Write Decimals to Thousandths in Word Form and Expanded Form

Students write decimals to thousandths in word form (e.g., "four and seven hundred thirty-two thousandths") and in expanded form using fractions or decimals (e.g., 4 + 7/10 + 3/100 + 2/1000). They move fluently between all three representations.

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Grade 5 · Reading, Writing, and Comparing Decimals to Thousandths · question 1 of 3

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20 rungs. A star at the top.

Felix waits in line at the post office with a mailing tube. He measures it as 1 whole meter and 81 hundredths of a meter more. Write the length of the tube as a decimal.

How it is taught

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A decimal can be written in words or as added place values.

Each digit has a place after the decimal point.

Read it: Read a decimal by its places

4.372 is 4 ones, 3 tenths, 7 hundredths and 2 thousandths. Each digit is worth its count of the place it stands under.

Read the place names across the top of the chart.
Say each digit with its place: 7 hundredths is 0.07.
The point sits between the ones and the tenths, and thousandths are the third place after it.

Each place is a tenth of the place to its left, so ten thousandths make one hundredth.

4.372 is 4 + 0.3 + 0.07 + 0.002: one part for each digit.

In words it is four and three hundred seventy-two thousandths, and the word "and" marks the point.

A digit's worth is its count of the place it stands in.

Writing four and twenty-five thousandths as 4.25, which is twenty-five hundredths.

Thousandths take three places after the point, so twenty-five thousandths is 0.025, and the number is 4.025.

6 + 0.2 + 0.09 + 0.003 = ___ — 6.293. 6 ones, 2 tenths, 9 hundredths and 3 thousandths make 6.293.

4.732

Let's take the decimal four point seven three two and write it three different ways.

First, we line up each digit in its place value column.

The four sits in the ones place, so we start by saying 'four and'.

The digits seven, three, two read together as 'seven hundred thirty-two'.

The last digit lives in the thousandths place — so that whole decimal part is in thousandths.

Now let's break the number apart by place value using fractions.

Start with four — that's the ones.

Plus seven tenths.

Plus three hundredths.

Plus two thousandths.

We can also write each piece as a decimal: four plus zero point seven plus zero point zero three plus zero point zero zero two.

Three ways to write the same number — four point seven three two!

Grade 5 · Three ways to write the same decimal

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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