Multiplying numbers in standard form | Maths | Quizalize & Oak National Academy

Starter quiz

Standard form is when a number is written in the form $A\times10^n$ . Which of the following is true for $A$ ?

$1 < A < 10$

$1\leq A<10$ ✓

$1\leq A\leq10$

$1< A\leq10$
Write $456\text{ } 000$ in standard form.

$45.6\times10^4$

$456\times10^3$

$4.56\times10^5$ ✓

$4.56\times10^3$
Write $0.000\text{ } 023\text{ } 5$ in standard form.

$2.35\times10^4$

$2.35\times10^{-4}$

$2.35\times10^{-5}$ ✓

$0.235\times10^{-4}$
Simplify $x^{-2}\times x^5$ .

$x^{-7}$

$x^{-5}$

$x^{-3}$

$x^{2}$

$x^{3}$ ✓
Simplify $x^{4}\div x^{-5}$ .

$x^{-1}$

$x^{3}$

$x^{5}$

$x^{9}$ ✓
Simplify ${x^8\times x^{-3}}\over x^4$ .

$x^9$

$x^7$

$x^2$

$x$ ✓

$x^{-1}$

Exit quiz

Standard form is when a number is written in the form $A × 10^n$ , where $1 ≤ A < 10$ and $n$ is an ______.

'integer' ✓
Calculate $(4.6\times10^4)\times(2\times10^3)$ .

$6.6\times10^7$

$9.2\times10^7$ ✓

$6.6\times10^{12}$

$9.2\times10^{12}$
Calculate $(3.8\times10^{-4})\times(2\times10)$ .

$7.6\times10^{-5}$

$7.6\times10^{-4}$

$7.6\times10^{-3}$ ✓

$5.8\times10^{-3}$

$5.8\times10^{-4}$
Aisha correctly rewrites the calculation $(2\times10^{-4})\times23\text{ } 000\times(2\times10^2)$ as an equivalent calculation using standard form. Which of these shows Aisha's calculation?

$(2\times10^{-4})\times(23\times10^3)\times(2\times10^2)$

$(2\times10^{-4})\times(2.3\times10^3)\times(2\times10^2)$

$(2\times10^{-4})\times(2.3\times10^4)\times(2\times10^2)$ ✓

$(2\times10^{-4})\times(0.23\times10^5)\times(2\times10^2)$
Calculate $(2\times10^{-4})\times23\text{ } 000\times(2\times10^2)$ .

$6.3\times10^2$

$6.3\times10^{-2}$

$9.2\times10^2$ ✓

$9.2\times10^{-2}$
The radius of Saturn is $6\times10^4$ km. What is the diameter of Saturn? Give your answer in standard form.

$3\times10^2$ km

$3\times10^4$ km

$12\times10^4$ km

$12\times10^8$ km

$1.2\times10^5$ km ✓

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Lesson Details

Key learning points

The commutative law allows the product of two numbers represented in standard form to be easily calculated.
Using your knowledge of the index laws, you can combine powers with the same base.
Standard form calculations can be done using a calculator.

Common misconception

When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents.

Pupils should be encouraged to rewrite their expression using the associative and commutative laws, with the number parts grouped and powers grouped. This hopefully avoids this error as they can see it is the product of the numbers.

Keywords

Standard form - Standard form is when a number is written in the form A × 10n, (where 1 ≤ A < 10 and n is an integer).
Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
Commutative - The commutative law states you can write the values of a calculation in a different order without changing the calculation; the result is still the same. It applies in addition and multiplication.
Associative - The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.