INDICES and STANDARD FORM
INDICES and STANDARD FORM
INDICES and STANDARD FORM
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Example 3.<br />
Work out the following. Give your answers in st<strong>and</strong>ard form.<br />
a) (3 × 10 7 ) + (1.4 × 10 5 ), b) (9.9 × 10 6 ) × (2 × 10 −3 ),<br />
c)<br />
−7<br />
4.5 × 10<br />
.<br />
−3<br />
3 × 10<br />
Solution.<br />
a) On a calculator (assuming it works the same way as a newish Casio!), press the<br />
following keys:<br />
( 3 × 1 0 x y 7) + ( 1 . 4 × 1 0 x y 5 ) =<br />
to get an answer of 30140000. Now convert to st<strong>and</strong>ard form as requested to<br />
get 3.014× 10 7 .<br />
b) Again simply use a calculator, including the bracket buttons, to get an answer<br />
of 19800.<br />
Convert to st<strong>and</strong>ard form to get 1.98 × 10 4 .<br />
c) Comment. This question ( is trying to catch us out by not putting brackets in. Let us<br />
−7<br />
4.5 × 10 )<br />
rewrite it correctly: . Now we simply grab a calculator!<br />
−3<br />
3 × 10<br />
Press the following keys:<br />
( )<br />
( 4 . 5 × 1 0 x y − 7 ) ÷ ( 3 × 1 0 x y − 3 ) =<br />
Minus button! NOT the subtract key.<br />
Answer = 0.00015 or, in st<strong>and</strong>ard form, 1.5 × 10 −4 .<br />
Comment.<br />
If your calculator is being lazy <strong>and</strong> displays the answer, 1.5 −04 , then simply remember<br />
to put in the ×10 <strong>and</strong> give your answer as 1.5 × 10 −4 . You see, not so daft after all<br />
these calculators !<br />
These days, GCSE examiners have a rather nasty habit of occasionally throwing the above<br />
types of calculations in the direction of the NON-CALCULATOR papers!<br />
Still, not to worry. I’ve included a whole bunch of these in the exercise below, which I advise<br />
you to stare at for a few days <strong>and</strong> nights <strong>and</strong> seek out your teacher if you require a more vocal<br />
explanation.<br />
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