Conversions & Standard Form (Edexcel GCSE Physics)

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Conversions

  • As well as prefix (powers of ten) conversions (eg. km into m) there are also common unit conversions
  • One such unit conversion are those for time
    • The main time conversions are shown in the table below:

Time Conversions Table

Time Conversions Table, downloadable IGCSE & GCSE Physics revision notes

Hours & Seconds

  • A common time unit conversion is between hours and seconds
    • 1 hour = 60 minutes
    • 1 minute = 60 seconds

  • Therefore 1 hour = 60 × 60 = 3600 seconds
    • To convert from hours → seconds, multiply by 3600
    • To convert from seconds → hours, divide by 3600

Hours × 3600 = Seconds

Seconds ÷ 3600 = Hours  

Kelvin & Degrees Celsius

  • A common temperature unit conversion is between Kelvin and degrees Celsius (ºC)
  • The scale is defined as: 0 K = -273.15 ºC
    • To convert from Kelvin → Celsius, subtract 273.15
    • To convert from Celsius → Kelvin, add 273.15

 K − 273.15 = oC

  oC + 273.15 = K

Worked example

A cyclist takes 3.5 hours to travel to their destination. Calculate their time travelled in seconds.

Step 1: State the conversion

1 hour = 3600 s

Seconds = Hours × 3600

Step 2: Calculate the time in seconds

3.5 × 3600 = 12 600 s

Examiner Tip

You will be expected to remember these unit conversions in your exam and to confidently convert between them, so make to practice these to achieve full marks in the calculation questions.

Significant Figures & Standard Form

Significant Figures

  • The significant digits are the digits in a number that contributes to the value of that number
    • These are sometimes called significant figures (s.f)

  • In physics, values are rounded to a certain number of significant figures instead of decimal places

  • Non-zero digits are always significant
    • 123 is 3 s.f
    • 1.78 is 3 s.f

  • Any zeros between two significant digits are significant
    • 108 is 3 s.f
    • 10003 is 5 s.f
    • 1.006 is 4 s.f

  • Only a final zero or trailing zeros in the decimal portion (after the decimal point) are significant
    • 0.183 is 3 s.f (the zero is before the decimal - so is not significant)
      • 1,8 and 3 are the significant figures

    • 1390 is 3 s.f. (the final zero is not after a decimal point - so is not significant)
      • 1,3 and 9 are the significant figures

    • 1.40 is 3 s.f (the final zero is after the decimal point - so is significant)
      • 1,4 and 0 are all the significant figures

    • 0.012 is 2 s.f (the zeros are either before the decimal point or is not the final zero - so not significant)
      • 1 and 2 are the significant figures

    • 1.9000 is 5 s.f (the trailing zeros are after the decimal point - so is significant)
      • 1, 9, 0, 0 and 0 are all the significant figures

  • When rounding to a certain number of significant figures, this is done in a similar way to round to decimal places using the following procedure:

    1. Find the number of significant figures to round to
    2. Go to the digit for this significant figure
    3. Look at the value after this digit

    • If the value is 5 or greater, round this significant digit up
    • If the value is less than 5, leave this significant digit as it is

Significant Figures Examples 1, downloadable IGCSE & GCSE Physics revision notesSignificant Figures Examples 2, downloadable IGCSE & GCSE Physics revision notes

Rounding to 2 or 3 significant figures

Examples:

  • The value 7.8 is 2 s.f
    • To 1 s.f this is equal to 8

  • The value 9.12 is 3 s.f
    • To 2 s.f this is equal to 9.1

  • The value 3.65 × 10-4 is equal to 3.s.f
    • To 2 s.f this is equal to 3.7 × 10-4

  • The value 1020 is equal to 3 s.f
    • To 2 s.f this is equal to 1000

Standard Form

  • Standard form is a system of writing large and small numbers which is useful for working with very large or very small numbers
    • This also means writing whole lines of zeros can be avoided

  • Numbers in standard form are in written as:

a × 10n

  • They follow these rules:
    • a is a number between 1 and 10
    • n > 0 for large numbers i.e how many times a is multiplied by 10
    • n < 0 for small numbers i.e how many times a is divided by 10

  • For example:
    • 3 × 108 = 300 000 000 (3 multiplied by 10, 8 times)
    • 2 × 10-5 = 0.00002 (2 divided by 10, 5 times)

Standard Form, downloadable IGCSE & GCSE Physics revision notes

  • When rounding a number in standard form to a certain number of significant figures, only the value of a is rounded (the × 10n value will not be significant)
    • For example, 5.18 × 106 to 2 s.f. is 5.2 × 106

Worked example

Write the number 143 000 000 in standard form to 2 significant figures

Step 1: Write the number in standard form

    • Standard form should look like: a × 10n
    • a is a number between 1 and 10, so for this number, it will be 1.43
    • n is how many times 1.43 is multiplied by 10 to give 143 000 000
      • This is 8 times

1.43 × 108

Step 2: Write the number to 2 s.f

    • The 2nd significant figure in this value is the 4
    • The value after is 3, which is < 5 therefore the 4 is left as it is

1.4 × 108

Examiner Tip

In exam questions, always round your answer to the lowest number of significant figures quoted in the question textFor example, if the question uses the values 2.3 (2 s.f) and 4.667 (4 s.f), then the answer should be given to 2 s.fIf in doubt, it is normally wise to give the answer to 2 or 3 s.f!

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.