P4 Decimals: Look Closer Between 0 and 1

A number line draws itself across the screen, with 0 at one end and 1 at the other. A blue pin drops onto it, somewhere in between, with a question mark on its flag. "Anya's pin sits between 0 and 1. Which number is it on?"

That is Decimals Up Close, a 30-second Primary 4 episode of our Topic Explainers series. To find the pin's number, the video looks closer at the line, again and again, and drops one digit into a place-value chart each time. Then it uses the same line to round, compare, add, subtract, multiply and divide. Watch it first, then read on for the method behind each step.

Decimals Up Close: look closer. Every digit has its place.

Everything in the video comes from Primary 4 Decimals in the Singapore syllabus: place values up to thousandths, comparing and ordering, writing decimals as fractions, and fractions with a denominator that is a factor of 10 or 100 as decimals, rounding to 1 and 2 decimal places, adding and subtracting, and multiplying and dividing by a 1-digit whole number.

The method

Look closer: every gap splits into 10 equal parts

Between 0 and 1 there are always more numbers to find. Split the gap from 0 to 1 into 10 equal parts and each part is one tenth: 0.1, 0.2, 0.3 and so on. Look closer at one of those gaps, say 0.3 to 0.4, and split it into 10 equal parts again. Each part is one hundredth: 0.31, 0.32, up to 0.39. Look closer once more and each hundredth splits into 10 thousandths.

That is the whole idea of decimal place value. Every place to the right of the decimal point is 10 times smaller than the place before it.

Ones	.	Tenths	Hundredths	Thousandths
0	.	3	7	5

So 0.375 is 3 tenths, 7 hundredths and 5 thousandths.

Compare from the left

To compare two decimals, line up the decimal points and compare the digits from the left, one place at a time. The first place where the digits differ decides which number is bigger. The number of digits does not.

Decimals as fractions

The place of the last digit tells you the denominator. Two decimal places means hundredths, so 0.38 is 38/100. One decimal place means tenths, so 0.4 is 4/10.

Round by looking at the next digit

To round to 2 decimal places, keep the hundredths and look at the thousandths digit. To round to 1 decimal place, keep the tenths and look at the hundredths digit. If the digit you look at is 5 or more, round up. If it is 4 or less, the kept digits stay as they are. On a number line, rounding simply means moving to the nearest mark.

Calculate in place value

Add and subtract with the decimal points lined up, so tenths go with tenths and hundredths with hundredths. To multiply or divide by a whole number, think of the decimal as a number of hundredths, work with whole numbers, then turn the answer back into hundredths.

Worked examples

All the numbers below are the ones in the video.

Example 1: which number is the pin on?

The pin sits between 0 and 1. Look closer to find its number.

Step 1: Tenths. Split 0 to 1 into 10 equal parts. The pin is between 0.3 and 0.4, so the tenths digit is 3.

Step 2: Hundredths. Look closer at 0.3 to 0.4 and split it into 10 equal parts. The pin is between 0.37 and 0.38, so the hundredths digit is 7.

Step 3: Thousandths. Look closer at 0.37 to 0.38 and split it into 10 equal parts. The pin is exactly on the 5th mark, so the thousandths digit is 5.

The pin is on 0.375: 3 tenths, 7 hundredths and 5 thousandths.

Example 2: round and compare

Round 0.375 to 2 decimal places and to 1 decimal place. Then put the three numbers in order.

Step 1: To 2 decimal places. Keep 0.37 and look at the next digit, 5. Five or more rounds up, so 0.375 ≈ 0.38. On the number line, 0.375 sits exactly halfway between 0.37 and 0.38, and halfway rounds up.

Step 2: To 1 decimal place. Keep 0.3 and look at the next digit, 7. Seven rounds up, so 0.375 ≈ 0.4.

Step 3: Write them as fractions. 0.38 has two decimal places, so it is 38/100. 0.4 has one, so it is 4/10.

Step 4: Put them in order. Line up the decimal points: 0.375, 0.380, 0.400. The tenths digits are 3, 3 and 4, so 0.4 is the biggest. Between the other two, the hundredths digits are 7 and 8, so 0.375 is smaller than 0.38.

