Chapter 3 · Place value and decimals
Read and Write Decimals to Thousandths
Learn the tenths, hundredths and thousandths places. Read decimals aloud, write them in words, and write them in digits with zeros holding empty places.
You already work with decimals such as . A decimal is a number written with a decimal point, the dot in the number. The digits on the left of the dot are the whole-number part. The digits on the right show an amount that is less than one whole.
You know the first two places after the decimal point: tenths and hundredths. Today you add a third place. To see what it means, picture one whole cut into equal parts.
- Cut 1 whole into 10 equal parts. Each part is one tenth.
- Cut each tenth into 10 equal parts. Now the whole has 100 equal parts. Each part is one hundredth.
- Cut each hundredth into 10 equal parts. Now the whole has 1,000 equal parts. Each part is one thousandth.
So a thousandth is one of 1,000 equal parts of one whole. Listen for the ths at the end: a thousand is a big number, but a thousandth is a tiny part. Each kind of part has its own place after the decimal point.
| Place | Where it sits | A 1 in this place is worth | In words |
|---|---|---|---|
tenths | 1st place after the decimal point | one tenth | |
hundredths | 2nd place after the decimal point | one hundredth | |
thousandths | 3rd place after the decimal point | one thousandth |
You write every number with digits, the symbols 0 to 9. The place of a digit is the spot where it sits in the number. The value of a digit is how much it is worth. To find the value, you need both the digit and its place.
The pattern you know from whole numbers keeps going to the right of the decimal point. Each place is worth of the place on its left. So 10 thousandths make 1 hundredth, 10 hundredths make 1 tenth, and 10 tenths make 1 whole.
To give the value of a digit, say the digit and then its place. In , the 7 sits in the hundredths place. Its value is 7 hundredths, which you can write as or . The table shows every digit in .
| Digit | Place | Value in words | Value as a number |
|---|---|---|---|
ones | 4 ones | ||
tenths | 2 tenths | ||
hundredths | 7 hundredths | ||
thousandths | 5 thousandths |
Worked example
Find the place and value of a digit
In , name the place of the digit and give its value. Then do the same for the digit .
Find the decimal point and count the places to its right. The 1st place is tenths, the 2nd is hundredths and the 3rd is thousandths. So 3 is in the tenths place, 8 is in the hundredths place and 4 is in the thousandths place.
The digit 4 is in the thousandths place, so its value is 4 thousandths. That is 4 of the 1,000 equal parts of one whole. To write this value as a decimal, keep the 4 in the thousandths place and write a 0 in each place before it.
The digit 3 is in the tenths place, so its value is 3 tenths. That is 3 of the 10 equal parts of one whole. Keep the 3 in the tenths place and write a 0 in the ones place.
Answer
In , the digit is in the thousandths place and is worth 4 thousandths, or . The digit is in the tenths place and is worth 3 tenths, or .
Now you can read the decimal part, the digits after the decimal point. Look at . You could name each digit by itself: 2 tenths, 7 hundredths and 5 thousandths. That is a lot to say. A shorter way is to trade every part for thousandths, the smallest part in this number.
- 2 tenths is the same amount as 200 thousandths, because each tenth holds 100 thousandths.
- 7 hundredths is the same amount as 70 thousandths, because each hundredth holds 10 thousandths.
- 5 thousandths stays 5 thousandths.
All together, that is thousandths. So you read as two hundred seventy-five thousandths.
The digits after the decimal point give you the number, 275. The place of the last digit gives you the name, thousandths. You already read tenths and hundredths this way, as the table shows.
| Decimal | Place of the last digit | In words | As a fraction |
|---|---|---|---|
tenths | two tenths | ||
hundredths | twenty-seven hundredths | ||
thousandths | two hundred seventy-five thousandths |
Key concept
The last place names the decimal part
After the decimal point, a digit's place tells you what kind of part it counts: tenths, hundredths or thousandths. The place of the last digit gives the decimal part its name.
To read a decimal with up to three digits after the decimal point:
- If the whole-number part is greater than 0, read it. Then say and for the decimal point. If it is 0, skip this step.
- Read the digits after the decimal point as one whole number. Do not say zeros that come in front.
- Say the place of the last digit: tenths, hundredths or thousandths.
So is four and two hundred seventy-five thousandths, and is two hundred seventy-five thousandths.
Worked example
Write a decimal in words
Read aloud and write it in words.
Start with the whole-number part. The digit to the left of the decimal point is 3, so say "three". This part is greater than 0, so say "and" for the decimal point.
Read the digits after the decimal point as one whole number. The digits are 0, 4 and 7. A zero in front does not change a whole number, so you read "forty-seven".
Name the place of the last digit. The 7 is the 3rd digit after the decimal point, so it sits in the thousandths place. The values agree: there are 0 tenths, the 4 hundredths are 40 thousandths, and 7 more thousandths make 47 thousandths.
Join the parts in order: three, then "and", then forty-seven thousandths. The line below shows the same amount as a whole number and a fraction.
Answer
In words, is three and forty-seven thousandths.
Now go the other way. You start with a word name, which is a number written in words, and you write it in digits.
When you read, the place of the last digit gives the name. So when you write, the place name tells you where the last digit must sit: the 1st place after the decimal point for tenths, the 2nd place for hundredths and the 3rd place for thousandths.
Sometimes this leaves empty places between the decimal point and your digits. Write a 0 in each empty place. A zero used this way is a placeholder. It is worth nothing itself, but it keeps the other digits in their correct places.
You have done this with hundredths. Nine hundredths is , with one zero holding the tenths place. Nine thousandths needs the 9 in the 3rd place, so two zeros hold the tenths and hundredths places: .
When there is no whole-number part, write a 0 in the ones place as well.
Worked example
Write a decimal in digits
Write twenty and thirty-six thousandths in digits.
Find the word "and". It stands for the decimal point. The words before it name the whole-number part, twenty. Write 20 and then a decimal point.
The decimal part is thirty-six thousandths. The place name is thousandths, so the last digit, 6, must sit in the 3rd place after the decimal point. The 3 sits just before it, in the 2nd place. The box marks the place that is still empty.
The empty place is the 1st place after the decimal point, the tenths place. Write a 0 there as a placeholder, so the 3 and the 6 stay in the hundredths and thousandths places.
Check by reading your number back. The whole-number part is twenty. The digits after the decimal point read thirty-six, and the last digit is in the thousandths place. That matches the word name.
Answer
In digits, twenty and thirty-six thousandths is .
Here is what to remember. After the decimal point, each digit counts the parts named by its place: tenths first, then hundredths, then thousandths. To read the decimal part, read its digits as one number and name the place of the last digit. To write a decimal from its word name, put the last digit in the place the name tells you and use zeros to hold any empty places.
Next, you will break a decimal apart into the values of its digits and write it in expanded form.