Chapter 3 · Place value and decimals

Read, Write, and Compare Decimals to Hundredths

Learn to read decimals aloud, write them in words and in digits, and compare them one place at a time. Find out why five tenths is more than forty-five hundredths.

12 min read

You already know that a tenth is 1 of 10 equal parts of a whole, and a hundredth is 1 of 100 equal parts. Now you will read decimals, write them and compare them. You will also solve a puzzle that tricks many people: which is greater, $0.5$ or $0.45$ ?

First, here are the words you need. A decimal is a number written with a decimal point, the dot you see in $0.45$ . Each digit (one of the symbols $0$ to $9$ ) sits in a place. A place is a position in the number, and it tells you what the digit counts. Just before the decimal point is the ones place. Just after it come the tenths place and then the hundredths place.

The digits before the decimal point are the whole-number part. The digits after it are the decimal part.

Look at $0.45$ . It has 4 tenths and 5 hundredths. Each tenth is the same as 10 hundredths, so 4 tenths is 40 hundredths. In all, $0.45$ is 45 hundredths. That is why you can read the decimal part as one number and name it by its last place, the place of the final digit. You say forty-five hundredths.

The word name of a decimal is the way you say it, written in words. To find it:

Read the whole-number part. If it is 0, skip this step and the next one.
Say and for the decimal point.
Read the decimal part as if it were a whole number, like 45 or 9. This tells how many parts there are.
Say the name of the last place, tenths or hundredths. This tells the size of the parts.

The table shows four decimals read this way.

Read the decimal part as a number, then name its last place.

Decimal	Whole-number part	Decimal part	Last place	Word name
$0.6$	$0$	$6$	tenths	six tenths
$0.45$	$0$	$45$	hundredths	forty-five hundredths
$2.9$	$2$	$9$	tenths	two and nine tenths
$5.18$	$5$	$18$	hundredths	five and eighteen hundredths

Worked example

Read a decimal with a zero in it

Write $3.07$ in words.

Read the whole-number part first. The digit before the decimal point is 3, so you start with the word “three”.
Say “and” for the decimal point. This word joins the whole-number part to the decimal part.
Read the decimal part as if it were a whole number. The digits after the decimal point are 0 and 7. The 0 tells you there are no tenths, so the count of parts is just 7. Say “seven”.
Name the last place. The last digit, 7, sits in the hundredths place, so the parts are hundredths. Now put the words together in order.
$3.07 = \text{three and seven hundredths}$

Answer

In words, $3.07$ is three and seven hundredths.

Now go the other way. You start with a word name and you write the digits.

The place name at the end tells you where the last digit must sit. Tenths means the last digit sits one place after the decimal point. Hundredths means the last digit sits two places after the decimal point.

Try six hundredths. The 6 must sit in the hundredths place. Six hundredths is too few to make even 1 tenth, because 1 tenth takes 10 hundredths. So the tenths place is empty, and you write $0$ there to hold the place. There are no wholes, so you also write $0$ for the ones. The result is $0.06$ .

The $0$ in the tenths place matters. Without it you would write $0.6$ . That is six tenths, which is the same as 60 hundredths, not 6 hundredths.

Worked example

Write digits from a word name

Write “eight and three hundredths” in digits.

Find the word “and”. It stands for the decimal point. The word before it is “eight”, so write 8 for the ones and then the decimal point.
Read the place name at the end: “hundredths”. The last digit must sit in the hundredths place, so you need two places after the decimal point. Draw one box for the tenths place and one box for the hundredths place.
$8.\,\square\,\square$
The count of parts is “three”. These parts are hundredths, so write 3 in the hundredths box, which is the second box.
$8.\,\square\,3$
The tenths box is still empty. Three hundredths is too few to make even 1 tenth, because 1 tenth takes 10 hundredths. So there are 0 tenths. Write 0 to hold that place.
$8.03$
Check by reading your digits back: 8, then “and”, then a count of 3, and the last place is hundredths. That gives “eight and three hundredths”, so it matches.

