Read and Write Tenths in Decimal Notation

Students translate between fractions with denominator 10 and decimal notation. They learn that the first decimal place represents tenths and practice reading and writing decimals such as 0.3 = 3/10 using place value charts and number lines.

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Grade 4 · Decimal Notation for Fractions · question 1 of 3

0 of 20

20 rungs. A star at the top.

0.5 = 10

How it is taught

0:00 of 3:36

The first place after the point is tenths.

A tenth is one of ten equal parts.

Read it: Count the steps past the whole

An arrow sits between 3 and 4 on a line cut into 10 equal steps. Where is it? Count the steps from 3: the arrow is 2 steps past 3, so it is 3.2.

Find the whole number the arrow is just past: 3.
Count the steps after 3, not the tick at 3: 2 steps.
Write the whole, a point, then the steps: 3.2, which is 3 2/10.

The gap from 3 to 4 is 1 whole cut into 10 equal steps, so each step is 1 tenth.

The tick at 3 is where the counting starts, not a step; counting it as a step gives 3.3, a step too far.

Cut the gap from 3.2 to 3.3 into 10 again and each step is 1 hundredth; then the last digit counts the steps.

The digits after the point count steps: tenths past the whole, then hundredths past the tenth.

Counting the tick at 3 as the first step, and calling the arrow 3.3.

Start at 3 and count the jumps, not the ticks: 1, 2. The arrow is at 3.2.

A number line runs from 5 to 6 in 10 equal steps, each one a tenth. Which decimal stands 7 steps past 5? — 5.7. 7 steps past 5 is 5.7 — the steps are counted from 5, which is not itself a step.

3/10 = 0.3

Imagine a chocolate bar split into ten equal pieces.

We eat three of them. Three out of ten — that's our fraction.

We write it as three over ten. The bottom number — the denominator — tells us how many equal parts make one whole.

There's another way to write tenths — with a decimal. Let's set up a place value chart.

This little dot is the decimal point. Anything to its right is smaller than one whole.

We have zero whole bars, so we write zero in the ones place.

We have three tenths, so we write three in the tenths place.

Grade 4 · Writing tenths as fractions and decimals

We read this as 'zero point three' — or 'three tenths'.

Let's check on a number line. From zero to one, we split it into ten equal jumps.

Three tenths lands right here, on the third tick.

So three tenths and zero point three are the same number, written two different ways!

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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