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To multiply and divide integers by numbers between 0 and 1, you need to be confident with multiplying and dividing by powers of 10 and with short multiplication and division.

• Multiplying by a number greater than 1 gives a greater answer than the original number. But when multiplying by a number greater than 0 and less than 1, the answer is smaller than the original number.

• Dividing by a number greater than 1 gives a smaller answer than the original number. But when dividing by a number greater than 0 and less than 1, the answer is greater than the original number.

• Multiplying and dividing whole numbers by numbers greater than 0 and less than 1 can be broken into a whole number calculation followed by multiplying or dividing by a power of 10, for example 10, 100 or 1000 and so on. This makes the calculation simpler to do.

To multiply a whole number by a number between 0 and 1:

1. Multiply the decimal by a power of 10 to get a whole number. This makes the calculation simpler.
2. Multiply the whole numbers.
3. Divide by the power of 10

To divide by a number greater than 0 and less than 1:

1. Multiply both the numerator and denominator by the same power of 10 to get whole numbers; this creates an equivalent expression which is easier to calculate.
2. Divide the whole numbers.

Practise multiplication and division of integers by numbers between 0 and 1 in this quiz.

Calculating a measure such as speed, density or pressure may involve division and multiplication by values between 0 and 1

This method can be useful to scientists, motor mechanics and product engineers.