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# Maths year 11

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1. (Original post by K-Man_PhysCheM)
Again, kind of correct, but a) and b) have too many excess 0s.
3.14159 is itself expressed to 6sf, and 3.14000 would imply rounded to 6sf, which is wrong. 3.14 (without excess 0s) is better.

c) is completely correct.

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2. (Original post by z_o_e)

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Ahh, maybe I wasn't clear enough. We only remove excess zeroes that appear after the decimal point. 43 and 43 000 are very different numbers, while 6.2000 and 6.2 are the same number, but to different degrees of accuracy.

So for the 2sf ones, a) and b) were correct before (with the zeroes), while c) had excess zeroes after the sig figs after the decimal points.

For the 3sf ones, a) and b) had too many excess zeroes (after the decimal point) but c) was correct before EDIT: c) is correct.
3. (Original post by K-Man_PhysCheM)
Ahh, maybe I wasn't clear enough. We only remove excess zeroes that appear after the decimal point. 43 and 43 000 are very different numbers, while 6.2000 and 6.2 are the same number, but to different degrees of accuracy.

So for the 2sf ones, a) and b) were correct before (with the zeroes), while c) had excess zeroes after the sig figs after the decimal points.

For the 3sf ones, a) and b) had too many excess zeroes (after the decimal point) but c) was correct before EDIT: c) is correct.
Done it

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4. These are all correct 0.05081 is 0.0.051 to 2sf and 500.6 is 501 to 3sf.
5. (Original post by B_9710)
These are all correct 0.05081 is 0.0.051 to 2sf and 500.6 is 501 to 3sf.
Is this correct?

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6. I agree with B_9710: they are all correct, but again the two which he mentioned have too many trailing 0s on the end, so it looks like you're expressing it to more significant figures than you are. That's a tiny detail, though, and you shouldn't worry too much about it, but it's good practice to avoid excess 0s after the decimal point and after the stated significant figures.

Here are some bounds questions (remember, bounds are the highest and lowest numbers that would round to the given number at its given accuracy).

1) Find the upper and lower bounds of the following:

a) 350, which has been rounded to 2sf (note: 347 = 350 to 2 sf)

b) 350, which has been rounded to 3sf (note: 347 this time = 347 to 3 sf, not 350)

c) 350.0, which has been rounded to 1 decimal place.

2) A calculator is 16cm long, to the nearest cm. What are the upper and lower bounds of its length?

3) A cube has side lengths 30cm, to 2 sig figs. What is the maximum possible volume of the box?
7. (Original post by K-Man_PhysCheM)
I agree with B_9710: they are all correct, but again the two which he mentioned have too many trailing 0s on the end, so it looks like you're expressing it to more significant figures than you are. That's a tiny detail, though, and you shouldn't worry too much about it, but it's good practice to avoid excess 0s after the decimal point and after the stated significant figures.

Here are some bounds questions (remember, bounds are the highest and lowest numbers that would round to the given number at its given accuracy).

1) Find the upper and lower bounds of the following:

a) 350, which has been rounded to 2sf (note: 347 = 350 to 2 sf)

b) 350, which has been rounded to 3sf (note: 347 this time = 347 to 3 sf, not 350)

c) 350.0, which has been rounded to 1 decimal place.

2) A calculator is 16cm long, to the nearest cm. What are the upper and lower bounds of its length?

3) A cube has side lengths 30cm, to 2 sig figs. What is the maximum possible volume of the box?
I tried the first one :/

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9. Questions C

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10. (Original post by z_o_e)
I tried the first one :/

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You don't want to eliminate the 0 from 350. Imagine spending £35 compared to £350 ---> there's a big difference. On the other hand, spending £35 or £35.00 is the same amount of money, but one has been expressed with greater precision.

You can also look back at your answer and think: do my bounds, when rounded to 2 sig figs, give 350? 34.5 and 35.5 would be the bounds for 35, but what are the bounds for 350?
11. (Original post by K-Man_PhysCheM)
You don't want to eliminate the 0 from 350. Imagine spending £35 compared to £350 ---> there's a big difference. On the other hand, spending £35 or £35.00 is the same amount of money, but one has been expressed with greater precision.

You can also look back at your answer and think: do my bounds, when rounded to 2 sig figs, give 350? 34.5 and 35.5 would be the bounds for 35, but what are the bounds for 350?
I got 350.5 as UB
And 340.5 for LB

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12. 350.05 and 349.95 DO round to 3 sig figs to give 350, but they are not the bounds. 349.6 also rounds to 3 sig figs to give 350, and 349.6 is lower than 349.95, so 349.95 cannot be the lower bound as there are lower numbers that, when rounded to 3 sig figs, give 350. The same is true for your upper bound. You need to be very careful.
13. (Original post by z_o_e)
I got 350.5 as UB
And 340.5 for LB

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Are you sure that 340.5 rounds to 2 sig figs to give 350?
Spoiler:
Show
The first 2 sig figs in 340.5 are 3 and 4. To the left of the 4 is a 0, so the 4 doesn't round up. So that means that 340.5 to 2 sig figs is 340. Hence 340.5 cannot be one of the bounds.

Also, 350.5 does round to 350, but is it really the upper bound? Doesn't 354 also round to 350, to 2 sf?
14. (Original post by K-Man_PhysCheM)
Are you sure that 340.5 rounds to 2 sig figs to give 350?
Spoiler:
Show
The first 2 sig figs in 340.5 are 3 and 4. To the left of the 4 is a 0, so the 4 doesn't round up. So that means that 340.5 to 2 sig figs is 340. Hence 340.5 cannot be one of the bounds.

