24 Basic Engineering Mathematics
(iii) Press Shift and = and the answer 0.0289 appears.
(iv) Press the ENG function and the answer changes
to 28.9 × 10 −3 , which is engineering form.
Hence, 0.17 2 = 28.9×10 −3 in engineering form. The
ENG function is extremely important in engineering
calculations.
Problem 5. Change 348620 into engineering
form
(i) Type in 348620
(ii) Press = then ENG.
Hence, 348620 = 348.62×10 3 in engineering form.
Problem 6. Change 0.0000538 into engineering
form
(i) Type in 0.0000538
(ii) Press = then ENG.
Hence, 0.0000538 = 53.8×10 −6 in engineering form.
Problem 7. Evaluate 1.4 3
(i) Type in 1.4
(ii) Press x 3 and 1.4 3 appears on the screen.
(iii) Press = and the answer
343
125
appears.
(iv) Press the S ⇔ D function and the fraction
changes to a decimal: 2.744
Thus, 1.4 3 = 2.744.
Now try the following Practice Exercise
Practice Exercise 13 Square and cube
functions (answers on page 341)
1. Evaluate 3.5 2
2. Evaluate 0.19 2
3. Evaluate 6.85 2 correct to 3 decimal places.
4. Evaluate (0.036) 2 in engineering form.
5. Evaluate 1.563 2 correct to 5 significant
figures.
6. Evaluate 1.3 3
7. Evaluate 3.14 3 correct to 4 significant
figures.
8. Evaluate (0.38) 3 correct to 4 decimal places.
9. Evaluate (6.03)
3 correct to 2 decimal places.
10. Evaluate (0.018) 3 in engineering form.
4.3.2 Reciprocal and power functions
The reciprocal of 2 is
1
2
, the reciprocal of 9 is
1
9
and the
reciprocal of x is
1
x
, which from indices may be written
as x −1 . Locate the reciprocal, i.e. x −1 on the calculator.
Also, locate the power function, i.e. x , on your
calculator and then check the following worked
examples.
Problem 8. Evaluate
1
3.2
(i) Type in 3.2
(ii) Press x −1 and 3.2 −1 appears on the screen.
(iii) Press = and the answer
5
16
appears.
(iv) Press the S ⇔ D function and the fraction
changes to a decimal: 0.3125
Thus,
1
3.2
= 0.3125
Problem 9. Evaluate 1.5 5 correct to 4 significant
figures
(i) Type in 1.5
(ii) Press x and 1.5 appears on the screen.
(iii) Press 5 and 1.5 5 appears on the screen.
(iv) Press Shift and = and the answer 7.59375
appears.
Thus, 1.5 5 = 7.594 correct to 4 significant figures.
Problem 10. Evaluate 2.4 6 − 1.9 4 correct to 3
decimal places
(i) Type in 2.4
(ii) Press x and 2.4 appears on the screen.
(iii) Press Shift and = and the answer 0.0289 appears.
(iv) Press the ENG function and the answer changes
to 28.9 × 10 −3 , which is engineering form.
Hence, 0.17 2 = 28.9×10 −3 in engineering form. The
ENG function is extremely important in engineering
calculations.
Problem 5. Change 348620 into engineering
form
(i) Type in 348620
(ii) Press = then ENG.
Hence, 348620 = 348.62×10 3 in engineering form.
Problem 6. Change 0.0000538 into engineering
form
(i) Type in 0.0000538
(ii) Press = then ENG.
Hence, 0.0000538 = 53.8×10 −6 in engineering form.
Problem 7. Evaluate 1.4 3
(i) Type in 1.4
(ii) Press x 3 and 1.4 3 appears on the screen.
(iii) Press = and the answer
343
125
appears.
(iv) Press the S ⇔ D function and the fraction
changes to a decimal: 2.744
Thus, 1.4 3 = 2.744.
Now try the following Practice Exercise
Practice Exercise 13 Square and cube
functions (answers on page 341)
1. Evaluate 3.5 2
2. Evaluate 0.19 2
3. Evaluate 6.85 2 correct to 3 decimal places.
4. Evaluate (0.036) 2 in engineering form.
5. Evaluate 1.563 2 correct to 5 significant
figures.
6. Evaluate 1.3 3
7. Evaluate 3.14 3 correct to 4 significant
figures.
8. Evaluate (0.38) 3 correct to 4 decimal places.
9. Evaluate (6.03)
3 correct to 2 decimal places.
10. Evaluate (0.018) 3 in engineering form.
4.3.2 Reciprocal and power functions
The reciprocal of 2 is
1
2
, the reciprocal of 9 is
1
9
and the
reciprocal of x is
1
x
, which from indices may be written
as x −1 . Locate the reciprocal, i.e. x −1 on the calculator.
Also, locate the power function, i.e. x , on your
calculator and then check the following worked
examples.
Problem 8. Evaluate
1
3.2
(i) Type in 3.2
(ii) Press x −1 and 3.2 −1 appears on the screen.
(iii) Press = and the answer
5
16
appears.
(iv) Press the S ⇔ D function and the fraction
changes to a decimal: 0.3125
Thus,
1
3.2
= 0.3125
Problem 9. Evaluate 1.5 5 correct to 4 significant
figures
(i) Type in 1.5
(ii) Press x and 1.5 appears on the screen.
(iii) Press 5 and 1.5 5 appears on the screen.
(iv) Press Shift and = and the answer 7.59375
appears.
Thus, 1.5 5 = 7.594 correct to 4 significant figures.
Problem 10. Evaluate 2.4 6 − 1.9 4 correct to 3
decimal places
(i) Type in 2.4
(ii) Press x and 2.4 appears on the screen.