Rounding Numbers

Y5: Rounding Numbers

How does it work?

What is rounding?

Rounding a number changes it to make it more convenient to remember and calculate with.

​

​A rounded number is simpler and also less exact.

Why should we round?

A rounded number is less exact, but easier to use.

​

​Add 12,364 + 9,647 vs Add 12,000 + 10,000

​

​It's useful when we don't need to be exact. For example when you:

​estimate prices,

​When to round

​"I have £7.00 and each bag of candy costs £1.79 That's about £2 each, so I can afford 3 bags of candy."

(7÷2= 3 r1 is much easier than 7÷1.79=3.91061453 and it's all I need to know for my purpose- buying as much candy as I can!)

​

"It takes me 25 minutes to walk to school, so I'd better round it off and leave 30 minutes before I need to get there."

​

​When to round

​"Kampala has about 4 million people and New York City has about 9 million, so Kampala has less than half as many residents."

​(3,469,510 people in Kampala compared with 8,804,190 in NYC)

​

​"I calculated 14,768 + 2,821 and I got 16,589, but if I check by rounding, 15,000+3,000= 18,000 so my answer seems too low. I'd better retry."

When NOT to round

When might rounding be a bad, or even dangerous, idea?

When NOT to round

​

When you have to be specific:

​

​taking medicine, setting the table for dinner, measuring the rocket fuel you need to get to space, programming a computer or machine, "clocking" your hours at work, programming missiles in the military, baking cookies, ...

Multiple Choice

What is the purpose of rounding a number?

• To change it. 

• To make it easier to work with.

• To make it less accurate.

• To make it lower.

Multiple Choice

When is a good time to round?

• When I need to estimate how many toys I can buy with my money.

• When I need an exact number of something.

• When a doctor is giving a specific amount of medicine.

• When I need to make a precise measurement.

Multiple Choice

Which happens when a number is rounded?

• It gets more accurate.

• It gets higher.

• It gets lower.

• It gets less accurate.

How do we round?

We can round to different place values depending on the precision we need.

​

​The more exact we need to be, the less we round the number.

​

​724,851

How do we round?

​724,851 = 724,850

​​724,851 = 724,900

​​724,851 = 725,000

​​724,851 = 720,000

​​724,851 = 700,000

Step 1: Identify which multiples the place value sits between.

Rounded to the TENS place, which multiples do these numbers sit between?:

​

​13

​47

​268

​1,456

Step 1: Identify which multiples the place value sits between.

Rounded to the TENS place, which multiples do these numbers fall between?:

​

​47

1,456

​40

50

​1,450

1,460

Step 1: Identify which multiples the place value sits between.

Rounded to the THOUSANDS place, which multiples do these numbers sit between?:

​

3,645

​3,000

4,000

​22,000

23,000

22,304

Step 1: Identify which multiples the place value sits between.

Rounded to the HUNDREDS place, which multiples do these numbers fall between?:

​

24,108

?

?

?

?

964

Step 1: Identify which multiples the place value sits between.

68

?

?

Rounded to the HUNDREDS place, which multiples do these numbers come between?:

​

12,986

2,071

Multiple Choice

Which multiples of 100 does 3,658 fall between?

• 600 and 700

• 3,000 and 4,000

• 3650 and 3750

• 3,600 and 3,700

Multiple Choice

Which THOUSANDS is 561 between?

• 500 and 600

• 1,000 and 2,000

• 0 and 1,000

• None

Multiple Choice

Which multiples of TEN-THOUSAND does 264,300 fall between?

• 264,300 and 264,400

• 260,000 and 270,000

• 200,000 and 300,000

• 264 and 274

​Step 2: Look at the place value on the right to determine which multiple the numeral is closest to.

​Step 1) decide which multiples the place value is between:

If rounding to the THOUSANDS, 14,687 is between 14,000 and 15,000.

