Rounding

Number

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Round $3.476$ to $1$ decimal place and to $2$ decimal places.

2 marks
Round $6840$ to $1$ significant figure and to $2$ significant figures.

2 marks
Round $0.004872$ to $2$ significant figures and to $3$ significant figures.

3 marks
A crowd of $18462$ people is reported to the nearest hundred and to the nearest thousand. Write both figures.

3 marks
Prices are rounded to the nearest $10$p. Which of £$2.34$, £$2.35$, £$2.44$ and £$2.45$ round to £$2.40$?

4 marks
Jonny rounds a number to the nearest integer and gets $8$. Write an inequality for the original number $x$.

4 marks
The attendances at four matches are $2386$, $2419$, $2444$ and $2462$. Round each attendance to the nearest ten, add the rounded values, then find the difference between that estimate and the exact total.

5 marks
A number $n$ rounds to $6.35$ to $2$ decimal places. Write the error interval for $n$. Then write the error interval for $4n$.

6 marks

Mark scheme

Answer. $3.5$ and $3.48$
- To $1$ d.p. the digit after the tenths is $7$, so $3.5$.
- To $2$ d.p. the digit after the hundredths is $6$, so $3.48$.
Answer. $7000$ and $6800$
- To $1$ s.f. the first digit is $6$ and the next digit is $8$, so $7000$.
- To $2$ s.f. the second digit stays $8$, so $6800$.
Answer. $0.0049$ and $0.00487$
- The first significant digit is $4$.
- To $2$ s.f. round the $8$ up, so $0.0049$.
- To $3$ s.f. the next digit is $2$, so $0.00487$.
Answer. $18500$ and $18000$
- Tens digit is $6$, so the nearest hundred is $18500$.
- Hundreds digit is $4$, so the nearest thousand is $18000$.
Answer. £$2.35$ and £$2.44$
- Numbers that round to $2.40$ are from $2.35$ up to, but not including, $2.45$.
- £$2.34$ rounds to £$2.30$.
- £$2.45$ rounds up to £$2.50$.
- £$2.35$ and £$2.44$ round to £$2.40$.
Answer. $7.5 \le x < 8.5$
- The lower end of the round-to-$8$ interval is $7.5$.
- The upper end is $8.5$, and $8.5$ itself rounds to $9$.
- $7.5 \le x < 8.5$
Answer. Rounded total $9710$, exact total $9711$, difference $1$
- Rounded values: $2390$, $2420$, $2440$, $2460$.
- Rounded total $= 9710$.
- Exact total $= 2386 + 2419 + 2444 + 2462 = 9711$.
- Difference $= 1$.
Answer. $6.345 \le n < 6.355$ and $25.38 \le 4n < 25.42$
- Half of $0.01$ is $0.005$.
- $6.345 \le n < 6.355$
- $4 \times 6.345 = 25.38$ and $4 \times 6.355 = 25.42$.
- $25.38 \le 4n < 25.42$