Also, 350.5 does round to 350, but is it really the upper bound? Doesn't 354 also round to 350, to 2 sf?
I don't understand this!!!

Any videos or anything!
I don't get this whole 3sf and 2sf and 1 dp.

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15. (Original post by z_o_e)
I don't understand this!!!

Any videos or anything!
I don't get this whole 3sf and 2sf and 1 dp.

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This video seems quite good and it has some worked examples:

16. What do you need help with? Any particular question?
17. (Original post by RDKGames)
What do you need help with? Any particular question?
How are these?

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18. (Original post by z_o_e)
How are these?

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Not quite. You need to understand the difference between significant figures and decimal places. The video he posted gives a good explanation on them.

Here's my explanation:

Rounding to Significant Figures: read a number from left to right and round to however figures you need to. The first digit is the first figure, the second digit is the second figure, and so on. If the first figure you encounter is 0, then this is NOT a significant figure, same goes for any 0's that follow it up until you encounter a digit which is not a 0. This would mark the first significant figure, and any number after that one, INCLUDING any 0s, will be considered to be significant. The number 3646 rounded to one s.f. would be 4000. You need to look at the first significant figure, then see whether the digit after that one would make it round 'down' or round up. For two s.f. it would be 3600. And for three s.f. it would be 3650. Of course when it comes to something like 0.00145, rounding to one s.f. would be 0.001, because the first three figures are 0s hence they are not considered to be significant. That number to two s.f. would be 0.0015.

Rounding to Decimal Places: you would ignore all the numbers from left to right until you hit the decimal point. From that point you need to count the decimal places that you are required for the question. For example; 32.5481 to one d.p. would be 32.50000. To two d.p. it would be 32.5500 (because the 8 after the 4 makes it round up), and to three d.p. it would simply be 32.5480. Of course, you can ignore any 0s at the very end of the decimal.

Hope this makes sense.

When it comes to 350 and its UB and LB, you are told that it is rounded to 2 s.f. which means you look for a number where the limits are gong to make it round to 350. This would be 345 (LB) and 355 (UB). You can check this because 345 rounded to 2 s.f. would be 350.

Try to apply this to other questions.
19. (Original post by RDKGames)
Not quite. You need to understand the difference between significant figures and decimal places. The video he posted gives a good explanation on them.

Here's my explanation:

Rounding to Significant Figures: read a number from left to right and round to however figures you need to. The first digit is the first figure, the second digit is the second figure, and so on. If the first figure you encounter is 0, then this is NOT a significant figure, same goes for any 0's that follow it up until you encounter a digit which is not a 0. This would mark the first significant figure, and any number after that one, INCLUDING any 0s, will be considered to be significant. The number 3646 rounded to one s.f. would be 4000. You need to look at the first significant figure, then see whether the digit after that one would make it round 'down' or round up. For two s.f. it would be 3600. And for three s.f. it would be 3650. Of course when it comes to something like 0.00145, rounding to one s.f. would be 0.001, because the first three figures are 0s hence they are not considered to be significant. That number to two s.f. would be 0.0015.

Rounding to Decimal Places: you would ignore all the numbers from left to right until you hit the decimal point. From that point you need to count the decimal places that you are required for the question. For example; 32.5481 to one d.p. would be 32.50000. To two d.p. it would be 32.5500 (because the 8 after the 4 makes it round up), and to three d.p. it would simply be 32.5480. Of course, you can ignore any 0s at the very end of the decimal.

Hope this makes sense.

When it comes to 350 and its UB and LB, you are told that it is rounded to 2 s.f. which means you look for a number where the limits are gong to make it round to 350. This would be 345 (LB) and 355 (UB). You can check this because 345 rounded to 2 s.f. would be 350.

Try to apply this to other questions.
How's this?

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20. (Original post by RDKGames)
Not quite. You need to understand the difference between significant figures and decimal places. The video he posted gives a good explanation on them.

Here's my explanation:

Rounding to Significant Figures: read a number from left to right and round to however figures you need to. The first digit is the first figure, the second digit is the second figure, and so on. If the first figure you encounter is 0, then this is NOT a significant figure, same goes for any 0's that follow it up until you encounter a digit which is not a 0. This would mark the first significant figure, and any number after that one, INCLUDING any 0s, will be considered to be significant. The number 3646 rounded to one s.f. would be 4000. You need to look at the first significant figure, then see whether the digit after that one would make it round 'down' or round up. For two s.f. it would be 3600. And for three s.f. it would be 3650. Of course when it comes to something like 0.00145, rounding to one s.f. would be 0.001, because the first three figures are 0s hence they are not considered to be significant. That number to two s.f. would be 0.0015.

Rounding to Decimal Places: you would ignore all the numbers from left to right until you hit the decimal point. From that point you need to count the decimal places that you are required for the question. For example; 32.5481 to one d.p. would be 32.50000. To two d.p. it would be 32.5500 (because the 8 after the 4 makes it round up), and to three d.p. it would simply be 32.5480. Of course, you can ignore any 0s at the very end of the decimal.

Hope this makes sense.

When it comes to 350 and its UB and LB, you are told that it is rounded to 2 s.f. which means you look for a number where the limits are gong to make it round to 350. This would be 345 (LB) and 355 (UB). You can check this because 345 rounded to 2 s.f. would be 350.

Try to apply this to other questions.
How's this?

,
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