What tells you whether the power of 10 is positive or negative when writing a number in scientific notation?

The size of the original number decides it. A number of 10 or more needs a positive power, because the front number is multiplied by 10 repeatedly, while a number less than 1 needs a negative power, because it is divided by 10 repeatedly.

How do you add two numbers in scientific notation when the powers of 10 are too large to write the numbers out in full?

Rewrite both numbers so that they use the same, highest power of 10. The front numbers can then be added, and that power of 10 is kept unchanged in the answer.

National 5MathsSQAFlashcardsNumerical SkillsScientific Notation

Scientific Notation (SQA National 5 Maths): Flashcards

Exam code: X847 75

1/12

0Still learning

Know0

FrontWriting in Scientific Notation
Define scientific notation.

Was this flashcard helpful?

Cards in this collection (12)

Define scientific notation.
Scientific notation, also called standard form, is a way of writing very large and very small numbers in the form $a \times 10^{n}$ .
It lets them be written concisely, compared easily and used in calculations.
Complete the condition that $a$ must satisfy for the number $a \times 10^{n}$ to be in scientific notation.
$______\leq a <______$
The completed condition is:
$1 \leq a < 10$
Note that 1 itself is allowed but 10 is not, so $a$ always has exactly one digit before its decimal point.
What tells you whether the power of 10 is positive or negative when writing a number in scientific notation?
The size of the original number decides it.
A number of 10 or more needs a positive power, because the front number is multiplied by 10 repeatedly, while a number less than 1 needs a negative power, because it is divided by 10 repeatedly.
Write 3 240 000 in scientific notation.
The front number is 3.24, and it has to be multiplied by 10 six times to reach 3 240 000.
The answer is $3.24 \times 10^{6}$ .
Write 0.000567 in scientific notation.
The front number is 5.67, and it has to be divided by 10 four times to reach 0.000567.
Dividing rather than multiplying makes the power negative, so the answer is $5.67 \times 10^{- 4}$ .
True or False?
Of the numbers $9 \times 10^{7}$ and $3 \times 10^{8}$ the first is the bigger, because 9 is bigger than 3.
False.
Compare the powers of 10 first, and compare the front numbers only when the powers are equal.
$3 \times 10^{8}$ is 300 000 000, whereas $9 \times 10^{7}$ is only 90 000 000.
How do you work out $(3 \times 10^{2}) \times (4 \times 10^{5})$ without a calculator?
Deal with the front numbers and the powers of 10 separately, so this becomes $(3 \times 4) \times (10^{2} \times 10^{5}) = 12 \times 10^{7}$ .
That result is not yet in scientific notation, so it is rewritten as $1.2 \times 10^{8}$ .
When dividing powers of 10, why does subtracting a negative index need extra care?
Subtracting a negative index is the same as adding, so $- 5 - (- 3) = - 5 + 3 = - 2$ .
Dividing $8 \times 10^{- 5}$ by $2 \times 10^{- 3}$ therefore gives $4 \times 10^{- 2}$ and not $4 \times 10^{- 8}$ .
How do you add two numbers in scientific notation when the powers of 10 are too large to write the numbers out in full?
Rewrite both numbers so that they use the same, highest power of 10.
The front numbers can then be added, and that power of 10 is kept unchanged in the answer.
Complete the rewriting of $2 \times 10^{48}$ so that it uses a power of $10^{50}$ instead.
$2 \times 10^{48} =______\times 10^{50}$
The completed line is:
$2 \times 10^{48} = 0.02 \times 10^{50}$
Raising the power by 2 makes it $10^{2}$ times larger, so the front number is made $10^{2}$ times smaller to compensate.
When adding two numbers in scientific notation, when is it a good idea to write them out in full first?
When the powers of 10 are small, so that the ordinary numbers are short enough to write down.
For example $(3.2 \times 10^{3}) + (2.1 \times 10^{2})$ becomes $3200 + 210 = 3410$ , which is $3.41 \times 10^{3}$ .
True or False?
$50 \times 10^{- 8}$ and $5 \times 10^{- 7}$ are the same number.
True.
Making the front number ten times smaller raises the power of 10 by one, which leaves the value unchanged.
Only the second version is written in scientific notation, but both stand for 0.000 000 5.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Laws of IndicesNext:Rounding

More Revision Notes you might like