J560 · 1.01–1.04, 2.01–2.04, 4.01Number FundamentalsFoundation & HigherGrades 1–3

Place Value & Ordering

Q: Does a zero at the end of a decimal change its value?

No. 2.5, 2.50 and 2.500 are all equal. Zeros before the first non-zero digit after the point do matter: 0.05 0.5.

Q: Is -0.5 bigger than -0.25?

No. On a number line -0.5 is further left, so -0.5 < -0.25.

Is $0.35$ bigger than $0.4$ ? Is $-7$ bigger than $-2$ ? Questions like these catch people out because the number that "looks" bigger is not always the one that is bigger. Place value — the idea that a digit is worth more or less depending on which column it sits in — is the tool that settles every one of them.

35 min Number Fundamentals

The big picture

Our number system uses ten digits and a set of columns, each worth ten times the column to its right. That single idea explains why multiplying by 10 shifts every digit one place left, why decimal points must line up in written addition, and why standard form works at all.

OCR rarely asks for a definition. Instead it mixes whole numbers, decimals, negatives and symbols like $<$ and $\ge$ in the same question and checks whether you can put them in order accurately and quickly.

Place Value - CorbettmathsCurated by Kepler, not produced by us. Watch it, then read the notes below.

Open on YouTube

Before you start

Try a short calculation from the preceding topic without the notes.
Check the tier and grade band shown in this lesson.

Watch, pause, try

Video by corbettmaths. The video’s own board label is retained; follow the specification reference and scope notes on this lesson for assessed content.

Viewing focus: State the value of any digit in a whole number or decimal

After watching, attempt these questions before opening the answers. You can also use the written lesson below.

After watching 1: What is the value of the 4 in $17.043$ ?

Show answer and reasoning

$0.04$ . The 4 is in the hundredths column.

After watching 2: Work out $0.52 \times 100$ .

Show answer and reasoning

$52$ . Digits move two places left.

What you'll learn

State the value of any digit in a whole number or decimal
Multiply and divide by powers of 10 using place value
Order integers, decimals and negative numbers
Use the symbols $=$ , $\neq$ , $<$ , $>$ , $\le$ and $\ge$ correctly

Columns and the value of a digit

Moving left, each column is worth ten times more: ones, tens, hundreds, thousands. Moving right past the decimal point, each is worth ten times less: tenths, hundredths, thousandths.

So in $6\,305.72$ , the $3$ is worth $300$ , the $7$ is worth $\tfrac{7}{10}$ and the $2$ is worth $\tfrac{2}{100}$ .

Zeros are placeholders. The $0$ in $405$ keeps the $4$ in the hundreds column; without it, the number would be $45$ .

Example 1Write down the value of the digit

8

in (a)

38\,120

and (b)

2.058

1(a) The 8 is in the thousands column.

2(b) The 8 is in the thousandths column.

Answer(a)

8000

(b)

\tfrac{8}{1000} = 0.008

Your turnSame method, new numbers — try it before moving on.

Write down the value of the digit 6 in $4.065$ as a decimal.

Your answer

Why this works

A digit has no size on its own — the column gives it one. That is why "the 5 in 0.5" and "the 5 in 500" differ by a factor of one thousand even though the digit is identical.

Multiplying and dividing by powers of 10

Multiplying by $10$ makes every digit ten times bigger, so each moves one column to the left. Multiplying by $100$ moves digits two columns; by $1000$ , three.

Dividing moves digits to the right. $47.3 \div 100 = 0.473$ .

The decimal point does not move — the digits do. Thinking of it this way avoids the "just add a zero" trap, which fails for $2.5 \times 10 = 25$ , not $2.50$ .

Example 1Work out (a)

0.064 \times 1000

and (b)

3.9 \div 1000

1(a) Digits move three places left:

64

2(b) Digits move three places right, filling with zeros:

0.0039

Answer(a)

64

(b)

0.0039

Your turnSame method, new numbers — try it before moving on.

Work out $0.72 \div 100$ .

Your answer

Ordering decimals and negative numbers

To compare decimals, line them up by the decimal point and pad with zeros so they have the same number of decimal places. $0.4 = 0.40$ , which is greater than $0.35$ .

For negative numbers, picture a number line: the further left, the smaller. So $-7 < -2$ , even though $7 > 2$ .

Ascending means smallest first; descending means largest first. Always write the final list using the original numbers.

Example 1Write in ascending order:

-1.5,\ 0.08,\ -0.6,\ 0.8,\ -1.05

1Negatives first, most negative first:

-1.5 < -1.05 < -0.6

2Then positives:

0.08 < 0.8

Answer

-1.5,\ -1.05,\ -0.6,\ 0.08,\ 0.8

Your turnSame method, new numbers — try it before moving on.

Which is the smallest: $-0.3$ , $-0.33$ or $-0.303$ ?

