Topics › KS3 › Number

Place value & ordering decimals

pv-01 Present from here

What is the value of the 7 in $3.072$?

Option A: 7 tens

Option B: 7 tenths

Option C: 7 hundredths

Option D: 7 thousandths

Answer and misconceptions

Option A: 7 tens ✗
Ignores the decimal pointReads 3.072 as 3072, so the 7 is in the tens column.

Option B: 7 tenths ✗
Ignores the zero placeholderSkips the 0 and treats the 7 as the first digit after the point.

Option C: 7 hundredths ✓ Correct

Option D: 7 thousandths ✗
Counts the decimal point as a columnTreats the point as the tenths place, pushing every digit one column right.
pv-02 Present from here

Which number is the largest?

Option A: $0.6$

Option B: $0.0625$

Option C: $0.098$

Option D: $0.62$

Answer and misconceptions

Option A: $0.6$ ✗
Thinks fewer decimal places means largerBelieves tenths beat hundredths, so the shortest decimal must be biggest.

Option B: $0.0625$ ✗
Reads digits after the point as a whole numberCompares 6, 625, 98 and 62 as whole numbers; 625 wins.

Option C: $0.098$ ✗
Ignores a zero straight after the pointReads 0.098 as 0.98, so thinks it is the largest.

Option D: $0.62$ ✓ Correct
pv-03 Present from here

Work out $3.06 \times 10$

Option A: $30.6$

Option B: $3.060$

Option C: $306$

Option D: $0.306$

Answer and misconceptions

Option A: $30.6$ ✓ Correct

Option B: $3.060$ ✗
Multiplies by 10 by adding a zero on the endUses the whole-number shortcut, which does not change a decimal's value.

Option C: $306$ ✗
Thinks multiplying by 10 removes the decimal pointDrops the point instead of moving digits one place left.

Option D: $0.306$ ✗
Moves digits the wrong way when multiplyingShifts digits right (dividing by 10) instead of left.
pv-04 Present from here

Work out $52 \div 100$

Option A: $5.2$

Option B: $0.52$

Option C: $0.052$

Option D: $5200$

Answer and misconceptions

Option A: $5.2$ ✗
Moves digits one place for dividing by 100Treats every division by a power of ten as dividing by 10.

Option B: $0.52$ ✓ Correct

Option C: $0.052$ ✗
Moves digits one place per digit of 100Counts the three digits in 100 and shifts three places instead of two.

Option D: $5200$ ✗
Adds zeros instead of dividingUses the "add zeros" shortcut for multiplying, even though this is a division.
pv-05 Present from here

Which list puts $3.7,\ 3.65,\ 3.802$ in ascending order (smallest first)?

Option A: $3.7,\ 3.65,\ 3.802$

Option B: $3.802,\ 3.65,\ 3.7$

Option C: $3.802,\ 3.7,\ 3.65$

Option D: $3.65,\ 3.7,\ 3.802$

Answer and misconceptions

Option A: $3.7,\ 3.65,\ 3.802$ ✗
Thinks longer decimals are largerOrders by number of digits after the point, like whole numbers.

Option B: $3.802,\ 3.65,\ 3.7$ ✗
Thinks shorter decimals are largerBelieves more decimal places means smaller pieces, so the longest is smallest.

Option C: $3.802,\ 3.7,\ 3.65$ ✗
Confuses ascending with descendingOrders the decimals correctly but largest first.

Option D: $3.65,\ 3.7,\ 3.802$ ✓ Correct
pv-06 Present from here

Work out $0.6 \div 0.02$

Option A: $30$

Option B: $0.3$

Option C: $0.012$

Option D: $3$

Answer and misconceptions

Option A: $30$ ✓ Correct

Option B: $0.3$ ✗
Divides the digits and keeps the decimal places of the first numberWorks out $6 \div 2 = 3$ and gives it one decimal place like $0.6$. Dividing by a number less than 1 makes the answer bigger.

Option C: $0.012$ ✗
Multiplies instead of dividingWorks out $0.6 \times 0.02 = 0.012$.

Option D: $3$ ✗
Multiplies the two numbers by different powers of 10Changes $0.6$ to $6$ (×10) but $0.02$ to $2$ (×100). Both must be multiplied by the same amount: $60 \div 2 = 30$.