You can use these techniques and exercises when planning lesson sequences in place value and ordering.
In primary school pupils will have worked extensively with the image of the number line. As their knowledge and experience of mathematics extends they will welcome the placevalue chart as a most flexible and useful image. It will help extend their ability to deal with large and small numbers.
The ability to multiply and divide by any integer power of 10 and to start writing numbers in standard form depends on a secure understanding of place value. This understanding is fundamental in manipulating large and small numbers, both mentally and in written form.
Multiply and divide integers and decimals by powers of 10 provides contexts in which pupils should develop mental processes in place value.
 Multiplying and dividing numbers by powers of 10

Use positive integer powers of 10 and refer to prior knowledge of the way in which a division fact can be derived from a known multiplication fact.
Include the vocabulary of multiplication and division as inverse operations.
Begin with multiplying and dividing by 10, 100, etc. For example:
$$5\xb732\times 10=53\xb72$$ $$53\xb72\xf710=5\xb732$$ $$6\xb795\times 100=695$$ $$695\xf7100=6\xb795$$ $$4\xb778\times 1000=4780$$ $$4780\xf71000=4\xb778$$ Extend the same approach and understanding to multiplying and dividing by 0.1, 0.01, etc. For example:
$$6\times 0.1=0.6$$ $$0.6\xf70.1=6$$ $$7\times 0.01=0.07$$ $$0.07\xf70.01=7$$ Understanding the effect of multiplying and dividing by numbers between 0 and 1
Use powers of 10 as the multiplier to help pupils recognise the logic of the emerging pattern.
Pupils should understand that multiplying by any number between 0 and 1 makes the number smaller. For example:
$$4.2\times 100=420$$ [makes bigger] $$4.2\times 10=42$$ [makes bigger] $$4.2\times 1=4.2$$ [stays the same] $$4.2\times 0.1=0.42$$ [makes smaller] $$4.2\times 0.01=0.042$$ [makes smaller]
Pupils should also understand that dividing by any number between 0 and 1 makes the number bigger. For example:$$4.2\xf70.01=420$$ [makes bigger] $$4.2\xf70.1=42$$ [makes bigger] $$4.2\xf71=4.2$$ [stays the same] $$4.2\xf710=0.42$$ [makes smaller] $$4.2\xf7100=0.042$$ [makes smaller] Multiplying and dividing decimals by any number between 0 and 1
Use mental calculations with whole numbers and adjust, using knowledge of the effect of multiplying or dividing by numbers between 0 and 1.
Multiplying:
$$31\times 0.4$$
$$31\times 4=124$$
10 times smaller is 12.4
$$0.25\times 0.03$$
$$0.25\times 3=0.75$$
100 times smaller is 0.0075
Dividing:
$$81\xf70.3$$
$$81\xf73=27$$
10 times bigger is 270
$$0.24\xf70.06$$
$$0.24\xf76=0.04$$
100 times bigger is 4
Alternatively, use the definition of fractions as division and knowledge of equivalent fractions.
$$81\xf70.3=27$$
$$\frac{81}{0.3}=\frac{810}{3}=\frac{270}{1}=270$$
$$0.24\xf70.06$$
$$\frac{0.24}{0.06}=\frac{24}{6}=\frac{4}{1}=4$$
Beginning to write numbers in standard form
Use movements on a placevalue grid. Relate numbers back to the ‘baseline’ of unit digits and describe movements in terms of multiplication, first by multiples of 10 then by powers of 10.
Ask pupils to write the following types of numbers in standard form:
 large numbers, for example $$235.7=2.357\times 102$$
 small numbers, such as $$0.00092=9.2\times 104$$
Pupils should also be able to order numbers in standard form, for example:
 $$6.92\times {10}^{4}$$, $$2.5\times {10}^{2}$$, $$3.7\times 102$$