While doing measurement homework, I discovered that I needed to use scientific notation. However, I never learnt it before so I had to teach myself. Being the lazy individual I am, I didn’t bother reading the notes and dove right into some practice questions, such as:

2. Express each number in scientific notation.

a) 2 300          b) 7 580 000          c) 41 000 000 000

All I knew was that I had to write it into (x and y represent integers). After struggling and repeatedly getting the answers wrong, I started to notice a pattern. I found that if I counted the numbers after the first one, the number I received became the exponent. Also, the numbers that aren’t 0 would be turned into a decimal less than 10 and more than 0. For example:

2 300

  There are 3 numbers after the 2, so the exponent is 3. 23 becomes 2.3. Written in scientific notation:

I tried this strategy for the rest of the questions and it worked! Until I ran into these sneaky questions:

0.000 023

Here, I figured out that I can count the number of digits after the decimal point, then subtract the number of digits that aren’t 0s. However, I need to leave out one digit when subtracting. Example:

000 023 = 6 digits

There are 2 digits that aren’t 0, but I need to leave one out, so:

,so

Through trial and error I also discovered that the exponent becomes negative when dealing with these tiny numbers. I was delighted to find out that my made-up strategy was similar to the one my math teacher taught, when we went over our homework.

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This week I had a bit of trouble with a couple of questions, including this one:

I had to arrange them in order. Since entire radicals are easier to organize than mixed radicals, I tried converting them. However, that did not go so well. I converted them by multiplying the coefficient by itself times ( = index). For example, on the first radical, . I got a ridiculously huge number, and since I was not allowed to use a calculator, I stopped multiplying after the 4th or 5th 7. I did the same for the remaining radicals, except for the last one which had me confused. As you can see, I received huge, huge numbers which aren’t very efficient for calculations…

After I ordered the first three radicals, I checked the answers, only to find that they were all incorrect. My strategy had worked in the past before, but for some reason I got the wrong answers with this conversion method.

I turned to my friend for help. She asked me what times itself 6 times equals 1, and I said 1. She then asked me to multiply 1 by 7, which is 7. And that’s the answer! Trying the same with the others, I converted them into simpler entire radicals without having to do complicated multiplication.

The last radical: 

——–>

, so !

 

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This week I had quite a bit of difficulty on the skills check, especially with the equation on the back:

However, while doing corrections I had a huge “Ah-Ha!” moment, and the solution made itself clear to me. My first try was a disaster:

     I got rid of the brackets with multiplication.

    Then, I added to the equation in order to remove the fraction on the left side.

    I multiplied the equation by 3 to turn into 4x and into 2.

---

Then I ran out of time…but clearly I had no clue what I was doing. Even if I did finish, the answer probably would have been wrong. My second try makes much more sense:

    I multiplied 2x and -1 by .

    I multiplied everything by 3.

    I added +2 to both sides.

    I multiplied the equation by 2.

    I subtracted 3x from both sides.

After dividing the equation by 5, I got the answer!

x = -10

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