Math Core

In fourth grade you worked with tenths and hundredths. Some measurements need even smaller pieces: a race can be won by 0.004 second, and a vitamin pill might weigh 0.125 gram. In this lesson you add the thousandths place and learn to read, write and break apart decimals like these.

The thousandths place

The place value pattern keeps going to the right of the decimal point. Each place is $\dfrac{1}{10}$ of the place to its left.

1 whole split into 10 equal parts gives tenths.
1 tenth split into 10 equal parts gives hundredths.
1 hundredth split into 10 equal parts gives thousandths.

So 1 whole is 1,000 thousandths, and 1 tenth is 100 thousandths.

Here is the number 263.841 in a place value chart.

hundreds	tens	ones	.	tenths	hundredths	thousandths
2	6	3	.	8	4	1

The 8 is in the tenths place, so it is worth $\dfrac{8}{10}$ , or 0.8. The 4 is worth $\dfrac{4}{100}$ , or 0.04. The 1 is worth $\dfrac{1}{1{,}000}$ , or 0.001.

Definition

Thousandth

One thousandth is one of 1,000 equal parts of a whole:

\frac{1}{1{,}000} = 0.001

It is the third place to the right of the decimal point.

Reading and writing decimals

To read a decimal in words:

Read the whole number part.
Say "and" for the decimal point.
Read the digits after the point as one whole number.
Finish with the name of the last place.

Worked example: Word form

0.047 is read "forty-seven thousandths." The last digit is in the thousandths place.
5.63 is read "five and sixty-three hundredths."
18.205 is read "eighteen and two hundred five thousandths."

Going the other way, the place name tells you how many digits come after the decimal point: tenths means 1 digit, hundredths means 2, and thousandths means 3. Use zeros as placeholders to fill the spots.

Worked example: Standard form

Write "nine and fourteen thousandths" as a decimal.

The whole number part is 9. Thousandths means 3 digits after the point, but fourteen has only 2 digits. Put a 0 in front as a placeholder: 014.

The number is 9.014.

Common mistake

Only say "and" for the decimal point. The number 300.07 is "three hundred and seven hundredths." If you say "three hundred and seven," people will hear 307.

Expanded form

Expanded form shows the value of every digit as a sum. For decimals, you can write the values as decimals or as fractions.

Expanded form of a decimal

\begin{aligned} 42.705 &= 40 + 2 + 0.7 + 0.005 \\ &= 4 \times 10 + 2 \times 1 + 7 \times \frac{1}{10} + 5 \times \frac{1}{1{,}000} \end{aligned}

A 0 digit adds nothing, so you can skip it. Here the hundredths digit is 0.

Worked example: From expanded form to standard form

Write $6 \times 100 + 3 \times 1 + 9 \times \dfrac{1}{100} + 2 \times \dfrac{1}{1{,}000}$ in standard form.

Put each digit in its place, and write a 0 in any place that is missing.

hundreds	tens	ones	.	tenths	hundredths	thousandths
6	0	3	.	0	9	2

The number is 603.092.

Digits in neighboring places

The "10 times" pattern works on both sides of the decimal point. In 0.55, the first 5 is worth 0.5 and the second is worth 0.05. Since $0.5 = 10 \times 0.05$ , the first 5 is worth 10 times as much.

Tip

To find a digit's value, keep the digit and change every other digit to 0. In 71.386, the value of the 8 is 0.080, which is 0.08.

Practice

Practice 1

What is the value of the digit 6 in 4.316?

Type a number.

Practice 2

Which digit is in the hundredths place in 58.917?

Practice 3

Write "three hundred eight thousandths" as a decimal.

Type a number.

Practice 4

Write "twelve and four hundredths" as a decimal.

Type a number.

Practice 5

Write in standard form: $700 + 5 + 0.06 + 0.001$ .

Type a number.

Practice 6

Which shows 8.403 in expanded form?

Practice 7

In 2.772, how many times as much is the 7 in the tenths place worth as the 7 in the hundredths place?

Type a number.

Practice 8

How many thousandths are in 0.35?

Type a number.