​Step 2) Look at the place value to the right:

The hundreds place to the right shows 6 hundreds.

That tells me the number is closer to 15,000.

15,000

14,000

​Step 1) decide which multiples the place value is between:

If rounding to the THOUSANDS, 14,687 is between 14,000 and 15,000.

​Step 2) Look at the place value to the right:

The hundreds place to the right shows 6 hundreds.

That tells me the number is closer to 15,000.

14,687

​ *

​Step 2: Look at the place value on the right to determine which multiple the numeral is closest to.

​Since 5 is in the middle of two multiples, we count it as closer to the LARGER multiple. That means 0-4 is closer to the smaller multiple and 5-9 is closer to moving up to the next round number.

​Step 1) decide which multiples the place value is between:

If rounding to the THOUSANDS, 14,687 is between 14,000 and 15,000.

​Step 2) Look at the place value to the right:

The hundreds place to the right shows 6 hundreds.

That tells me the number is closer to 15,000.

​0

​1

​2

​3

​4

​5

​6

​7

​8

​9

​10

Multiple Choice

Which place value is to the RIGHT of the thousands?

• ones

• tens

• thousands

• hundreds

Multiple Choice

Which place value is to the RIGHT of the hundreds?

• ones

• tens

• thousands

• hundreds

Multiple Choice

Which place value is to the RIGHT of the ten thousands?

• ones

• tens

• thousands

• hundreds

Multiple Choice

Which digits to the right of the place value tell us we are closer to the next multiple up (rounding up)?

• 0, 2, 4, 6, 8

• 0, 1, 2, 3, 4

• 1, 3, 5, 7, 9

• 5, 6, 7, 8, 9

Multiple Choice

Which digits to the right of the place value tell us we are closer to the last multiple down (rounding down)?

• 0, 2, 4, 6, 8

• 0, 1, 2, 3, 4

• 1, 3, 5, 7, 9

• 5, 6, 7, 8, 9

​Step 3:

Round down if the place value to the right has 0-4

​Round up if the place value to the right has 5-9

Round to the TENS: 34,786

​Step 1) decide which multiples the place value is between

​Step 2) Look at the place value to the right

​Step 3) Round: 34,786 rounds up to the nearest TENS multiple 34,790

​Step 1) decide which multiples the place value is between:

If rounding to the THOUSANDS, 14,687 is between 14,000 and 15,000.

​Step 2) Look at the place value to the right:

The hundreds place to the right shows 6 hundreds.

That tells me the number is closer to 15,000.

​34,780

​34,790

​*

​Step 3:

Round down if the place value to the right has 0-4

​Round up if the place value to the right has 5-9

Round to the THOUSANDS: 14,341

​Step 1) decide which multiples the place value is between

​Step 2) Look at the place value to the right

​Step 3) Round: 14,341 rounds down to the nearest THOUSANDS multiple 14,000

​Step 1) decide which multiples the place value is between:

If rounding to the THOUSANDS, 14,687 is between 14,000 and 15,000.

​Step 2) Look at the place value to the right:

The hundreds place to the right shows 6 hundreds.

That tells me the number is closer to 15,000.

​14,000

15,000

​*

Multiple Choice

Does 456 round up or down to the TENS place?

• rounds up in the 10s

• rounds down in the 10s

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Choose the number which rounds DOWN to the TENS place.

• 309

• 744

• 1,317

• 2,095

Multiple Choice

Choose the number which rounds UP to the THOUSANDS place.

• 3,561

• 9,088

• 421

• 13,498

Multiple Choice

Choose the number which rounds UP in the HUNDREDS place.

• 5,735

• 10,326

• 548

• 1,362

Multiple Choice

Choose the number which rounds UP in the TEN THOUSANDS place.

• 4,724

• 14,971

• 86,401

• 23,468

Open Ended

Write any number which rounds DOWN in the TENS and HUNDREDS, but rounds UP in the THOUSANDS.