Higher November 2019 Paper 3 Q7
7
Asma was asked to compare the following two numbers.
\(A = 6.212 \times 10^8\) and \(B = 4.73 \times 10^9\)
She says,
“6.212 is bigger than 4.73 so A is bigger than B.”
You must give a reason for your answer. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(3.246 \times 10^7\) | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| 0.00496 | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| No with explanation | C1 | No and explanation that B is bigger as the power of 10 is bigger. |
Additional guidance
Acceptable examples
She is incorrect as \(10^8\) is smaller than \(10^9\)
No, because B has more digits than A
No, A is millions but B is billions
No, if you subtract A from B the answer is positive (but if you subtract B from A the answer is negative)
A = 621200000, B = 4730000000, B is bigger
No because she did not take into account standard form
No as when you find the ordinary number B is greater than A
Not acceptable examples
Yes…
A = 5 zeros after the number where as B = 7 zeros after the number
No as \(4.73 \times 10^9\) is one more than \(6.212 \times 10^8\)
6.212 is to the power of 8 and 4.73 is to the power of 9 so there is an extra digit
Asma is wrong because she has more numbers behind the decimal point which means that it will be bigger than A
No B has more zeros
Decision eg “No” may be seen by the question.
“She is incorrect” is equivalent to “no”