**Standard form and bounds**

Starter

(a) Write the number 128000000 in standard form.

(b) Write down the upper and lower bounds of the number 128000000.

(c) Write down your answers to (b) in standard form.

Activity

Complete the worksheet finding the upper and lower bounds for each quantity.

Example

The speed of light is 2.998 x 10 ms correct to 4 s.f. The distance to Proxima Centauri (the closest star to the sun) is 4.01 x 10 metres correct to 3 s.f. Work out the upper and lower bounds of the time in seconds it takes for light from Proxima Centauri to reach us.

Use your answers to suggest a suitable value for the time it takes light from Proxima Centauri to reach us.

**L.O. - Calculate upper and lower bounds of measured values given in standard form.**

Starter

(a) Write the number 128000000 in standard form.

(b) Write down the upper and lower bounds of the number 128000000.

(c) Write down your answers to (b) in standard form.

1.28 x 10

128500000 127500000

1.285 x 10 1.275 x 10

8

8

8

8

16

-1

Example

The speed of light is 2.998 x 10 ms correct to 4 s.f. The distance to Proxima Centauri (the closest star to the sun) is 4.01 x 10 metres correct to 3 s.f. Work out the upper and lower bounds of the time in seconds it takes for light from Proxima Centauri to reach us.

Upper Bound = 4.015 x 10 ÷ 2.9975 x 10 = 1.339 x 10 seconds.

Lower Bound = 4.005 x 10 ÷ 2.9985 x 10 = 1.335 x 10 seconds.

Use your answers to suggest a suitable value for the time it takes light from Proxima Centauri to reach us.

1.34 x 10 seconds.

8

16

-1

16

16

8

8

8

8

8

Example

The mass of a proton is 1.673 x 10 grams.

The mass of a neutron is 1.675 x 10 grams.

The mass of an electron is 9.110 x 10 grams.

All values are given to 4 s.f.

An atom of helium has 2 protons, 2 neutrons and 2 electrons.

Work out the upper and lower bounds of the mass of an atom of helium.

-24

-24

-28

Example

The mass of a proton is 1.673 x 10 grams.

The mass of a neutron is 1.675 x 10 grams.

The mass of an electron is 9.110 x 10 grams.

All values are given to 4 s.f.

An atom of helium has 2 protons, 2 neutrons and 2 electrons.

Work out the upper and lower bounds of the mass of an atom of helium.

-24

Upper bound: 1.6735 x 10 x 2 + 1.6755 x 10 x 2 + 9.1105 x 10 x 2

3.347 x 10 + 3.351 x 10 + 1.8221 x 10

3.347 x 10 + 3.351 x 10 + 0.0018221 x 10

6.670 x 10 grams

-24

-28

-24

-24

-24

-24

-28

-27

-24

-24

-24

-24

Lower bound: 1.6725 x 10 x 2 + 1.6745 x 10 x 2 + 9.1095 x 10 x 2

3.345 x 10 + 3.349 x 10 + 1.8219 x 10

3.345 x 10 + 3.349 x 10 + 0.0018219 x 10

6.696 x 10 grams

-24

-24

-24

-24

-24

-24

-24

-24

-28

-27

Activity

Complete the worksheet finding the upper and lower bounds for each quantity.

1.14 x 10 and 1.12 x 10

9

9

6.2 x 10 and 4.143 x 10

2

2

4 x 10 and 2 x 10

-7

-7

5.38 and 4.63

Dust mite by between 1.405 x 10

and 1.295 x 10

-3

-3

Between 1.97% and 1.91%

Between 82.25 kg and 56.25 kg

Dione: 1.43 x 10 and 1.42 x 10

Enceladus: 1.29 x 10 and 1.28 x 10

Iapetus: 1.16 x 10 and 1.15 x 10

Rhea: 1.33 x 10 and 1.32 x 10

Tethys: 1.211 x 10 and 1.208 x 10

Titan: 1.896 x 10 and 1.885 x 10

3

3

3

3

3

3

3

3

3

3

3

3

i) 4.66 x 10 and 4.64 x 10

ii) 7.325 x 10 and 7.295 x 10

iii) 3 x 10 and 2.988 x 10

-26

-26

-26

-26

-26

-26

Activity

It has been said that if you unravel your DNA it would stretch all the way to the moon. Is this true?

You are given:

The number of cells in the human body is 3.27 x 10 .

Each cell contains 3 x 10 base pairs.

Each base pair is 3.4 x 10 metres long.

The Moon is 3.8 x 10 metres from Earth.

12

9

-10

8

Activity

It has been said that if you unravel your DNA it would stretch all the way to the moon. Is this true?

Yes, in fact a minumum of nearly 10 km further!

You are given:

The number of cells in the human body is 3.27 x 10 .

Each cell contains 3 x 10 base pairs.

Each base pair is 3.4 x 10 metres long.

The Moon is 3.8 x 10 metres from Earth.

12

9

-10

8

**Activities**

**Activity**

Answers

Answers

**Key**

Examples

Examples

**Worked**

Example

Example

**Worked**

Example

Example