Unit 1 · Topic 04 · Number System & Notation
The shopkeeper added up Anaya's basket in about four seconds and said 'roughly eight hundred'.
The till took twenty seconds and said 790.
He had not guessed. He had rounded — and he knew before the till did that eight hundred was close enough.
Anaya was buying supplies for a class project: 478 rupees of card, 312 rupees of paint. She was still reaching for her phone's calculator when the shopkeeper said, "About eight hundred."
Anaya typed it in anyway. 790. She looked up, ready to correct him, and stopped. Eight hundred was not the answer — but it was very nearly the answer, and he had got there before she had unlocked her phone.
"How?" she asked.
"478 is nearly 500," he said, wrapping the card. "312 is nearly 300. Five hundred and three hundred is eight hundred. I do not need the exact number to know you have enough in your hand."
At school the next day Anaya asked Ms. Rao whether that counted as maths or as cheating.
Ms. Rao wrote 478 on the board and drew a number line from 400 to 500, marking 450 in the middle. "Where does 478 sit?"
"Past the middle," said Anaya.
"So it is closer to 500 than to 400. That is the whole rule. You are not guessing — you are choosing the nearer landmark."
Then she wrote 312 and drew 300 to 400 with 350 in the middle. 312 sat well to the left. Closer to 300.
"But how do you decide without drawing a line every time?" asked Kabir.
"You look at ONE digit," said Ms. Rao. "The one just to the right of where you are rounding. For hundreds, that is the tens digit. In 478 the tens digit is 7, which is 5 or more, so it goes up. In 312 the tens digit is 1, which is under 5, so it stays."
Anaya tried 6,450 to the nearest thousand. The hundreds digit was 4. Under five. It stayed at 6,000.
"So rounding is not being lazy," she said.
"It is knowing how much accuracy the question actually needs," said Ms. Rao. "The shopkeeper needed to know you could pay. He did not need the paisa."
Rounding replaces a number with a nearby landmark that is easier to work with. You lose some exactness and gain a great deal of speed.
To round, look at ONE digit only: the digit immediately to the RIGHT of the place you are rounding to. If it is 5 or more, the rounding digit goes up by one. If it is 4 or less, the rounding digit stays as it is.
Everything to the right of the rounding place then becomes zero. That part is not optional — 4567 rounded to the nearest hundred is 4600, never 4567 with a mark over it.
Estimation is rounding put to work. Round each number first, then add, subtract or multiply the easy numbers. The result is not the exact answer and is not meant to be — it is a check that tells you instantly if an exact answer is wildly wrong.
Add up a shopping bill in your head by rounding every item to the nearest ten, then check with a calculator.
Write down how far off your estimate was. Do it again next week and see whether the gap shrinks.
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