A recurring decimal is one that has an infinite number of digits after the decimal point.

An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0.

A terminating decimal is one that has a finite number of digits after the decimal point.

Converting any recurring decimal to a fraction

Maths

Checking and securing understanding of prime factorisation

Checking and securing understanding of LCM and HCF

Checking and securing understanding of roots and integer indices

The laws of indices - multiplication

The laws of indices - division

The laws of indices - raising a power to a power

The laws of indices - negative and zero exponents

The laws of indices - fractional exponents

Advanced problem solving with the laws of indices

In this unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

The conditions for standard form mean that pupils have explored how different powers of 10 can be written in the prior unit. In this unit, this understanding is generalised and the index laws formalised.

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

Arithmetic procedures: index laws

Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

Prime factors are the factors of a number that are, themselves, prime.

Prime factorisation is a method to find the prime factors of a given integer.

HCF is an abbreviation for highest common factor.

LCM is an abbreviation for lowest common multiple.

An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).

16 is the fourth power of 2. Alternatively this can be written as 2^4 which is read as “2 to the power of 4”.

A numerical coefficient is a constant multiplier of the variables in a term.

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

An operation is associative if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.

A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

Arithmetic procedures: index laws

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