0.375 < 0.38 < 0.4

Example 3: add, subtract, multiply and divide

Work out 0.38 + 0.4, then 1 − 0.78, then 3 × 0.38, then 1.14 ÷ 3.

Add. Write 0.4 as 0.40 so the places line up. 38 hundredths and 40 hundredths make 78 hundredths: 0.38 + 0.4 = 0.78.

Subtract. Write 1 as 1.00, which is 100 hundredths. 100 hundredths take away 78 hundredths is 22 hundredths: 1 − 0.78 = 0.22. So 0.78 and 0.22 together make a whole.

Multiply. 0.38 is 38 hundredths. 3 × 38 = 114, so the answer is 114 hundredths: 3 × 0.38 = 1.14. On the number line, that is three spans of 0.38 placed end to end, landing at 0.38, 0.76 and then 1.14.

Divide. 1.14 is 114 hundredths. 114 ÷ 3 = 38, so the answer is 38 hundredths: 1.14 ÷ 3 = 0.38. The long span shares back into three equal short spans, which is a good check on the multiplication.

Try one at home

A pin sits at 0.462. Round it to 2 decimal places and to 1 decimal place, then put all three numbers in order.

To 2 decimal places, the next digit is 2, so it stays: 0.46. To 1 decimal place, the next digit is 6, so it rounds up: 0.5, which is 5/10. In order: 0.46 < 0.462 < 0.5.

Common mistakes

Thinking a longer decimal is bigger. Many children say 0.375 is more than 0.4 because 375 is more than 4. Line up the decimal points and compare tenths first: 3 tenths is less than 4 tenths.
Reading decimals like whole numbers. Decimals are read digit by digit after the point: 0.38 is "zero point three eight", not "zero point thirty-eight". Reading the digits one by one keeps each place in view.
Adding without lining up the decimal points. 0.38 + 0.4 is not 0.42. Writing 0.4 as 0.40 first shows that it is 40 hundredths, not 4.
Rounding half down. 0.375 to 2 decimal places is 0.38, not 0.37. When the next digit is 5, round up.
Rounding in two steps. To round 0.345 to 1 decimal place, look only at the hundredths digit, 4, so the answer is 0.3. Rounding to 0.35 first and then to 0.4 gives the wrong answer.
Putting the decimal point in the wrong place. 3 × 0.38 is not 11.4 or 0.114. A quick estimate helps: 3 lots of about 0.4 is about 1.2, so 1.14 is the right size.

Parent tips

Draw the look-closer line. Draw a number line from 0 to 1 and mark the tenths. Then draw a second, longer line under it for just one gap, such as 0.6 to 0.7, and mark its hundredths. Ask your child to place a number like 0.64 on both lines.
Use price tags. A price like $0.38 is 38 cents, and 100 cents make a dollar, so it is 38 hundredths of a dollar. Ask which is more, $0.38 or $0.40, and why.
Make a place-value chart. Write Ones, Tenths, Hundredths and Thousandths across a sheet of paper and use digit cards. Read each number aloud, digit by digit, then say what each digit is worth.
Estimate before calculating. Before any multiplying or dividing, ask, "About how big will the answer be?" It catches most decimal point slips.
Check one way with the other. After multiplying, divide back; after adding, subtract back. If the answer returns to the start, the working is right.

Looking closer at your own progress

Near the end of the video, the number line slides away and a progress ring labelled "Decimals" appears. Then the ring looks closer too: it opens into smaller rings for the skills inside it. "The skill map opens each topic into the skills inside it."

That is the interactive skill map in Singapore Math Drills: every curriculum topic as a progress ring, opening into precise mastery, nested focus skills, and how much practice is available. If decimals feel shaky, it shows whether the trouble is place value, rounding or calculating, so practice can go there. Our post on the skill map and targeted drills shows how to use it.

And practice stays calm by design: no guilt-tripping over a missed day and no dark patterns, with your child's progress only ever measured against their own. Look closer. Every digit has its place.

Try a sample

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