Topic 4 of 9

Decimal place value to thousandths

Step 7 · Fraction and decimal arithmetic topics

Extend place value to thousandths, read and write decimals in expanded form, compare them, and round them to any place.

Thousandths

Each place is ten times the place to its right, and that carries on past the decimal point: tenths, hundredths, then thousandths. A thousandth is one of 1,000 equal parts of a whole.

Number	Ones	Tenths	Hundredths	Thousandths
3.482	3	4	8	2
0.705	0	7	0	5

In expanded form, 3.482 = 3 + 0.4 + 0.08 + 0.002, or $3 + \frac{4}{10} + \frac{8}{100} + \frac{2}{1000}$ .

Example: Ten times as much

What is 0.035 × 10?

Each digit moves one place to the left.
3 hundredths become 3 tenths, and 5 thousandths become 5 hundredths.

Answer0.35

Comparing decimals

Line up the decimal points and compare place by place from the left. Writing zeros at the end can help: 0.5 = 0.500.

Example: Comparing

Which is greater, 0.5 or 0.499?

Write 0.5 as 0.500.
Tenths: 5 beats 4.

Answer0.5

0.499 sits just below 0.5.

Longer is not bigger: 0.499 has more digits but is less than 0.5.

Rounding decimals

Round a decimal the same way as a whole number: look at the digit just to the right of the place you are rounding to.

Example: Rounding to the nearest hundredth

Round 2.736 to the nearest hundredth.

The hundredths digit is 3, so it is between 2.73 and 2.74.
The next digit is 6, which is 5 or more.
So round up.

Answer2.74

Example: Rounding to the nearest whole

Round 14.48 to the nearest whole number.

The tenths digit is 4.
4 is less than 5, so round down.

Answer14

Try it yourself

Work each one on paper first, then open the answer to check.

What is the value of the 7 in 4.217?
Show answer
7 thousandths, 0.007.
Write 6 + 0.3 + 0.05 + 0.009 as a decimal.
Show answer
6.359.
Which is greater, 0.62 or 0.617?
Show answer
0.62. It is 0.620, and 2 hundredths beats 1.
Round 5.146 to the nearest tenth.
Show answer
5.1.
What is 2.5 ÷ 10?
Show answer
0.25.