Standard Form

This form is very useful to express really large or really small numbers. It is very useful for science (atoms, molecules, cells, astronomy).

A∗10nA number (can be a decimal) between 1 - 9.n number of digits the number should move by \begin{aligned} &A * 10^n \\ &A \text{ number (can be a decimal) between 1 - 9.} \\ &n \text{ number of digits the number should move by} \end{aligned}

With this format you can express any number.

"Write 2350 in standard form":

  1. count the number of digits (after the first one) (4−1)(4-1)
  2. add a decimal point between the first and second number 2.352.35
  3. put the two values into the formula above to get: 2.35∗104 2.35 * 10^4

To express really small numbers you need a SLIGHTLY different method (spot the difference):

"Write 0.00034 in standard form":

  1. count the number of digits after the decimal place and before the last digit 44
  2. make the number negative: −4 -4
  3. add a decimal point between the last and second last number 3.43.4
  4. put the two values into the formula above to get: 3.4∗10−43.4*10^{-4}

If you think you got it wrong, you could always check your answer by typing it in on the calculator.

For the next part you should try and learn "Laws of indices" first.

Multiplying and dividing

Firstly, you can always convert the numbers to decimals and just multiply and divide like normal. But thats boring and a waste of time.

For these questions, just remember to group the similar bits together and then work it out.

For example "Multiply 3∗105 3 * 10^5 by 5∗103 5 * 10^3:" (3∗5)∗(105∗103)=15∗105+3=15∗108 (3 * 5) * (10^5 * 10^3) = 15 * 10^{5+3} = 15 * 10^8

"Divide 2∗103 2 * 10^3 by 3.5∗1043.5 * 10^4":

2∗1033.5∗104=23.5∗103104=23.5∗103−4=23.5∗10−1 \dfrac{2 * 10^3}{3.5*10^4} = \dfrac{2}{3.5} * \dfrac{10^3}{10^4} = \dfrac{2}{3.5} * 10^{3-4} = \dfrac{2}{3.5} * 10^{-1}

Adding and Subtracting

It is probably simpler to convert to normal numbers and add and subtract normally.

However, you can do this method:

  1. Make sure the powers of 10 are the same
  2. add or subtract the numbers
  3. make sure the number is between 1 and 9

"Calculate 2.5 x 10^3 - 1.2 x 10^2:"

2.5∗103−1.2∗102=2.5∗10∗103÷10−1.2∗102=25∗102−1.2∗102=(25−1.2)∗102=23.8÷10∗102∗10=2.38∗103 \begin{aligned} 2.5 * 10^3 - 1.2 * 10^2 &= 2.5 \color{red}{* 10} * 10^3 \color{red}{\div 10} - 1.2 * 10^2 \\ &= 25 * 10^2 - 1.2 * 10^2 \\ &= (25 - 1.2) * 10^{2} \\ &= 23.8 \color{red}{\div 10} * 10^2 \color{red}{* 10} \\ &= 2.38 * 10^3 \end{aligned} 2.5∗103−1.2∗102=2500−120=2380 \begin{aligned} 2.5 * 10^3 - 1.2 * 10^2 &= 2500 - 120 = 2380 \end{aligned}

results matching ""

    No results matching ""