007 whole-number places decimal places

Example: read 4,582.307 aloud

Say the whole-number part, then the decimal part.

  1. four thousand five hundred and eighty-two The 4 is the thousands group and 582 the ones group: four thousand, then five hundred and eighty-two.
  2. 0.307 is 307 thousandths The last decimal digit stands in the thousandths place, so all three decimal digits count thousandths together.
  3. four thousand five hundred and eighty-two, and three hundred and seven thousandths An “and” joins the two parts.

Read digit by digit, the decimal part is “point three zero seven”; the place reading, three hundred and seven thousandths, is the one that says what the digits are worth. Three tenths, no hundredths and seven thousandths are counted in three different places, so each is written in thousandths first:

3 tenths = 300 thousandths

300 thousandths + 7 thousandths = 307 thousandths

From words to figures

six million, three hundred and twelve thousand and forty-seven, and eighty-six hundredths

Constructing 6,312,047.86 from words Four groups of words point to their matching digit groups. Six million becomes 006, three hundred and twelve thousand becomes 312, forty-seven becomes 047, and eighty-six hundredths puts 8 in the tenths place and 6 in the hundredths place, with the thousandths place empty. Separate the words by place-value group six million three hundred and twelve thousand forty-seven eighty-six hundredths 0 0 6 3 1 2 0 4 7 . 8 6 0 hundreds tens ones hundreds tens ones hundreds tens ones tenths hundredths thousandths millions group thousands group ones group decimal places

Read the whole-number groups separately: 6 million, 312 thousand and 47 give 6,312,047. A zero keeps the hundreds place in the last group.

The decimal part is eighty-six hundredths, or 0.86. Put the two parts together to get 6,312,047.86.

Explore place value

    In words:

    Key points

    • A digit's value depends on its place. Each place is ten times the one to its right.
    • Zeros keep other digits in their places: 3,005 is not 305.
    • A trailing decimal zero does not change the value: 0.80 = 0.8.
    • Read and write large whole numbers in groups of millions, thousands and ones.

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    Ordering integers, decimals and negatives

    Ordering numbers, including negatives and decimals of different lengths.
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