Answer

In digits, eight and three hundredths is $8.03$ . The $0$ holds the empty tenths place.

To compare two numbers means to decide which one is greater, or whether they are equal. The symbol $>$ means is greater than. The symbol $<$ means is less than.

Now for the puzzle: which is greater, $0.5$ or $0.45$ ? You can compare two counts fairly only when they count parts of the same size. Here they do not. The number $0.5$ is 5 tenths, but $0.45$ is 45 hundredths.

So change the tenths into hundredths. Each tenth is the same as 10 hundredths, so 5 tenths is the same as 50 hundredths. In symbols, $0.5 = 0.50$ .

The two grids below show both numbers. Each grid is one whole cut into 100 equal parts, so each small part is one hundredth. The first grid shows $0.5$ : 50 parts are shaded. The second grid shows $0.45$ : 45 parts are shaded.

The number

0.5

: five tenths is the same as fifty hundredths, so 50 of the 100 equal parts are shaded.

The number

0.45

: forty-five hundredths, so 45 of the 100 equal parts are shaded.

Look at the shaded parts. The first grid has 50 shaded hundredths. The second grid has 45 shaded hundredths. Both wholes are the same size, and both are cut into hundredths. Now the two counts are fair to compare, and 50 is 5 more than 45.

In words: fifty hundredths is greater than forty-five hundredths.

In symbols: $0.50 > 0.45$ , so $0.5 > 0.45$ .

Key concept

Compare place by place, starting from the left

Line up the two decimals so that ones match ones, tenths match tenths and hundredths match hundredths. If a number has no digit in the hundredths place, it has 0 hundredths, so you may write a $0$ there.

Start at the left end and compare the digits one place at a time. If the digits are the same, move one place to the right. The first place where the digits differ decides. The number with the greater digit in that place is the greater number.

This works because 1 in any place is worth more than all the digits to its right put together. For example, 1 tenth is 10 hundredths, but the hundredths place holds at most 9. So for $0.5$ and $0.45$ , the ones match and the tenths decide: $5 > 4$ , so $0.5 > 0.45$ .

Worked example

Compare when the first digits match

Which is greater, $4.6$ or $4.63$ ? Write your answer with $>$ or $<$ .

Line up the places. The number 4.63 has a digit in the hundredths place, but 4.6 does not. No digit there means 0 hundredths, so you can write 4.6 as 4.60 without changing the amount. Now both numbers show ones, tenths and hundredths.
$4.6 = 4.60$
Start at the left with the ones place. Both numbers have 4 ones. The digits are the same, so this place does not decide. Move one place to the right.
$4 \text{ ones} = 4 \text{ ones}$
Compare the tenths. Both numbers have 6 tenths. The digits are the same again, so move one more place to the right.
$6 \text{ tenths} = 6 \text{ tenths}$
Compare the hundredths. The number 4.60 has 0 hundredths, and 4.63 has 3 hundredths. This is the first place where the digits differ, and 0 is less than 3, so 4.60 is the smaller number.
$0 \text{ hundredths} < 3 \text{ hundredths}$
Write the result with the numbers as they were given. Here the longer decimal is greater, but only because of the 3 in its hundredths place. In the puzzle with 0.5 and 0.45, the shorter decimal was greater. The digits in each place decide, not how many digits there are.
$4.6 < 4.63$

Answer

The greater number is $4.63$ , so $4.63 > 4.6$ . You can also write $4.6 < 4.63$ .

The big idea: a digit gets its meaning from its place.

To read a decimal, read the decimal part as a number and name its last place. $0.45$ is forty-five hundredths.
To write a decimal, put the last digit in the place that the name tells you. Use $0$ to hold an empty tenths place. Seven hundredths is $0.07$ .
To compare decimals, match the places and start from the left. The first place where the digits differ decides.

That is why $0.5 > 0.45$ . Five tenths is the same as fifty hundredths, and fifty hundredths is more than forty-five hundredths.

Up next

Ten Times as Much and One Tenth as Much

15 min read

Continue