Why is 0.45 smaller than 0.6, even though 45 is bigger than 6?

Because the digits aren't in the same place-value column. 0.6 is six tenths. 0.45 is four tenths and five hundredths — less than half a tenth more than 0.4. You compare from the left column inwards: 6 tenths beats 4 tenths, and the comparison stops there.

Why is 0.7 not the same as 7%?

0.7 is seven tenths, which is the same as 70 hundredths, which is 70%. 7% is seven hundredths, which is 0.07. The digit 7 is in different columns: tenths versus hundredths. Read aloud — 'zero point seven' is 'seven tenths', not 'seven percent'.

How do I check where the decimal point goes in a multiplication answer?

Estimate first: 1.5 × 1.5 must be a bit more than 1 × 1 = 1 and less than 2 × 2 = 4. Then count decimal places: one in each factor, so two in the answer. 15 × 15 = 225, with two decimal places that's 2.25, not 22.5. The estimate confirms the placement.

GCSE Maths Foundation · AQA · Decimals

Decimal place value: why 0.45 is not bigger than 0.6

Decimal place value sits underneath every Foundation paper — money, measurement, percentages, probability, standard form, statistics. AQA examiners flag the same errors every series: ordering decimals by digit-count rather than column position, dropping the decimal point in arithmetic, and crossing the decimal-to-percentage bridge with the wrong scale. On 1F NOV24 Q5 the examiner noted some students "thought 0.7 was 7%".

The thirty-second fix is to anchor on the decimal point. Position of digit determines magnitude, not count of digits. Once you read the digits column-by-column from the decimal point outwards, the longer-is-bigger trap, the lost decimal point and the 0.7 vs 7% bridge all collapse into one rule.

Already know this is your gap? Skip the diagnostic and jump straight into the targeted lesson.

How to spot it in your own work

You wrote " $0.45 > 0.6$ " because 45 is bigger than 6.
You said $\dfrac{1}{4} > \dfrac{1}{2}$ after correctly converting to $0.25$ and $0.5$ — because 25 looked bigger than 5.
You answered $22.5$ for $1.5 \times 1.5$ , or $0.225$ instead of $2.25$ .
You wrote " $0.7 = 7\%$ " or " $0.07 = 7$ " when converting between decimals, fractions and percentages.

An exam question that triggers it

Here is a question very close to AQA 3F NOV24 Q4(b), which catches the same trap even after the student converts correctly:

Put these numbers in order, smallest first:

0.45,\quad 0.6,\quad 0.305,\quad 0.27

The longer-is-bigger answer is $0.27,\ 0.6,\ 0.305,\ 0.45$ — students count digits and rank by "how big the digit string looks".

The correct order is $0.27,\ 0.305,\ 0.45,\ 0.6$ . Compare tenths first: 0.27 has 2 tenths, 0.305 has 3, 0.45 has 4, 0.6 has 6. The comparison is done once the tenths disagree. Digit-count is irrelevant.

Why students fall for this

Primary maths teaches whole-number ordering exclusively: $45 > 6$ because 45 has more digits. The brain over-learns "longer is bigger" before it ever meets a decimal point. When the decimal point arrives, students treat it as a punctuation mark separating two whole numbers, rather than as the anchor that fixes where each digit lives.

The same shortcut produces the lost-decimal-point error in arithmetic: students run $15 \times 15 = 225$ as a procedure, then place the decimal point by feel rather than by counting columns. On 1F NOV24 Q19 the examiner reported that "the decimal point was often in the wrong place, even when multiplication had gone smoothly" — the procedure ran cleanly, but the place-value reasoning came afterwards and failed.

The fix — Anchor on the decimal point

Position-of-digit determines magnitude, not count-of-digits. The decimal point is the anchor. Every digit's value is fixed by how far it sits from the decimal point — one place left is units, two places left is tens; one place right is tenths, two places right is hundredths. Two decimals are compared column-by-column from the decimal point outwards. If the tenths column already disagrees, the rest of the digits don't matter.

This single rule fixes all three failure modes. For ordering, compare columns outwards. For multiplication, count decimal places in the inputs and use them to count the places in the answer. For the decimal-to-percentage bridge, count two places: $0.7$ has the 7 in the tenths column, which is $\dfrac{70}{100} = 70\%$ , not $\dfrac{7}{100} = 7\%$ .

Worked example

Order $0.45,\ 0.6,\ 0.305,\ 0.27$ from smallest to largest.

Line the numbers up by the decimal point.
$0.45\ \ \ \ 0.60\ \ \ \ 0.305\ \ \ \ 0.27$
Pad the shorter ones with a zero so every column has a digit. The zero is a place-holder, not a value-changer: $0.6 = 0.60 = 0.600$ .
Compare the tenths column first. Tenths digits are 4, 6, 3, 2. So $0.27 < 0.305 < 0.45 < 0.60$ already, because the tenths column gives a decisive answer.
If the tenths agree, drop to hundredths, then thousandths. For this set the tenths don't agree, so we stop there. For $0.45$ vs $0.453$ , the tenths and hundredths agree, and the thousandths column tips it: $0.45 < 0.453$ .
Write the order. $0.27,\ 0.305,\ 0.45,\ 0.6$ . Sanity check: 0.6 is six tenths, more than half. 0.27 is just over a quarter. That ordering is consistent.

Notice the digit-count told you the wrong answer: $0.305$ has the longest string, but it's only the second-smallest. The decimal point — not the string length — was the anchor.

Find out if this is costing you marks

The 10-minute diagnostic checks for this pattern (and four others) using AQA-style GCSE Higher items. Free, no signup, anonymous.

Take the diagnostic →

Common questions

How do I order $\dfrac{1}{2}$ and $\dfrac{1}{4}$ if I convert them to decimals?: $\dfrac{1}{2} = 0.5$ and $\dfrac{1}{4} = 0.25$ . Compare tenths first: 5 tenths beats 2 tenths, so $0.5 > 0.25$ , i.e. $\dfrac{1}{2} > \dfrac{1}{4}$ . AQA examiners specifically flagged students saying $\dfrac{1}{2} < \dfrac{1}{4}$ after correctly converting — the conversion was right, the comparison was done by digit-count.
What about $1.5 \times 1.5$ — how do I place the decimal point?: Multiply as whole numbers first: $15 \times 15 = 225$ . Count decimal places in the inputs: one in 1.5, one in 1.5, so two in the answer. Move the decimal point two places left: $2.25$ . An estimate confirms it: $1.5 \times 1.5$ is between $1 \times 1 = 1$ and $2 \times 2 = 4$ , so 2.25 sits in the right range and $22.5$ does not.
What's the difference between 0.7 and 7%?: $0.7$ means seven tenths, or $\dfrac{70}{100} = 70\%$ . $7\%$ means seven hundredths, or $0.07$ . The digit 7 is in the tenths column in the first case and the hundredths column in the second. Always count two places when converting between decimal and percentage — percentages live in the hundredths column.
Does adding a zero on the end of a decimal change its value?: No. $0.6 = 0.60 = 0.600$ . Trailing zeros after the decimal point are place-holders that make the column count obvious — they don't add any value. This is the trick that lets you line up decimals of different lengths and compare column-by-column without worrying about which is "longer".

Related misconceptions

Percentage change family— The decimal-to-percentage bridge sits inside every multiplier calculation.
Fraction additive— Converting fractions to decimals and back is the other place column reasoning bites.
Area-perimeter conflation— Decimal arithmetic feeds geometry — a misplaced point makes the area wrong by a factor of ten.

← All GCSE Maths Higher misconceptions