WEBVTT
00:00:01.160 --> 00:00:04.560
What is the reciprocal of 0.08?
00:00:05.720 --> 00:00:11.600
For a number đť‘Ą, the reciprocal of đť‘Ą is given by one over đť‘Ą or one divided by đť‘Ą.
00:00:13.320 --> 00:00:18.080
Another way of saying this is that the product of a number and its reciprocal is always one.
00:00:19.360 --> 00:00:26.000
That means then that the reciprocal of 0.08 is one divided by 0.08.
00:00:27.120 --> 00:00:32.640
In a calculator exam, we can type this into our calculator, giving us an answer of 12.5.
00:00:32.640 --> 00:00:35.800
However, we might get asked this in a non-calculator exam.
00:00:35.800 --> 00:00:38.240
So itâ€™s useful to know how to answer this question.
00:00:39.920 --> 00:00:45.520
0.08 is equivalent to eight one hundredths, since eight is in the hundredths column.
00:00:46.720 --> 00:00:56.240
We might choose to simplify this immediately by dividing both the numerator and the denominator by four to get two twenty-fifths, although we could actually complete this step later.
00:00:57.360 --> 00:01:04.440
The reciprocal then of two twenty-fifths is one over two twenty-fifths or one divided by two twenty-fifths.
00:01:05.880 --> 00:01:09.760
To divide by a fraction, we change the divide sign to a multiply.
00:01:09.760 --> 00:01:11.480
Then we flip the second fraction.
00:01:12.560 --> 00:01:16.200
That is to say, we swap the numerator and the denominator.
00:01:16.200 --> 00:01:22.240
That gives us one multiplied by 25 over two, which is simply 25 over two.
00:01:23.440 --> 00:01:31.360
In fact, we can generalize this by saying that, to find the reciprocal of any fraction, we simply swap the numerator and the denominator.
00:01:32.320 --> 00:01:36.200
The reciprocal of two twenty-fifths is 25 over two.
00:01:37.440 --> 00:01:42.160
And our final step is to perform that division, 25 divided by two.
00:01:43.000 --> 00:01:45.520
Half of 25 is 12.5.
00:01:46.600 --> 00:01:51.720
So weâ€™ve correctly calculated the reciprocal of 0.08 without a calculator.
00:01:53.360 --> 00:02:02.440
Calculate cos of 36 degrees plus 3.9 divided by 19 multiplied by 0.12 all cubed.
00:02:02.960 --> 00:02:05.040
Give your answer correct to two decimal places.
00:02:06.800 --> 00:02:09.920
This is a question thatâ€™s testing our ability to use our calculator.
00:02:11.440 --> 00:02:16.920
Now many scientific calculators possess all the buttons we need to be able to answer this in one step.
00:02:18.320 --> 00:02:27.440
Typing this sum in with the brackets as shown and a fraction inside the first pair of brackets will give us the answer we need.
00:02:28.400 --> 00:02:32.880
And then once weâ€™ve done this, we can perform an intermediate step and write this down.
00:02:32.880 --> 00:02:40.760
Itâ€™s sensible to do this whenever we type a long sum into our calculator as it provides us with method mark should we make a mistake when inputting values.
00:02:42.000 --> 00:02:52.320
However, if weâ€™re not using a scientific calculator to answer this question, then we need to know how to perform each of the intermediate steps to help us answer this question.
00:02:53.480 --> 00:02:57.400
Weâ€™ll start by calculating the value of the numerator and the denominator.
00:02:58.520 --> 00:03:02.280
Cos of 36 degrees is 0.809.
00:03:03.640 --> 00:03:08.680
Many scientific calculators will open up a bracket automatically when we type cos.
00:03:08.680 --> 00:03:11.960
We must make sure to close those brackets when weâ€™re doing our calculations.
00:03:13.160 --> 00:03:16.480
Cos of 36 is equal to 0.809.
00:03:17.520 --> 00:03:23.080
That means that cos of 36 plus 3.9 is 4.709.
00:03:23.080 --> 00:03:25.120
Notice the use of these three dots.
00:03:25.120 --> 00:03:27.800
Itâ€™s a way of showing that weâ€™ve not yet rounded our answer.
00:03:28.440 --> 00:03:33.400
Rounding too early can cause errors in our final solution, so we want to avoid doing that wherever possible.
00:03:34.640 --> 00:03:38.800
19 multiplied by 0.12 is 2.28.
00:03:39.600 --> 00:03:45.760
So our sum becomes 4.709 divided by 2.28 all cubed.
00:03:46.880 --> 00:03:56.160
Remember, that fraction line means divide, so weâ€™ll divide our answer of 4.709 by 2.28 to get 2.065.
00:03:57.400 --> 00:04:04.200
Finally, we can cube this to get 8.8102, which is what we would have got had we typed this sum into our calculator.
00:04:05.320 --> 00:04:08.520
We mustnâ€™t forget to round our answer to two decimal places.
00:04:08.520 --> 00:04:11.200
And that gives us a solution of 8.81.