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

Starter quiz

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

'Standard' ✓
Calculate $(2.3\times10^7)\times(3\times10^2)$

$5.3\times10^9$

$6.9\times10^9$ ✓

$5.3\times10^{14}$

$6.9\times10^{14}$
Calculate $(2.6\times10)\times(2\times10^{-2})$ .

$4.6\times10^{-3}$

$5.2\times10^{-3}$

$4.6\times10^{-1}$

$5.2\times10^{-1}$ ✓
Jacob correctly rewrites the calculation $(2\times10^{-2})\times110\text{ }000\times(3\times10^4)$ as an equivalent calculation using standard form. Which of these shows Jacob's calculation?

$(2\times10^{-2})\times(11\times10^4)\times(3\times10^4)$

$(2\times10^{-2})\times(11\times10^3)\times(3\times10^4)$

$(2\times10^{-2})\times(1.1\times10^4)\times(3\times10^4)$

$(2\times10^{-2})\times(1.1\times10^5)\times(3\times10^4)$ ✓
Calculate $(2\times10^{-2})\times110\text{ }000\times(3\times10^4)$ .

$6.1\times10^2$

$6.1\times10^7$

$6.6\times10^2$

$6.6\times10^7$ ✓
The radius of Jupiter is $7.1\times10^4$ km. What is the diameter of Jupiter? Give your answer in standard form.

$3.55\times10^2$ km

$3.55\times10^4$ km

$14.2\times10^4$ km

$1.42\times10^5$ km ✓

$1.42\times10^8$ km

Standard form is when a number is written in the form $A × 10^n$ . When numbers are written in standard form the value of $A$ must be greater than or equal to one and less than ______.

'10' ✓
Calculate $(9\times10^6)\div(3\times10^2)$ .

$6\times10^3$

$3\times10^4$ ✓

$3\times10^3$

$3\div10^4$

$6\div10^4$
Calculate $(5.6\times10^{5})\div(2\times10^{-3})$ .

$3.6\times10^2$

$3.6\times10^8$

$2.8\times10^2$

$2.8\times10^8$ ✓

$2.8\times10^5$
Calculate $96\text{ } 000\div(3\times10^{-1})$ .

$3.2\times10^2$

$3.2\times10^3$

$3.2\times10^4$

$3.2\times10^5$ ✓

$3.2\times10^6$
Calculate ${(1.4\times10^4)\times(3\times10^{-5})}\over(8.4\times10^2)$ . Give your answer in standard form.

$0.5\times10^{-3}$

$0.5\times10^{-4}$

$5\times10^{-3}$

$5\times10^{-4}$ ✓
A grain of rice has a mass of $3\times10^{-2}$ g. How many grains of rice are there in $12$ kg? Give you answer as an ordinary number.

'400 000' ✓

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Equivalent fractions can be used to calculate the quotient when dividing with two numbers represented in standard form.
Using your knowledge of the index laws, you can combine powers with the same base.
Standard form calculations can be done using a calculator.

When the dividing numbers written in standard form changing the multiplication symbol between the number and power of ten to a division symbol.

Encourage pupils to write any division as a fraction. This makes the maintenance of the multiplication symbol easier to see.

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 for 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.