Your answer

Tip — Padding with zeros never changes a decimal’s value: $0.3 = 0.30 = 0.300$ . It just makes the comparison visible.

Inequality symbols

$<$ means "is less than" and $>$ means "is greater than". The narrow end points at the smaller number.

$\le$ means "less than or equal to" and $\ge$ means "greater than or equal to". $\neq$ means "is not equal to".

These symbols reappear throughout the course, from error intervals to solving inequalities, so reading them fluently now pays off later.

Example 1Insert

<

>

=

between each pair: (a)

-3.2 \ \square \ -3.12

(b)

0.70 \ \square \ 0.7

1(a)

-3.20

is further left on a number line than

-3.12

2(b) Trailing zeros do not change the value.

Answer(a)

-3.2 < -3.12

(b)

0.70 = 0.7

Think like an examiner

Give the final ordered list in full — working alone may not earn the mark.
When asked for the value of a digit, write the value (e.g. $0.008$ ), not the column name.
Check negative decimals against a number line before committing to an order.

Place value

\times 10^{n}: \text{ digits move } n \text{ places left}

Multiplying by powers of 10.

\div 10^{n}: \text{ digits move } n \text{ places right}

Dividing by powers of 10.

a < b \iff b > a

Reading inequality symbols.

Watch out for these

Thinking

0.35 > 0.4

because 35 is bigger than 4.

Compare column by column:

0.40 > 0.35

Ordering

-7

after

-2

in ascending order.

The more negative number is smaller:

-7 < -2

Writing

4.6 \times 10 = 4.60

The digits move left:

46

Reading

x \ge 3

as "

x

is greater than 3".

It includes 3: "greater than or equal to 3".

Stretch yourself

Using each of the digits $2$ , $5$ , $7$ and $9$ exactly once, and one decimal point, write the number closest to $6$ . Explain why no other arrangement is closer.

Hint — The units digit matters most. Which digits could go immediately before the decimal point?

Questions students ask

Does a zero at the end of a decimal change its value?

No.

2.5

2.50

and

2.500

are all equal. Zeros before the first non-zero digit after the point do matter:

0.05 \neq 0.5

How do I order fractions and decimals together?

Convert everything to decimals (or everything to fractions with a common denominator) first, then compare.

-0.5

bigger than

-0.25

No. On a number line

-0.5

is further left, so

-0.5 < -0.25

Key takeaways

Each column is worth ten times the column to its right.
Multiplying or dividing by powers of 10 moves the digits, not the decimal point.
Compare decimals by lining up the decimal points and padding with zeros.
For negatives, further left on the number line means smaller.
Read $<$ , $>$ , $\le$ , $\ge$ and $\neq$ precisely.

Exam-style questions

Practise it the way it is examined

2 original questions · 3 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.

Question 1Grade 21 mark

Write these numbers in order of size, starting with the smallest: $\ 5.07, \ 5.7, \ 5.007, \ 5.077$ [1]

Question 2Grade 32 marks

$64 \times 38 = 2432$ .

(a)Work out $6.4 \times 3.8$ .[1]
(b)Work out $2432 \div 0.38$ .[1]

Unlimited practice

Skill drill

A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.

0 / 0 first-time correct Streak 0Best at this level: 0

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OCR J560 official specification (opens in a new tab)
Check the assessed scope and practical or mathematical requirements.
Read or explore this topic (opens in a new tab)
An external explanation or interactive activity to use alongside the lesson. It may include extension material.

Return to this tomorrow

Close the notes and answer from memory. Revisit any explanation you cannot yet reconstruct.

Which is the largest?
Which list is in descending order?
Work out $73 \div 1000$ .
Which statement is true?

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

Related lessons

All 6 lessons

Place Value & Ordering

0.35

bigger than

0.4

? Is

-7

bigger than

-2

? Questions like these catch people out because the number that "looks" bigger is not always the one that is bigger. Place value — the idea that a digit is worth more or less depending on which column it sits in — is the tool that settles every one of them.

35 min Number Fundamentals

Watch, pause, try

Video by corbettmaths. The video’s own board label is retained; follow the specification reference and scope notes on this lesson for assessed content.

Viewing focus: State the value of any digit in a whole number or decimal

After watching, attempt these questions before opening the answers. You can also use the written lesson below.

After watching 1: What is the value of the 4 in $17.043$ ?

Show answer and reasoning

$0.04$ . The 4 is in the hundredths column.

After watching 2: Work out $0.52 \times 100$ .

Show answer and reasoning

$52$ . Digits move two places left.

Practise it the way it is examined

Question 1Grade 21 mark

Write these numbers in order of size, starting with the smallest: $\ 5.07, \ 5.7, \ 5.007, \ 5.077$ [1]

Question 2Grade 32 marks

$64 \times 38 = 2432$ .

(a)Work out $6.4 \times 3.8$ .[1]
(b)Work out $2432 \div 0.38$ .[1]