1MA1 · N1–N2NumberFoundation & 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.

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

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 $=$ , $\neq =$ , $<$ , $>$ , $\leq$ and $\geq$ 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 $\frac{7}{10}$ and the $2$ is worth $\frac{2}{100}$ .

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

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

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

Answer(a)

8000

(b)

\frac{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 $2.50$ .

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.

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.

$\leq$ means "less than or equal to" and $\geq$ 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.

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 1 0^{n} : digits move n places left

Multiplying by powers of 10.

\div 1 0^{n} : digits move n places right

Dividing by powers of 10.

a < b ⟺ 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 \geq 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 $<$ , $>$ , $\leq$ , $\geq$ 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

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Place Value & Ordering

Columns and the value of a digit

Multiplying and dividing by powers of 10

Ordering decimals and negative numbers

Inequality symbols

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Skill drill

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Related topics

Place Value & Ordering

Columns and the value of a digit

Multiplying and dividing by powers of 10

Ordering decimals and negative numbers

Inequality symbols

Practise it the way it is examined

Skill drill

Practise this topic

Related topics