The document contains examples of calculating: 1) Density of various substances using their mass and volume 2) Calculating the radius and diameter of a sphere given its volume and density 3) Performing multi-step calculations involving units conversion, division, subtraction and multiplication 4) Converting between units such as kilometers to meters, feet to meters, liters to cubic meters and milligrams to grams.

1. 1.12
(a) air – homogenous mixture
(b) tomato juice – heterogeneous mixture ( it separates)
(c) iodine crystals – pure substance
(d) sand – heterogeneous mixture
1.28
(a)
1.25 cm
76.31g
3 3
= 22.61g / cm3
1.500 cm
(b) ρ Ti= 4.51g/cm3
1cm3
4.51g / cm3 * 125ml * = 564 g
1ml
(c) ρ Ben=0.8787g/ml
0.8787 gBen 1000ml
* 0.1500 L * = 131.8 gBen
ml 1L

2. 1.32
M=2.17Kg
16.8cm
2.33g
ρSi = V = Πr 2
cm3
1cm 3 1000 g
2.17 Kg * * = 931cm 3
2.33 g 1Kg
931cm3 = Π 2 * h
r
931cm3 = 3.14 * r 2 *16.8cm
17.6cm = r 2 2
4.20cm = r ⇒d = 2r = 8.40

3. 1.40
(a) 320.5 – (6104.5/2.3) divide first, sf=2
320.5 – (2700) subtract, sf=2
-2,400
(b) {(283.5x105) – (1.200 x 103)} x 2.854 in brackets least decimals is 1, sf=4
2.835 x 107 x 2.845 sf=4
8.066 x 107
(c) (0.0045 x 20,000.0) + (2813 x 12) sf of the first bracket is 4, the second is 2
90.00 + 34,000 least decimal places has a sf of 2
34,000
(d) 863 x [1255 – (3.45 x 108)] inner bracket sf=3
863 x [1255- 373] neither bracketed number has decimals so sf = 3 (smallest number)
863 x 882 sf=3
761,000
1.44
(a) V light = 2.998 m/s
m 1km 3600s km
V = 2.998 *108 * * = 1.079 *109
s 1000m 1hr h
(b)
.3048m
1454 ft * = 443.2m
1 ft
(c)
1000l
3,666,500m * = 3.665 * 10 9 l
3
m3

4. (d)
232mgCh 1000ml 1gCh
* * * 5.2 L = 12 gCh
100ml 1L 1000mgCh