Grade by Grade
B. Number · Number Sense: Numbers to One Million, Integers, Decimals and Fractions

Decimal Thousandths: Reading, Writing and Showing

B1.4About 40 minutes
Learning goals
  • I can explain what a thousandth is.
  • I can read and write decimal numbers to thousandths in numerals and in words.
  • I can write a decimal in expanded form and name the value of each digit.
  • I can show thousandths with grids, number lines and metric measurements.

Words to know

thousandth
One of 1000 equal parts of a whole. 1/1000 = 0.001.
thousandths place
The third place to the right of the decimal point. In 2.345 the 5 is worth 5 thousandths (0.005).
decimal point
The dot that separates the whole number part from the part less than one.
equivalent decimals
Decimals that name the same amount, like 0.4 = 0.40 = 0.400.

Remember from Grade 5

In Grade 5 you learned decimal tenths and hundredths. One whole cut into 10 equal parts gives tenths (0.1). Cut each tenth into 10 equal parts and you get hundredths (0.01). You showed them with hundred grids, money and metre sticks. This year we zoom in one more time!

Zooming in

An athlete's sled race time shows 47.316 seconds. A recipe asks for 0.125 kg of butter. Some numbers need a third decimal place.

Take one hundredth and cut it into 10 equal parts. Each tiny part is one thousandth.

  • 10 thousandths = 1 hundredth (0.010 = 0.01)
  • 100 thousandths = 1 tenth (0.100 = 0.1)
  • 1000 thousandths = 1 whole (1.000 = 1)
1 whole1 hundredth =10 thousandths
The grid is 1 whole. 23 hundredths are shaded (0.23). One more hundredth (outlined in yellow) is zoomed in on the right and split into 10 thousandths; 5 of them are shaded. Altogether the shaded amount is 0.235.
Ones.TenthsHundredthsThousandths
2.345
20.30.040.005
2.345 in a place value chart.

Reading thousandths

To read a decimal:

  1. Read the whole number part.
  2. Say "and" for the decimal point.
  3. Read the digits after the decimal point as one number, then say the name of the last place.

So 2.345 is "two and three hundred forty-five thousandths".

In expanded form: 2.345 = 2 + 0.3 + 0.04 + 0.005.

As a fraction: 0.345 = 345/1000, so 2.345 = 2 345/1000.

Thousandths in metric measurement

The metric system is built on 10s, 100s and 1000s, so thousandths are everywhere:

  • 1 m = 1000 mm, so 1 mm = 0.001 m
  • 1 kg = 1000 g, so 1 g = 0.001 kg
  • 1 L = 1000 mL, so 1 mL = 0.001 L

A pencil that is 172 mm long is 0.172 m long. A 1375 g bag of rice holds 1.375 kg.

00.10.20.30.40.50.60.70.80.91
0.235 on a number line from 0 to 1 is between 0.2 and 0.3.
0.20.210.220.230.240.250.260.270.280.290.3
Zoom in: from 0.2 to 0.3 by hundredths. 0.235 is exactly halfway between 0.23 and 0.24.
0.230.24
Zoom in again: from 0.23 to 0.24 by thousandths (each small tick is 0.001). 0.235 is the fifth small tick.
Worked example

Example 1: Read and write in words

Write 0.047 and 6.008 in words.

  1. 0.047: no whole number. The digits after the point make 47, and the last place is thousandths: "forty-seven thousandths".
  2. 6.008: "six and" for the whole and the point. The digits make 8, and the last place is thousandths: "eight thousandths".

0.047 = forty-seven thousandths. 6.008 = six and eight thousandths.

Worked example

Example 2: Write the numeral

Write "three and fifty-two thousandths" as a decimal.

  1. The whole part is 3.
  2. Fifty-two thousandths must end in the thousandths place, which is 3 places after the point. 52 has only 2 digits, so put a 0 in the tenths place: .052.

3.052. Check: 0.052 = 52/1000.

Worked example

Example 3: Metric measurements

A puppy has a mass of 4 kg 260 g. Write the mass in kilograms.

  1. 260 g is 260 thousandths of a kilogram: 0.260 kg.
  2. Add the whole kilograms: 4 + 0.260.

4.260 kg, which is the same as 4.26 kg.

Zeros at the end

Adding a zero at the end of a decimal doesn't change its value: 0.4 = 0.40 = 0.400 (4 tenths = 40 hundredths = 400 thousandths). But a zero right after the decimal point does matter: 0.4 and 0.04 are very different!

Just for fun

A thousandth of a second is quicker than a blink. One blink takes roughly 100 to 400 thousandths of a second (0.1 to 0.4 s). So sliding races can be won in less than a blink!

Hands-on activity

Millimetre detective

You need: a ruler or measuring tape with millimetres, a pencil and paper. A kitchen scale (in grams) is a bonus.

  1. Measure five small objects in millimetres: a pencil, a spoon, a crayon, a book, a phone or remote.
  2. Write each length in a table in mm and then in metres to the thousandth. For example, 172 mm = 0.172 m.
  3. Read each metre measurement aloud in words: "one hundred seventy-two thousandths of a metre".
  4. Bonus: Look at food packages in your kitchen. Find masses in grams (like 454 g) and write them in kilograms (0.454 kg).

Math talk: Why does every length in mm under 1000 become a decimal less than 1 in metres?

Your turn

1

Write 0.629 in words.

2

Write "five and seven thousandths" as a decimal.

3

What is the value of the 8 in 3.148?

4

Write 1.506 in expanded form.

5

Write 385 mm in metres.

6

Write 2 kg 75 g in kilograms.

7

Write 0.7 as an equivalent decimal in thousandths.

More practice: warm-up

1

How many thousandths make one hundredth?

2

Write 1/1000 as a decimal.

3

Which digit is in the thousandths place in 4.072?

4

Write 0.25 in thousandths.

5

Write "nine thousandths" as a decimal.

More practice: on your own

1

Write 12.304 in words and in expanded form.

2

Write "forty and forty thousandths" as a decimal.

3

Write 0.083 as a fraction.

4

A bottle holds 355 mL. Write this amount in litres.

5

What decimal is 3 tenths + 5 thousandths? Explain where the zero goes.

Challenge

1

What decimal is 2 + 14 hundredths + 26 thousandths?

2

How many thousandths are in 0.4? In 1.25?

3

Liam says 0.5 has fewer digits than 0.125, so 0.5 is smaller. Use thousandths to explain whether he is right.

Check your understanding

Quiz

1.

How do you write "sixty-four thousandths"?

2.

What is the value of the 3 in 0.153?

3.

Which is equal to 0.6?

4.

1 mm is what part of a metre?

5.

Which is the expanded form of 7.209?

6.

A cat's mass is 5 kg 40 g. In kilograms, that is...

For parents and teachers

Big idea: B1.4 asks Grade 6 students to read, represent, compare and order decimal numbers to thousandths. Grade 5 stopped at hundredths, so the thousandths place is new this year.

Common difficulties:

  • Forgetting placeholder zeros. "Fifty-two thousandths" is often written 0.52. Remind your child that thousandths end in the third place after the point.
  • Reading decimals digit by digit. "Zero point three four five" is fine for quick talk, but reading "three hundred forty-five thousandths" builds understanding of place value.
  • Thinking more digits means bigger. 0.125 is not greater than 0.5 (see the next lesson).

How to help: Metric measurement is the best tool. Measure things in millimetres and convert to metres; read grams on food packages and convert to kilograms. Many Canadian kitchen scales show grams, which works perfectly.