Non Calculator Methods

Question 1

What’s a non-calculator method to multiplying with decimals?
Eg. 5.2*0.45

Answer 1

Pretend the decimal isn’t there and multiply that
Then count how many decimals there were in the questions and put the decimal there
Eg. 52*45=2,340 —> 2.340

Question 2

What’s a non calculator method to dividing with decimals?
Eg. 5.2/0.08

Answer 2

Multiply the numbers by the same number so they are easier to divide
Eg. 5.2/0.08 —> 520/8=65

Question 3

How to estimate answers?

Answer 3

Round all the numbers into 1 significant figure unless stated otherwise

Question 4

How to estimate square root of numbers?
Eg. √ 67

Answer 4

Find the nearest square
Eg. ≈√ 64 —>8

Question 5

How to turn recurring decimals into fractions?
Use 0.6 ̇57 ̇

Answer 5

1) make x the recurring decimal —> 0.657657657…
2) depending on where the recurring dot is, make it either 10x/100x/1000x etc. so that the repeating part is is fully on the left side (10 if just 1 dot after decimal (eg.0.2 ̇). If it has 2 dots after the decimal (eg. 0.5 ̇2 ̇) then make it 100x. If it has a dot after a number (eg 0.28 ̇) then do 100x and 10x) —> 1000x= 657.657657…
3) subtract the 10…x by the original x unless the recurring sign isn’t right after the decimal to get rid of the recurring part —> 657.657…- 0.657..= 657 & 1000x-x= 999
4) then divide the the …x by it so it turns into x —> 657/999

Question 6

What happens if there are more than 2 recurring points?

Answer 6

One at the start of the recurring and 1 at the end
Eg. 0. 5 ̇ 67 ̇ —> 0.567567567…

Question 7

How to find the upper and lower bound of something by adding (x+y)
Use:x= 200 to 1 significant figure
Y= 5 to 1 significant figure

Answer 7

Upper bound = upper bound + upper bound —> 250+5.5=255.5
Lower bound = lower bound + lower bound —> 150+4.5=154.5
U can also put it into an inequality if it asks —> 154.5 ≤ x <255.5

Question 8

How to find the error interval of something?
Use: 4.5 to 1 decimal point

Answer 8

Lowest it could go before it rounds down —>4.45
Highest it could go before it rounds up —>4.55
Put it into an inequality … ≤x<… —> 4.45 ≤ x <4.55
(Remember it’s not always ≤ if the answer is rounded

Question 9

How to find the upper and lower bound of something by subtracting (x-y)
Use:x= 200 to 1 significant figure
Y= 5 to 1 significant figure

Answer 9

Upper bound= upper bound-lower bound —>250-4.5=245.5
Lower bound= lower bound-upper bound —>150-5.5=144.5
U can also put it into an inequality if it asks —> 144.5 ≤ x <245.5

Question 10

How to find the upper and lower bound of something by multiplying (x*y)
Use:x= 200 to 1 significant figure
Y= 5 to 1 significant figure

Answer 10

Upper bound = upper bound * upper bound —> 2505.5=1,375
Lower bound = lower bound * lower bound —> 1504.5=675
U can also put it into an inequality if it asks —> 675≤ x <1375

Question 11

How to find the upper and lower bound of something by dividing(x/y)
Use:x= 200 to 1 significant figure
Y= 5 to 1 significant figure

Answer 11

Upper bound= upper bound/lower bound —>250/4.5=55.556
Lower bound= lower bound/upper bound —>150/5.5=27.273
U can also put it into an inequality if it asks —> 27.273 < x <55.556

Question 12

How to add fractions?

Answer 12

1) find common denominators
2) add the numerator
3) but keep the same denominator

Question 13

How to subtract fractions?

Answer 13

1) find common denominators
2) subtract the numerator
3) but keep the same denominator

Question 14

How to multiply fractions?

Answer 14

1) multiply the numerators together
2) multiply the denominators together

Question 15

How to divide fractions?

Answer 15

1) flip the second fraction
2) multiply the numerators together
3) multiply the denominators together

Question 16

How to turn fractions into recurring decimals?

Answer 16

Just do normal division

OR

If the denominator is 9, 99 or 999 etc. (also see if u can multiply it to make it that) .just make whatever the numerator is as the repeating part
Eg. 18/99= 0.1°8°

Question 17

How to know if a fraction is recurring?

Answer 17

If it’s a prime number other than 2 or 5