�3 2.1 Upper and lower bounds of accuracy

195

1 The length of a rod is 80 cm correct to the nearest cm. What is the largest possible length the rod could have?

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2 The mass of a block is 6 kilograms correct to the nearest kilogram. What is the smallest possible mass the block can have?

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3 The length of a rectangle is 6 cm correct to the nearest millimetre. What is the largest possible length the rectangle could have?

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4 Write down the lower bound of each of these numbers written correct to 1 decimal place.

a 6.6 ........................................... b 10.8 ...........................................

c 11.1........................................... d 12.0 ...........................................

5 Write down the lower bound of each of these numbers written correct to 2 decimal places.

a 3.48 ........................................... b 14.67 ...........................................

c 5.60 ........................................... d 12.00 ...........................................

6 Write down the upper bound of each of these numbers written correct to 1 decimal place.

a 6.6 ........................................... b 10.8 ...........................................

c 11.1 ........................................... d 12.0 ...........................................

7 Write down the upper bound of each of these numbers written correct to 2 decimal places.

a 3.48 ........................................... b 14.67 ...........................................

c 5.60 ........................................... d 12.00 ...........................................

8 Write down the lower bound of each of these numbers when written to the number of signi� cant � gures shown.

a 46 (2 significant figures) ........................................... b 3.8 (2 significant figures) ...........................................

c 400 (1 significant figures) ........................................... d 400 (2 significant figures) ...........................................

9 Write down the upper bound of each of these numbers when written to the number of signi� cant � gures shown.

a 68 (2 significant figures) ........................................... b 370 (2 significant figures) ...........................................

c 3.14 ( 3 significant figures) ........................................... d 2.718 (4 significant figures) ...........................................

1 0 The area of a � eld is 2800 m2 correct to 2 signi� cant � gures. Write down the upper bound of the area.

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For 1 decimal place, the lower bound is found by subtracting 0.05.

For 2 decimal places, the lower bound is found by subtracting 0.005.

Guided practice worksheet

B

A

Questions are targeted at the grades indicated

�3 2.2 Calculating the bounds of an expression

197

1 a = 4.0 (1 decimal place) b = 2.4 (1 decimal place)

Work out the a upper bound of a + b b lower bound of a + b

a .......................................................................................................... b ..........................................................................................................

2 c = 342 (3 signi� cant � gures), d = 122 (3 signi� cant � gures)

Work out the a upper bound of c + d b lower bound of c + d

a .......................................................................................................... b ..........................................................................................................

3 x = 6.4 (2 signi� cant � gures), y = 7 (1 signi� cant � gure)

Work out the a upper bound of xy b lower bound of xy

a .......................................................................................................... b ..........................................................................................................

4 p = 0.82 (2 signi� cant � gures), q = 0.056 (2 signi� cant � gures)

Work out the a upper bound of pq b lower bound of pq

a .......................................................................................................... b ..........................................................................................................

5 x = 6.8 (1 decimal place), y = 4.5 (1 decimal place).

Work out the a lower bound of x – y b upper bound of x – y

a ..........................................................................................................

b ..........................................................................................................

6 a = 16.4 (3 signi� cant � gures) b = 3.8 (2 signi� cant � gures)

Work out the a lower bound of ab b upper bound of

ab

a .......................................................................................................... b ..........................................................................................................

7 p = 2.00 (2 decimal places), q = 1.80 (2 decimal places)

Work out the a upper bound of p – q b upper bound of pq

a .......................................................................................................... b ..........................................................................................................

8 y a bc= +

a = 3.2 (2 significant figures), b = 4.8 (2 significant figures) c = 2.5 (2 significant figures). Work out the a lower bound of y b upper bound of y

a .......................................................................................................... b ..........................................................................................................

9 A rectangle has a length of 12.8 cm correct to the nearest mm anda width of 6.4 cm correct to the nearest mm. Work out the upper bound of the area of the rectangle. Give your answer in cm2.

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1 0 The area of a triangle is 121 cm2 correct to the nearest cm2. The base of the triangle is 4.5 cm correct to the nearest mm. Calculate the lower bound of the height. Give your answer in cm.

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To � nd the lower bound of a di� erence, x – y, use the smallest possible value of x and the largest possible value of y.

12.8 cm = 128 mm, so the lower bound is 127.5 mm (=12.75 cm) and the upper bound is 128.5 mm (=12.85 cm).

Guided practice worksheet

A

Questions are targeted at the grades indicated