Place Value Chart & Expanded Form

About the Place Value Chart & Expanded Form

Type any number — up to 18 digits before the point and 6 after — and see every digit in its column of a place value chart, in both the Indian system (ones, thousands, lakhs, crores …) and the international system (ones, thousands, millions, billions …). Choose a digit to see its place, its face value and its place value in both systems.

The page also writes the number in expanded form five ways (4,00,000 + 50,000 + …, digits × place values, decimals as fractions, powers of ten, and place names), in words in either system — with decimals read with “point” or as tenths, hundredths and thousandths — and lists the face value and place value of every digit. Everything is worked out from the digits themselves, so nothing is ever rounded.

For teachers, Printable place value chart makes a PDF chart to fill in — blank, or with your numbers already in their columns for an answer key.

Common uses

• Homework on place value, expanded form and number names, in the Indian or the international system.
• Converting between lakh and crore and million and billion: 2.5 crore is 25 million.
• Checking the place value of a digit, or the difference between its face value and its place value.
• Reading long decimals correctly — to thousandths and beyond — in words.
• Printing blank place value charts, or charts filled in as an answer key, for a class.

The Indian and international systems

Both systems start the same way — ones, tens, hundreds, then thousands and ten thousands — and differ after that. The international system gives a new name to every third place: thousands, millions, billions, trillions, so its digits are grouped in threes (1,234,567). The Indian system names every second place after the thousands — lakhs and crores — so its digits are grouped as 12,34,567: the first three from the right, then in pairs.

• 1 lakh = 1,00,000 = 100,000 (one hundred thousand)
• 10 lakh = 10,00,000 = 1,000,000 (one million)
• 1 crore = 1,00,00,000 = 10,000,000 (ten million)
• 100 crore = 1,00,00,00,000 = 1,000,000,000 (one billion)
• 1 lakh crore = 10¹² (one trillion)

Above ten crores, the traditional Indian names are arab (100 crore), kharab (100 arab), neel, padma and shankh, and the chart uses them; in everyday Indian English most people keep counting in crores instead (100 crore, 1 lakh crore), which is how the words are written. Numbers of ten or more digits are also written with arab and kharab.

Expanded form, five ways

• Place values added: each non-zero digit times the value of its place: 4,00,000 + 50,000 + 6,000 + 700 + 80 + 9.
• Digits × place values: (4 × 1,00,000) + (5 × 10,000) + … + (9 × 1).
• Decimals as fractions: the same, with decimal places written as fractions: (3 × 1/10) + (7 × 1/100).
• Powers of ten: (4 × 10⁵) + (5 × 10⁴) + … + (9 × 10⁰) + (3 × 10⁻¹): the exponent is the place, counted from the ones.
• Place names: 4 lakhs + 5 ten thousands + … + 3 tenths.

Zero digits are left out of every form, as textbooks usually do: 9,08,07,060 = 9,00,00,000 + 8,00,000 + 7,000 + 60 has no ten lakhs, ten thousands, hundreds or ones term. The face value table still lists the zeros, with a place value of 0.

Face value and place value

The face value of a digit is the digit itself, wherever it stands. Its place value is the digit times the value of its place: in 4,56,789 the 5 has face value 5 and place value 5 × 10,000 = 50,000. A 0 has face value and place value 0 in every place. In 0.375, the 7 is in the hundredths place, so its place value is 7 × 1/100 = 0.07.

Reading decimals

There are two usual ways to say a decimal. With point, the digits after the point are read one by one: 12.345 is “twelve point three four five”. As a fraction of the last place, the digits after the point are read as one number, followed by the name of the last place: “twelve and three hundred forty-five thousandths” — the way many American textbooks write the word form. A zero in the last place still counts: 2.50 is “two and fifty hundredths”.

Printable charts

The PDF chart has a column for every place from the highest place you choose — thousands to ten kharabs in the Indian system, thousands to hundred trillions in the international one — and, if you like, tenths, hundredths and thousandths after a decimal point column. Period headings (Lakhs, Crores … or Thousands, Millions …) and a short heading (L, TL, HTh …) with the full place name sit at the top, with heavier lines between periods. Choose the number of blank rows, list numbers to fill in their own rows (for an answer key or a worked example), add a column to write each number, a title and a name line. Wide charts are turned to landscape, and long ones continue on a new page with the headings repeated.

Limitations

• Up to 18 digits before the decimal point (hundreds of quadrillions, or shankhs in the Indian system) and 6 after it (millionths). Round a longer decimal first; the message suggests the rounded number.
• Words are written in English. The Indian words use the crore-based style (twelve thousand three hundred forty-five crore …); the arab and kharab style is shown as well for numbers of ten or more digits. Numbers must be typed in digits: “2 lakh 50 thousand” is understood, “two lakh fifty thousand” is not.
• A negative number’s digits are shown like any other, with “minus” in front of the words; place value is about the digits, not the sign.
• The printable chart’s PDF uses the standard Helvetica and Symbol fonts, so a title in a non-Latin script is printed with “?” for those letters (the page tells you); the place names and digits always print.

Privacy

Everything is worked out in your browser and nothing you type is uploaded. Your last number and your choices (number style, system, paper) are kept in this browser’s storage.