Unit 1 · Topic 02 · Number System & Notation
Kabir wrote a cheque for four lakh five thousand rupees.
He wrote the figures as 4,05,000 and the words as 'four lakh fifty thousand'.
The bank returned it. One zero had cost him forty-five thousand rupees.
Kabir's father had asked him to fill in the amount on a cheque, carefully, in both figures and words. Kabir liked this job. He wrote the figures first: 4,05,000.
Then he wrote the words underneath. He looked at the 4, wrote 'four lakh'. He looked at the 5 and wrote 'fifty thousand'. He signed it and felt pleased.
The bank sent it back with a slip attached. Figures and words do not match.
Kabir was certain the bank was wrong. There was a 5 in the number, and he had written a five in the words. He took it to Ms. Rao.
Ms. Rao did not tell him the answer. She drew a place value chart on the board and asked him to drop each digit into its own column: 4 in lakhs, 0 in ten-thousands, 5 in thousands, 0 in hundreds, 0 in tens, 0 in ones.
"Now read me the 5," she said. "Not the digit. What it is worth."
Kabir looked at the chart. The 5 was sitting in the thousands column. Five thousand. Not fifty thousand.
"But it's a five," he said.
"It is always a five," said Ms. Rao. "That never changes. What changes is where it sits. In your number the ten-thousands column has a zero in it — and you read straight past that zero as if it were not there."
She wrote both numbers one above the other: 4,05,000 and 4,50,000. Same digits. The 5 had moved one column left in the second one, and the number had grown by forty-five thousand rupees.
Kabir looked at the two lines for a long moment. "The zero was doing a job," he said.
"Holding the place," said Ms. Rao. "That is the entire job of a zero, and it is not a small one."
Every digit in a number carries two different values, and mixing them up is what went wrong on Kabir's cheque.
The FACE value of a digit is just the digit itself. The face value of 5 is 5, wherever it sits, always.
The PLACE value of a digit is what it is worth because of the column it occupies. In 4,05,000 the 5 sits in the thousands column, so its place value is 5,000. Move that same 5 one column left and its place value becomes 50,000.
Expanded form writes a number as the sum of the place values of its digits: 4,05,000 becomes 400000 + 5000. A zero contributes nothing, so it is simply left out of the sum — but it must still be written in the number itself, because it is holding a column open.
Write today's date as a single number, then your house number, then your pin code.
For each one, circle a digit and say both its face value and its place value out loud. They should be different every time except in the ones column.
Loading questions…