Sec 1 Mathematics Approximation & Estimation topical questions

Round 8.2461 as instructed.

1. (a)to 1 decimal place[1]
2. (b)to 2 decimal places[1]
3. (c)to the nearest whole number[1]

Round each number to 2 significant figures.

1. (a)6 381[1]
2. (b)0.092 77[1]
3. (c)54 296[1]

State the number of significant figures in each of these measured values.

1. (a)407 km[1]
2. (b)0.0052 s[1]
3. (c)23.0 °C[1]

A number is rounded to 5.2 to 1 decimal place. State the smallest and largest values it could have taken.

Round 27.9583 as instructed.

1. (a)to 2 decimal places[1]
2. (b)Round 4.099 to 1 decimal place.[1]
3. (c)Round 356.5 to the nearest whole number.[1]

Round each number to 2 significant figures.

1. (a)0.006 507[1]
2. (b)84 999[1]
3. (c)0.040[1]

Estimate the value of each expression by rounding to 1 significant figure.

1. (a)72.6 × 3.8[2]
2. (b)(6 120 + 2 890) ÷ 29[2]

A school fundraiser collected $3 846.20 from 173 students.

1. (a)Estimate the average amount collected per student.[2]
2. (b)The exact average is $22.23. Explain why your estimate is close to this.[2]

A sprinter’s time is recorded as 11.8 s, correct to 1 decimal place.

1. (a)Could the exact time be 11.79 s? Explain.[2]
2. (b)State the complete range of exact times consistent with the recording.[2]

A supermarket receives a delivery of 2 465 packets of noodles, packed into cartons that each hold 48 packets.

1. (a)Find the number of cartons needed to pack every packet.[3]
2. (b)Estimate the number of cartons by rounding to 1 significant figure, and comment on the difference.[1]

The number X is given as 3.24, correct to 2 decimal places.

1. (a)Write an inequality for the possible values of X.[2]
2. (b)Could X equal 3.235? Explain.[1]
3. (c)Could X equal 3.246? Explain.[1]

A number N is rounded to 2 significant figures and the result is 470. Rounding the same number to 1 significant figure gives 500.

1. (a)Write an inequality for the possible values of N.[2]
2. (b)Give one specific value N could take, and explain why it satisfies both roundings.[2]

A repeating decimal X satisfies: X is between 0.4 and 0.5, and X rounded to 2 decimal places equals 0.45. Explain whether X could equal four-ninths (0.444... recurring).

A tour company runs minibuses of 15 seats for a group of 96 people, and each trip to the venue takes 12 minutes with a 5-minute turnaround between trips. The first trip starts at 09:00.

1. (a)Find the number of full trips needed for everyone, and justify the direction of rounding.[2]
2. (b)Estimate the total time needed, by rounding the trip time to 1 significant figure.[1]
3. (c)The exact calculation gives 7 trips × 12 min + 6 turnaround gaps × 5 min = 114 min. Compare this with your estimate and comment.[2]

m = 24.6 and n = 5.2, each correct to 1 decimal place.

1. (a)Write inequalities for the possible values of m and of n.[2]
2. (b)Find the greatest possible value of m + n.[1]
3. (c)Find the smallest possible value of m × n, giving your answer correct to 3 significant figures.[2]