What is the advantage of using standard form for very large or small numbers?

Standard form lets us represent very large or very small numbers in a concise and manageable way using powers of 10. This means we can write them more neatly, compare them more easily, and carry out calculations more efficiently.

True or False? There is always one non – zero digit before the decimal point in a standard form number.

True. There is always one (and only one ) non – zero digit before the decimal point in a standard form number.

True or False? Scientific notation is another term for standard form.

True. Scientific notation is another term for standard form.

True or False? The exponent k in standard form must always be positive .

False. The exponent k in standard form can be positive , negative , or zero .

Define the term exponent .

An exponent is a power that a number (called the base ) is raised to.

What number do you get when you raise any non-zero number to the power of zero , e.g. 2 0 ?

Any non-zero number raised to the power of 0 is equal to 1 . E.g. 2 0 = 1.

True or False? Index laws only work with terms that have the same base .

True. Index laws only work with terms that have the same base .

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What is the advantage of using standard form for very large or small numbers?

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What is the advantage of using standard form for very large or small numbers?
Standard form lets us represent very large or very small numbers in a concise and manageable way using powers of 10. This means we can write them more neatly, compare them more easily, and carry out calculations more efficiently.
True or False?
In standard form, numbers are always written in the form $a \times 10^{k}$ , where $1 \leq a \leq 10$ and $k$ is an integer.
False.
In standard form, numbers are always written in the form $a \times 10^{k}$ , where $1 \leq a < 10$ (not $1 \leq a \leq 10$ ) and $k$ is an integer.
In standard form, the value of a must be greater than or equal to 1 and less than 10 .
True or False?
There is always one non – zero digit before the decimal point in a standard form number.
True.
There is always one (and only one) non – zero digit before the decimal point in a standard form number.
What does $a E n$ mean on a calculator display?
On a calculator display, $a E n$ means $a \times 10^{n}$ in standard form.
(Some calculators use that form of notation instead of the usual standard form notation.)
True or False?
Scientific notation is another term for standard form.
True.
Scientific notation is another term for standard form.
True or False?
The exponent k in standard form must always be positive.
False.
The exponent k in standard form can be positive, negative, or zero.
Define the term exponent.
An exponent is a power that a number (called the base) is raised to.
What number do you get when you raise any non-zero number to the power of zero, e.g. 2⁰?
Any non-zero number raised to the power of 0 is equal to 1.
E.g. 2⁰ = 1.
True or False?
If you raise a non-zero number to the power of 1, you get 1.
False.
Any number raised to the power 1 is just itself.
E.g. $6^{1} = 6$ .
What do you get if you raise a non-zero number to the power of -1,
e.g. 3^-1?
If you raise a non-zero number to the power of -1 you get the reciprocal of the number.
E.g. $3^{- 1} = \frac{1}{3}$ .
What do you get if you raise a positive number to the power of ½,
e.g. 5^1/2?
If you raise a non-zero number to the power of ½ you get its positive square root.
E.g. $5^{\frac{1}{2}} = \sqrt{5}$ .
What is the index law for $x^{m} \times x^{n}$ ?
$x^{m} \times x^{n} = x^{m + n}$
If you multiply two powers with the same base number, you add the indices together.
This formula is not given in the exam formula booklet.
What is the index law for $x^{m} \div x^{n}$ ?
$x^{m} \div x^{n} = x^{m - n}$
If you divide two powers with the same base number, you subtract one index from the other.
This formula is not given in the exam formula booklet.
What is the index law for ${(x^{m})}^{n}$ ?
${(x^{m})}^{n} = x^{m \times n}$
If you raise a power to another power, you multiply the indices.
This formula is not given in the exam formula booklet.
What is the index law for ${(x y)}^{m}$ ?
${(x y)}^{m} = x^{m} y^{m}$
A power outside brackets is applied to each factor inside the brackets individually.
This formula is not given in the exam formula booklet.
But note that ${(x + y)}^{m} \neq x^{m} + y^{m}$ , i.e. you can only use this index law when the things inside the bracket are multiplied together.
Define the term reciprocal in relation to exponents.
In relation to exponents, the reciprocal of $x^{m}$ is $x^{- m}$ , which equals $\frac{1}{x^{m}}$ .
True or False?
Index laws only work with terms that have the same base.
True.
Index laws only work with terms that have the same base.