Unit 14 Section 3 : Calculator Use

In this section we consider how to make the best use of calculators. We focus on the use of brackets. We will then look at the use of the memory functions. Calculators vary a great deal both in the number of memories available and in how they are used. It is essential for you to learn how your calculator memory works.

Example 1

Calculate , giving your answer to 3 decimal places.

Use the following keys to obtain the correct answer:

( 4 . 7 + 3 . 2 ) ÷
( 8 . 6 – 3 . 1 ) =

You should obtain 1.436363636, which rounds to 1.436 to 3 decimal places.

Note how brackets have been used around both the numerator and the denominator of the fraction.

Example 2

Zarah uses her calculator to obtain an answer to,

She obtains the answer –3.75 to 2 decimal places.

(a)

Use estimation to show that her answer is incorrect.

≈ ≈ = 0.05

The estimate indicates that Zarah's negative answer must be incorrect.

(b)

Describe the error she made when using her calculator, and write down the calculation that she actually carried out.

Zarah forgot to include brackets around the denominator of the fraction. She actually calculated

– 3.8

(c)

Calculate the correct answer, correct to 3 significant figures.

The correct answer can be obtained by using the following sequence of keys:

4 . 7 ÷ ( 1 0 2 – 3 . 8 ) =

This gives a value of 0.047861507, which is 0.0479 to 3 significant figures.

Note that this compares well with the estimate.

Exercises

Question 1

Calculate the answers to the following, giving your answers to 2 significant figures:

(a)
(b)
(c)
(d)
(e)
(f) –
(g)
(h)
Question 2

Calculate the following, giving your answers correct to 3 significant figures:

(a)(6.72 – 3.8)2
(b)(4.62 + 3.84)3
(c)
(d)(3.68 + 2.41) × (8.21 – 3)
(e)6.22 × (14.2 – 8.03)
(f)11.42 + (3.8 – 4.2)2
Question 3

For each calculation below, first obtain an estimate of the answer and then calculate the actual answer, where necessary rounding the value to 3 significant figures.

(a)

Estimation:

Calculation:

(b)

–

Estimation:

Calculation:

(c)

Estimation:

Calculation:

(d)

Estimation:

Calculation:

Question 4

Joseph and Jenny use their calculators to try to calculate,

When they round to 3 significant figures, Joseph obtains the answer 5.63 and Jenny gets 2.73.

(a)

Use estimation to decide who has the incorrect answer.

≈ so has the incorrect answer.
Joseph calculated 3.7 +
(b)

Check that the other answer is correct.

= (to 3 s.f.)
Question 5

Dee and Daniella press the keys on their calculators in the following sequences:

Dee
4 ÷ 7 + 6 = ÷ 3 =
Daniella
4 ÷ 7 + 6 ÷ 3 =
(a)

What answers do they obtain?

Dee obtains (to 3 s.f.)

Daniella obtains (to 3 s.f.)

(b)

has calculated + 6 ÷ 3

has calculated +

Question 6

Adrian calculates the number of seconds in 2 hours and 40 minutes as 2520. His brother, Richard, says that he is wrong and that the correct answer is 9600 seconds.

(a)

Use an estimate to show that Adrian must be wrong.

2 hours 40 minutes ≈ 2 hours = seconds
(b)

Write down the calculation that Richard did to obtain his answer.

(2 × + ) ×
Question 7

Denise says that she can obtain the answer to

+

using her calculator, but without using brackets. Hannah disagrees.
Who is correct?

is correct
Scientific calculators incorporate the BODMAS rule, so will divide 3.6 by 17.2, and 8.6 by 3.5, then add the results together, as required.
Question 8

Which of the following can be calculated on a calculator, without using brackets or a memory?

3 × 7 + 8 × 32
+
Question 9

For each of the following calculations, first obtain an estimate and then calculate the actual value, where necessary giving your answer correct to 3 significant figures.

(a)
 ≈  Correct answer:
(b)
+  ≈  Correct answer:
(c)
 ≈  Correct answer:
(d)
 ≈  Correct answer:
Question 10

Calculate the number of seconds in 3 days, 4 hours and 28 ½ minutes with your calculator.

seconds
{[(3 × 24) + 4] × 60 + 28.5} × 60 = 275 310
Question 11

David is studying blood cells through a microscope.

The diameter of a red cell is 0.000714 cm and the diameter of a white cell is 0.001243 cm.

(a)

Use a calculator to work out the difference between the diameter of a red cell and the diameter of a white cell. Give your answer in millimetres.

mm
(b)

David wants to explain how small the cells are. He calculates how many white cells would fit across a full stop which has a diameter of 0.65 mm.

How many whole white cells would fit across the full stop?

white cells
Question 12

Rectangles with length and width in the special ratio 1 : .

Some artists use them because the proportions look attractive.

(a)

Work out .

Write this using 6 decimal places.

You may use your calculator efficiently to work out

e.g.
2 ÷ ( 1 + √ 5 ) =
or
1 + √ 5 = MS 2 ÷ MR =
(b)

Four faces of this cuboid are golden rectangles. The volume of the cuboid is:

× × 1

Use a short and accurate method on your calculator to calculate this. Write the volume using 6 decimal places.

e.g.
2 ÷ ( 1 + √ 5 ) = x²
or
1 + √ 5 = MS 2 ÷ MR = x²