125 practice questions covering A Peek Beyond the Point, organised into 1 topics.
125 questions include a written explanation.
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One jar holds $\frac{4}{5}$ litre of oil and another holds $0.75$ litre. Which jar holds more, and by how much?
AThey hold the same amount
BThe first, by $0.5$ litre
CThe first, by $0.05$ litre
DThe second, by $0.05$ litre
Show answer and explanation
Correct answer: C - The first, by $0.05$ litre
Since $\frac{4}{5}=\frac{8}{10}=0.8$ litre, the first jar holds more, and $0.80-0.75=0.05$ litre. Choosing the second jar reverses the comparison, $0.5$ litre comes from subtracting the digits carelessly, and the two amounts are not equal.
Q2
hard
A student works out $12.6-8.9$ and writes $4.7$. What does estimation tell us about this answer?
AIt is right; the estimate is also $4.7$
BIt is wrong; the answer should be about $21$
CIt is right, because estimation cannot check a subtraction
DIt is wrong; the answer should be about $4$, and exactly $3.7$
Show answer and explanation
Correct answer: D - It is wrong; the answer should be about $4$, and exactly $3.7$
Rounding gives $13-9=4$, and the exact difference is $3.7$, so the written answer $4.7$ is a whole unit too large. An estimate near $21$ would come from adding the two numbers, and estimation is a perfectly good check on a subtraction.
Q3
medium
Priya claims that no decimal lies between $0.7$ and $0.8$. Which example shows that she is wrong?
A$0.87$
B$0.07$
C$0.75$
D$0.8$
Show answer and explanation
Correct answer: C - $0.75$
The number $0.75$ has $7$ in the tenths place and $5$ in the hundredths, so it sits between $0.70$ and $0.80$ and disproves her claim. The value $0.87$ is larger than $0.8$, $0.07$ is far smaller than $0.7$, and $0.8$ is an endpoint rather than a number in between.
Q4
medium
Find the sum of the place values of the two digits that come after the decimal point in $9.36$.
A$0.9$
B$3.6$
C$9$
D$0.36$
Show answer and explanation
Correct answer: D - $0.36$
The digit $3$ is worth $0.3$ and the digit $6$ is worth $0.06$, and $0.3+0.06=0.36$. The value $9$ is the whole part, $0.9$ adds the digits $3$ and $6$ as if both were tenths, and $3.6$ ignores the places altogether.
Q5
hard
A ribbon exactly $1$ metre long is cut into $10$ equal pieces. Meera gives $3$ of these pieces to her sister. How much ribbon does the sister get?
A$0.3\ \text{m}$, which is $3\ \text{cm}$
B$0.3\ \text{m}$, which is $30\ \text{cm}$
C$0.03\ \text{m}$, which is $3\ \text{cm}$
D$3\ \text{m}$, which is $300\ \text{cm}$
Show answer and explanation
Correct answer: B - $0.3\ \text{m}$, which is $30\ \text{cm}$
Each piece is one tenth of a metre, so three pieces make $\frac{3}{10}=0.3\ \text{m}$. Since $1\ \text{m}=100\ \text{cm}$, that length is $30\ \text{cm}$. The value $0.03\ \text{m}$ is three hundredths, $3\ \text{m}$ is longer than the whole ribbon, and $0.3\ \text{m}$ cannot equal $3\ \text{cm}$.
Q6
medium
Inserting a zero to turn $0.4$ into $0.04$ changes the number in what way?
AIt makes the number ten times smaller
BIt makes the number a hundred times smaller
CIt makes the number ten times larger
DIt leaves the value unchanged
Show answer and explanation
Correct answer: A - It makes the number ten times smaller
In $0.4$ the digit $4$ is in the tenths place, and in $0.04$ it has slipped to the hundredths place, which is worth a tenth as much. So the value falls from four tenths to four hundredths, ten times smaller rather than larger, unchanged or a hundred times smaller.
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