Primary 4 Decimals Study Guide

Primary 4 decimals in six short steps: what decimals are, then place value, number lines, comparing, rounding and fractions, with something to try at each step and worked examples to finish.

Start here

What are decimals?

Every step to the right is ten times smaller.

Split one whole into ten equal parts: each part is one tenth, 0.1. Split a tenth into ten: each part is one hundredth, 0.01. Once more gives one thousandth, 0.001.

In this chapter, your child uses this to:

  • read a number line by finding what one small step is worth;
  • compare decimals place by place, from the left;
  • round by finding which neighbour a number is nearer to;
  • write a fraction as tenths or hundredths, then read it as a decimal.
1

Step 1

Decimal place value

Every digit has a place. After the decimal point come tenths, hundredths and thousandths. The place a digit sits in tells you what it is worth.

Tap a digit

.
onestenthshundredthsthousandths
3+0.4+0.07+0.002= 3.472
Tap any digit of 3.472 to see what it is worth.
Try it

In 5.638, what is the value of the digit 3?

▶ Watch the lesson: Decimal place valuePractise 13 questions →
2

Step 2

Reading decimals on a number line

Find what one step is worth. On a number line, count the equal steps between two labelled numbers. Work out what one step is worth, then count on.

Try it

From 2 to 3 there are 10 equal steps. An arrow points 4 steps past 2. What number is it?

▶ Watch the lesson: Reading a number linePractise 8 questions →
3

Step 3

Comparing and ordering decimals

Compare from the left. Line up the decimal points. Fill an empty place with 0, so 0.5 becomes 0.50. Then compare place by place, starting from the left.

Try it

Which is greater, 0.7 or 0.68?

▶ Watch the lesson: Compare and order decimalsPractise 7 questions →
4

Step 4

Rounding decimals

Round to the nearer neighbour. Find the two numbers it sits between at the place you are rounding to. Whichever is nearer wins. Exactly halfway rounds up.

Drag the slider

Try it

Round 7.248 to 2 decimal places.

▶ Watch the lesson: Rounding decimalsPractise 6 questions →
5

Step 5

Fractions and decimals

Turn fractions into hundredths. Make the denominator 10 or 100 by multiplying the top and bottom by the same number. Then read the decimal straight off.

Try it

Write 0.6 as a fraction in its simplest form.

▶ Watch the lesson: Fraction and decimalPractise 7 questions →

Primary 4 decimals questions, worked step by stepTry each question first. Then show a hint, or the working one line at a time.

Place valueBasic

Write 3 tens, 8 tenths and 6 thousandths as a decimal.

Write the headings first: tens, ones, tenths, hundredths, thousandths. A place with nothing in it still needs a 0.
  1. 3 tens is 30, so the ones place is 0.
  2. 8 tenths: the first place after the point is 8.
  3. No hundredths are given, so that place holds a 0.
  4. 6 thousandths: the third place after the point is 6. Together: 30.806.
Answer: 30.806
Number linesIntermediate

A number line from 4.6 to 4.8 is divided into 10 equal parts. An arrow points to the 7th mark after 4.6. What number does the arrow show?

The gap is not 0.1 this time. Work out the whole gap first, then share it into 10 equal parts.
  1. The whole gap is 4.8 minus 4.6, which is 0.2.
  2. Shared into 10 equal parts, each part is 0.02.
  3. 7 parts are 7 × 0.02 = 0.14.
  4. Count on from 4.6: 4.6 + 0.14 = 4.74.
Answer: 4.74
Comparing and orderingIntermediate

Arrange these numbers in order, beginning with the smallest.
2.08   2.8   2.088   2.808

Give every number the same number of decimal places, then compare one place at a time from the left.
  1. Write each with 3 decimal places: 2.080, 2.800, 2.088, 2.808.
  2. The ones are all 2. Look at the tenths: 0, 8, 0, 8. So 2.080 and 2.088 are the two smaller ones.
  3. 2.080 and 2.088 match until the thousandths: 0 is less than 8, so 2.080 < 2.088.
  4. 2.800 and 2.808 also differ only in the thousandths, so 2.800 < 2.808.
Answer: 2.08, 2.088, 2.8, 2.808
Fractions and decimalsIntermediate

Write 2 and 7/20 as a decimal.

The whole number stays as it is. Turn 7/20 into hundredths: what times 20 makes 100?
  1. 20 × 5 = 100, so multiply the top and bottom by 5.
  2. 7/20 = 35/100, which is 0.35.
  3. Add the whole number: 2 + 0.35 = 2.35.
Answer: 2.35
RoundingChallenge

A number with 2 decimal places is rounded to 1 decimal place. The answer is 6.4.
(a) What is the smallest the number can be?
(b) What is the largest the number can be?

Picture the number line around 6.4. Which numbers are nearer to 6.4 than to 6.3 or 6.5? Remember that exactly halfway rounds up.
  1. Halfway between 6.3 and 6.4 is 6.35. Halfway rounds up, so 6.35 rounds to 6.4.
  2. Any 2-decimal-place number below 6.35, such as 6.34, rounds down to 6.3. So the smallest is 6.35.
  3. Halfway between 6.4 and 6.5 is 6.45, which rounds up to 6.5. So it cannot be 6.45.
  4. The 2-decimal-place number just below 6.45 is 6.44, which rounds to 6.4.
Answer: (a) 6.35   (b) 6.44
6

Step 6

Check yourself

Five quick questions, one from each step. Answers are not saved; they show where to practise next.

1. Write 4 tenths and 9 thousandths as a decimal.

2. Which is the smallest: 0.3, 0.29 or 0.305?

3. Round 12.96 to 1 decimal place.

4. Write 0.08 as a fraction in its simplest form.

5. A number line runs from 6.2 to 6.3 in 10 equal steps. An arrow is 7 steps past 6.2. What number is it?

0/5
Answer all five to see where to practise next.
For parents

How to use this guide. Sit with your child for the first two steps. Before they tap, ask "What do you think the 7 is worth?" Saying it aloud is half of the learning. Each step takes two or three minutes; the whole guide about fifteen.

The worked examples show how the same method is used in a test question. Let your child try first, then reveal the working one line at a time and ask what comes next.

More study guides

Before this: Rectangles and SquaresNext: Four Operations of DecimalsPrimary 4 Numbers to 100 000 study guidePrimary 4 Factors and Multiples study guidePrimary 4 Four Operations of Whole Numbers study guide
Lessons and practice

P4 Decimals lessons and practice

5 lesson videos and 45 questions across five subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →