Approximation and Errors

Hong Kong

Stage 1 - Stage 3

Lesson

When we make an estimation of something, we do more than just guess. We use logic, and look for things we might be able to work out, without solving a problem fully. This can be useful to make decisions on purchases, how long something may take, or how far away something is.

Rounding is a way to simplify our numbers, to help us with estimating. With whole numbers, we might round to the nearest ten, or hundred. With decimals, we might round to the nearest unit, tenth or hundredth. It's the same as asking if $13$13 closer to $10$10, or closer to$20$20?

In Video 1, we work through some examples of rounding, and finish off identifying the rule we can follow for any number.

When we know how to round, can use our rounded answers to estimate the answer to number problems. The leading digit, is the first digit in our number. (Think of the word 'leading' as 'going first'). Once we know that, we can round our number, and work out an estimate to our problem. Take a look at how we use leading digit estimation to solve addition and subtraction problems in Video 2.

We can also use leading figure estimation to make a logical guess with multiplication

and division problems. In fact, this is where it is a great help, especially when you consider some real life problems.

What if we are asked to round a number to a decimal place? You might be asked to round a number to the nearest tenth, hundredth etc. to add some scores together. In Video 2, we'll look at each of these scenarios, and see more of the powers of estimation. Remember, with decimals, we can still think of the place value of each digit.

Remember!

Leading figure estimation means we look at which place the first, or leading, digit is in. That's the place we round our number to.

By leading figure estimation, approximate the value of $2692+3669$2692+3669

By leading figure estimation, approximate the value of $448\times39$448×39

Consider the place-value chart for the number $8739142$8739142.

Millions period | Thousands period | Ones period | ||||||||

hundreds | tens | ones | hundreds | tens | ones | hundreds | tens | ones | ||

$8$8 | $7$7 | $3$3 | $9$9 | $1$1 | $4$4 | $2$2 |

In order to round $8739142$8739142 to the nearest million, we have to look at the millions digit.

What is the millions digit?

What is the digit to the right of the millions place?

What should happen to the digit that is to be rounded?

We add $1$1 to it.

AWe do not change it.

BHence, what is $8739142$8739142 rounded to the nearest million?