2. Lesson focus
• Basic maths: converting units & indices
Learning objectives
At the end of the lesson you will be able to:
• convert between units and their multiple and submultiples;
• correctly handle indices.
Motion
3. Converting units LOs
Convert each of the following quantities:
a) 400 cm to m b) 24 x 104 mm into m c) 0.050 watt in mW
d) 2.5 x 10-3 kN to N e) n kW to W f) n milliwatt to W
g) 3.5 x 2.2 mA to A h) 3.4 x 103 x y gram to kg
Trickier
1. Convert an area of: a) 350 cm2 to m2 b) 0.06 m2 to cm2
2. Convert a volume of: b) 2.5 mm3 to m3 b) 0.07 m3 to mm3
3. Convert a density of 8 g per cm3 to kg per m3
Motion
4. Using indices - 1 LOs
1. Write as powers of ten:
a. 1/10 b) 1/10 000 c) 1/10-4
2. What is the reciprocal of:
a. 10-4 b) 102 c) 10-19
Motion
5. Using indices: rules LOs
General rules for using indices (‘powers’ or ‘exponents’) are:
multiplication 10a x 10b = 10a+b
division 10a/10b = 10a-b
raising to a power (10a)b = 10ab
meanings: y1/a = a√y (the ‘ath root of y’)
y a/b = b√ya (the ‘bth root of y to the a)
y0 = 1
Motion
6. Using indices - 2 LOs
1. Simplify the following:
a. y6 x y7 b. y8 ÷ y5 c. (y3)4 d. 3y2 x 4y3
2. Write as a single power:
a. 1/10 x 103 b. 1000 x 10-2 c. 104/10 d. 10-8 x 1012
e. 10-3 x 10-4 f. x-2 x x-2 g. x5 x x-2 h. 1/x2
i. 1/x-6 j. x8/x3 l. (x4)-6 m. √x3√(1/x5)
Motion
