Question

1. danita wants to install new cupboards in her kitchen. the space available in her kitchen is 130 cm wide, measured to the nearest centimetre. she plans to buy pre - built cupboards. the sizes available are 41 cm, 65 cm, and 24 cm wide. if danita were to buy one of each size of the cupboards, can she safely assume that they will fit in the available space? why or why not?

practise your new skills

1. convert the values in the table into each of the other si units of measure.

units of length in the système international

millimetre (mm)	centimetre (cm)	decimetre (dm)	metre (m)	decametre (dam)	hectometre (hm)	kilometre (km)
	315.9
					29.15

1. round each measurement to the indicated degree of precision.

a) 1.0925 km to the nearest hundredth
b) 29.51 cm to the nearest whole unit
c) 6021.139 mm to the nearest tenth

1. would you expect the following methods to give accurate measurements? why or why not?

a) measuring the amount of water in a tub using a tablespoon.

Explanation:

Step1: Calculate total width of cupboards

Add the widths of the three cupboards: $41 + 65+24=130$ cm.

Step2: Consider measurement uncertainty

The available space is 130 cm measured to the nearest centimetre. The actual available space could be as low as 129.5 cm and the total width of the cupboards could be 130 cm. So, there is a risk that the cupboards may not fit.

for converting SI units (for question 1 in the image):

Step1: Recall conversion factors

$1$ m = 10 dm = 100 cm = 1000 mm, $1$ dam = 10 m, $1$ hm=100 m, $1$ km = 1000 m.

Step2: Convert 123.1 m

To mm: $123.1\times1000 = 123100$ mm; to cm: $123.1\times100=12310$ cm; to dm: $123.1\times10 = 1231$ dm; to dam: $123.1\div10 = 12.31$ dam; to hm: $123.1\div100 = 1.231$ hm; to km: $123.1\div1000=0.1231$ km.

Step3: Convert 315.9 cm

To mm: $315.9\times10 = 3159$ mm; to dm: $315.9\div10 = 31.59$ dm; to m: $315.9\div100 = 3.159$ m; to dam: $315.9\div1000 = 0.3159$ dam; to hm: $315.9\div10000 = 0.03159$ hm; to km: $315.9\div1000000=3.159\times10^{- 4}$ km.

Step4: Convert 29.15 km

To hm: $29.15\times10 = 291.5$ hm; to dam: $29.15\times100 = 2915$ dam; to m: $29.15\times1000 = 29150$ m; to dm: $29.15\times10000 = 291500$ dm; to cm: $29.15\times100000 = 2915000$ cm; to mm: $29.15\times1000000 = 29150000$ mm.

for rounding (for question 2 in the image):

Step1: Round 1.0925 km to nearest hundredth

Look at the thousandths place. Since 2 < 5, we keep the hundredths place as it is. So, $1.0925\approx1.09$ km.

Step2: Round 29.51 cm to nearest whole unit

Look at the tenths place. Since 5 $\geq$ 5, we round up. So, $29.51\approx30$ cm.

Step3: Round 6021.139 mm to nearest tenth

Look at the hundredths place. Since 3 < 5, we keep the tenths place as it is. So, $6021.139\approx6021.1$ mm.

for question 3 in the image (a):

Step1: Analyze the method

A tablespoon is a very small unit of volume. A tub contains a large amount of water. Measuring a large volume with a very small - capacity measuring tool will require a large number of measurements and is likely to lead to cumulative errors.

Answer:

No, she cannot safely assume they will fit because of measurement uncertainty. The actual available space might be less than the total width of the cupboards when considering the rounding - off in measurement.