Decimals

NZ Level 5

Compare numbers with decimal components beyond thousandths

Lesson

We can compare decimals just like we compare whole numbers. Decimals are written to the right hand side of the decimal point on the place value table. Just like whole numbers, this pattern continues through tenths, hundredths, thousandths and many more!

The tenths column is the biggest in value after the decimal point. So if we're comparing decimals, the larger one will be the one with the largest number in the tenths column, regardless of what numbers are after it. If there is no number written, then just imagine that there is a zero there instead (eg. $0.7$0.7 is the same as $0.70$0.70).

**Evaluate:** Which decimal is bigger $0.87$0.87 or $0.23$0.23?

**Think: **We can think of $0.87$0.87 as $\frac{87}{100}$87100 and $0.23$0.23 as $\frac{23}{100}$23100

If we say the number out loud, sometimes the bigger one becomes obvious. Lets try it,

$87$87hundredths and $23$23 hundredths. Because they have the same name (hundredths) its easy to see the $87$87 hundredths is bigger.

**Do:** $0.87$0.87

Try another one,

**Evaluate:** Which decimal is bigger $0.3$0.3 or $0.15677$0.15677?

**Think:** In this case, saying the number aloud doesn't help us yet,

($3$3 tenths and $15677$15677 hundred thousandths) This is because the names are not the same. We could try to convert them to be numbers of the same name, this would give us $0.30000$0.30000 which is $30000$30000 hundred thousandths and $15677$15677 hundred thousandths - but maybe there is an easier way.

And there is!

If we just look at the value in the columns and compare them from left to right we can find the bigger (or smallest number).

One number has a $3$3 in the tenths column and the other has a $1$1, so the one with the $3$3 is bigger.

**Do:** $0.3$0.3

But what about when they have the same number in the tenths column? Well that's when we look to the next column (the hundredths column) and compare which number is bigger/ smaller in just the same way.

Evaluate**: **Which number is smaller $0.13$0.13 or $0.121$0.121?

**Think: **The tenths columns both have ones so we need to look at the hundredths columns- one has a $3$3 and one has a $2$2 so the decimal with the $2$2 is smaller.

We can still do this question by making them have the same name,

$130$130 thousandths vs $121$121 thousandths. Here we can see that the $121$121 thousandths is smaller.

**Do:** $0.121$0.121

Think you've got it? Let's do one more example to make sure.

**Evaluate: **Which number is bigger $0.55$0.55 or $0.552$0.552

**Think: **The numbers in the tenths and hundredths columns are the same in both numbers, so now we will look at the thousandths- $0$0 and $2$2.

And also, we could do this one this way, $550$550 thousandths vs $552$552 thousandths. So here the $552$552 thousandths is bigger.

**Do: **$0.552$0.552

Once we know how to tell the size of numbers with decimals, we can arrange them in different orders.

If you need a refresher on symbols that tell us about the size of numbers and how to order them, please click here.

Is $0.4$0.4 greater than $0.33$0.33?

Yes

ANo

BYes

ANo

B

Arrange $0.19$0.19, $0.392$0.392, $0.499$0.499 and $0.278$0.278 in ascending order.

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Reason with linear proportions.